They throw in word words the kids should know, 99% of the time I get stuck on soemthing helping my kid, I ask, “how did you learn this” and they’ll show me a quick easy thing and it’ll click in my head, there’s always a random word for me that I have no idea what they mean lol. Like in this it was “addend” or whatever that word was, remove that word and I’m good hahahah
@@موسى_7Yeah, I'm pretty good at math, and I truly do not think I was ever taught the words "addend," "aguend," nor "summand." I know "term" and "sum," but not the others.
Honestly this feels more like a language comprehension question than a math question If i were to construct the question i would write: Use the following numbers to construct a valid equation by filling in the boxes below 2,2,6,6,8,8,0,0,0 [] [] [] + [] [] + [] = [] [] []
@@TraceguyRuneAugend + addend = sum. But it does seem that "addend" is being used here to refer to either operand of an addition, rather than specifically referring to the second one.
exactly, the equation can be written as my first answer (which is 6 + 20 + 800 = 826 aka I only used the digits listed in the question). The thing is, you can TECHNICALLY add more digits to your equation since the question never stated that you should ONLY use the digits listed in the question (for example: 6 + 20 + 800 + 826 = 1452, aka my second answer, nobody said I couldn't add a "1452" to my equation). This makes the question more complicated than what it's probably initially intended for (aka ONLY using the numbers listed to make an addition equation). edit: I saw another viable solution that makes sense which also bends the supposed "rules" of the question, as nowhere in the question states that you ONLY need a 1-, 2-, and 3-digit addend, resulting in this addition equation: 8 + 68 + 206 + 0 + 0 = 828 The thing that stumps most people the most, however, is the fact that they have no idea what an addend is, and since English is a second language to most people in my country, I get it (lucky for me, I grew up speaking English AND we were taught about "addends", "subtractor/subtrahend", "factor", "dividend/divisor", etc. where I live so it's just an advantage for people like me).
And it's easy to overcomplicate because they used digits that add up to each other. Makes you think the two has to add to the six to make eight, or 2+8 to make a 0.
@@LtPowers I'm pretty sure that makes it much easier. anyone with half a brain would know that when you add 8+2 you don't just get zero, you also add 1 to the next column, which automatically means you can't have 8+2 in a column as there are no odd numbers.
I actually think the question is not specific enough. You must ONLY use a single 1-digit, a single 2-digit, and a single 3-digit addend and your equation and sum can ONLY contain the following list of numbers. Then it gets much more clear.
I am 68 and just learnt what addend is. I have never heard that word before. I have o and a level maths. But the problem is not the maths it is the English. How about arrange the above digits to form a 1 digit, a 2 digit and 3 digit number which when added together make a number formed of the remaining digits.. Simple!!
I agree that's much better wording. In fact I believe much of the problem so many people have with math and word problems is not the math, but the way the problems are written.
@@kmbbmj5857 A poor tradesman blames his tools. It's the not the fault of the question writer that you don't understand fundamental mathematics terminology - that obviously would have been taught in this class.
The 3 zeroes are the key. Once you realize there are only 2 of everything else, you understand that everything that appears in the addends also has to appear in the sum, and there are enough zeroes to make that happen. There are no odd numbers available to do any kind of carry logic. It's actually probably easier for a second grader, who doesn't have a lot of experience carrying digits forward yet, so they see the obvious solution right away.
Simple, but I wonder what practical use it has. Just realizing that adding a 0 with a digit (an integer in the range [0,9]) yields the digit being added?
I really like the compliment to her for trying for an hour before asking for help. And I fully agree! Giving it a proper try *and* asking for help once you’re sure you need it are both amazing habits
Primary school homework should never take more than 30 min. and it should be practice and nothing else. Go have 3 kids and put 3h in every week day. ffs.
@@Fred-yq3fs 1. I agree that her spending half an hour on the question would’ve already been enough 2. One problem taking an hour once isn’t even bad as long as they’re typically much shorter 3. I can commend her habits without thinking it should take that long
I wonder if this is the intention? It makes the math of the problem MUCH easier, and that kind of logic, while not something most of us were taught in second grade, is something that I think a second grader could grasp, especially if they're already being taught what an equation is. I mean, I mostly remember second grade math focusing on doing basic addition quickly, and they probably don't have to spend nearly as much time on that in the "you DO keep a calculator in your pocket at all times" era.
This is only possible if you also have an additional addend (which is also not specified, so the question is still underspecified). If you have 1 more digit, it has to go somewhere - and if your addends are defined, you'll need a 4 digit sum (so you can fit all the given digits and your new one). A+BB+CCC=DDDD requires the 4 digit sum to start with a 1, since a 1 digit number + a 2 digit number + a 3 digit number is at most 9+99+999=1107. Since 1 is not part of the given digits, it must be the new digit you added (assuming no leading 0s). So to get this you need to use 6 of the given digits to add together to a 4 digit number. However, the largest of the given digits is an 8, and 8+88+888 < 1000, so you cannot create a 4 digit sum using the given digits, so the total number of digits matches the number of given digits.
I get why people might be confused, but probably just because the wording and phrasing is rough for people who have been out of school for a long time and don't do math regularly. It took me a minute to see what the teacher's intent was but I think it's pretty fair for second graders who were just learning it in class that week.
A student in that class would be introduced to the Wording before these questions. Once they know these words, the question can "make sense" for them. The poor parents, who learned the "old" language, won't know what is being asked.
@@hrayz That's a problem in and by itself. There is no "new wording" to be had, especially not in primary school. It's basic knowledge. it's thousands of years old. No need to make it new every 2 years... except for the bottom line of text book editors of course.
Took me longer to figure out what the problem wanted me to do than to solve it. It's asking for us to use those 9 digits to make a valid addition problem: 3 digits to make one of the addends, 2 to make another, 1 to make a 3rd, and then the last 3 to make the total. Took me 5 minutes to work that out and 1 minute to come up with 600 + 20 + 8 = 628.
Good one- here's what I did: 0+0+[permutation of 2, 6, and 8]=[3-digit number] (I thought "stretch your thinking" meant "0 doesn't have to be a single digit.")
@@sanamite the sufficiency case was one solution, as it would have been for the second graders. I intuited several solutions by digital permutation but didn’t go to the trouble to count them.
It is most probable that the question was set as homework in order to reinforce the lesson taught in class that day. Before you help your child with their homework it is a good idea to ask them what they were taught, and to show you the relevant pages in their work books. This will often guide you towards the sort of answers required.
That's a good point. I definitely remember being taught in elementary school how to break numbers down using their place values, such as: 135 = 100 + 30 + 5 So if that was the lesson taught, it would be obvious the answer would be in the form: a00 + b0 + c = abc, where a, b, c have values 2, 6, 8 in some order.
that is a very good question to ask.. I remember this Fox Trot cartoon decades ago. He was in either in elementary school doing a normal word problem or maybe Algebra at worst... But he solves the problem using Calculus... :) Farmer Joe wants to build a fence that is 10 by 20 feet what is the area of that fenced in area... and he sets up an integral of x going from 0 to 10 for 20 dx. The last panel the teacher returns the quiz or test from the previous week its 1 foot tall of stacked papers.
@@ericbaer9089 you can use calc to find something like the minimum length of fence or maximum area fenced in, but you wouldn't set up the equation that way.
Guessing was never a permitted part of math classes, not even when estimation was taught. We had to learn the teacher’s way of solving problems and be able to duplicate it in any problem we encountered.
Every time it's "student's math problem stumps parents" I guarantee it's something the teacher already explained in class but the student wasn't paying attention.
Neither did the parents, and they even lack the basic deductive skills to find that "addend" probably means one of the numbers being *add*ed. I'm a non-native English speaker on the verge of failing English literature, but it only took me about 30 seconds to figure this one out. And no, I haven't seen that word once in my life.
@@shadesoftime Same crap. We use the word "слагаемое" and it took me exactly 11 seconds to deduce what addend means. And it's not like you can google it and have the wiki page of pretty much any mathemical operation contain the table listing, specifically, names of the operations or terms involved. Which gives really unfortunate implications about how your average Joe is completely helpless when doing even the basic "research", and expects everything to be chewed out and spoonfed to them. Really makes you think.
Last I checked, there is no maths requirement to procreate. But to be less glib, a generation or two has been taught socially relative "math" that is intentionally opaque to anyone that knows real math.
The problem didn’t state that you should only use the given digits, just that they must all be used, so adding extra terms would open up a huge number of additional solutions.
First of all, once I did a search to find out what an "addend" was, it was quite easy for me to find a solution. And, like many others, I had never had a math teacher, professor, etc. ever use the term "addend". Secondly, using "02", etc. and "002", etc. as two and three-digit numbers is invalid - the only times I've ever seen such a notation was when teachers or textbooks used it to explain the addition of numbers with a different number of digits (as in the problem in this video).
Maybe the operating systems / spreadsheet programs / etc. are smarter about it these days, but I remember computers having trouble with alphabetical sorting of things like file names with letters and numbers in them where you might get "file100" sorted out of what we'd expect to be the logical order so it gets slipped in front of "file10" (or something like that, it's not set up to recognize numbers within the string of characters so it's just sorting based on the ASCII values of each character in the string), so as a workaround you get used to a convention of including leading zeroes to avoid any potential issues like that (even if you end up never actually naming that many files anyway) because the computer will correctly sort "file010" earlier than "file100". My example is completely off topic for the subject of this video though.
14 years of math including 2 years of calculus and I don't remember being taught the word addend, but if I replace it with number, I come up with 600 + 20 + 8 = 628.
the trick of this question is context: i'd say that this exercise is in a chapter in the school textbook probably teaches about "tens, hundreds, thousands", and/or how to write and manipulate summations with "carry over", what to do with leading zeroes, etc this exercise is training the students'ability to comprehend and interpret the text, but is also to help the _teacher_ discern the individual students' abilities 1) the student that goes for the low effort answer: 0+00+268=268 (or permutations) 2) the student that struggles to find an answer, whether they do it or not - most of them will be in this category 3) the student that finds a couple of answers or possibly a _pattern_ in those answers and i guess a 4th category would be *you,* the obviously-not-a-second-grader
Those aren't really addition equations. They are equations, but from what I can find addition equation means two or more numbers added together with the sum on the other side of the equals sign. If you have anything but just the sum over there it isn't an addition equation..
@@HarvardHeinous Honestly I just Googled it. Some websites listed that as a definition. I'm not sure how official it is, but I didn't find anything that gave any other definition. But it is Mathematics. Everything has definitions.
I think a part of these “super hard” problems is knowing what the person is learning at the time. Assuming they were probably learning about how 862 is 8 100’s plus 6 10’s plus 2 1’s, it feels more intuitive
Exactly. As with any of these viral "impossible" homework problems, they only become "impossible" if you fail to take into account that when 7 year olds get set mathematics homework, it's about consolidating the stuff they've been learning in class. They will already have been exploring and solving this kind of question with their teacher. And the inclusion of three zeroes is undoubtedly not a coincidence, because that means easy solutions like 200+60+8 = 268 are available. Solutions like that show us that this is really just a question about understanding place value (units, tens, hundreds), and place value is a completely normal thing for 7 year olds to be learning about.
The real question is more "what does this question mean?" I thought the sum wasn't supposed to be part of the digits. So my answer was 006+062+822=890 which is a stretch to the definition of an "n digit number".
Same. I never even considered that the answer HAD to be from within the remaining digits and therefore couldn't solve it. Although that is a failure on my part since the question didn't state otherwise either
The way I see it, there are 216 separate solutions. You can’t include leading zeros but you can count 200+80+6=286, 80+6+200=286, and 286=200+80+6 as three separate valid responses. Just because the responses are equivalent doesn’t make them redundant.
I see 108 solutions, once an initial candidate is found: - 6 column assignment combinations for the 3 non-zero pairs, - 6 row arrangements for the 1, 2, and 3 digit numbers, and - 3 arrangements for the last column (assuming that 0 counts as a stand-alone 1-digit number). (I did not allow leading zeros beyond the lone zero.)
IM0, using 0 as an addend is acceptable, but 00 or a number with a leading zero is not as that's not how numbers are typically described. Yes, 00 is 0 and is valid, but I think most teachers would flag that. Also, the answer should not have a leading zero. eg: 8+60+200=268
I honestly found it ridiculously easy once I figured out where to put the zeros. Took me about 5 minutes in total. Hats off to anyone who can find any solutions with two non-zero numbers in the same column with no leading zeros.
I messed with that avenue for a while, but realized there were roadblocks. Can't carry a one, because no odd numbers. Can only carry a two from the first column (6+6+8), but then run out of sixes and nothing else works. Presh's simulation of all possible combos shows the range of answers is all of similar types. Nothing exotic turned up.
i was stunned a first and tried to figure it out while you were explaining, it clicked in my brain as soon as you showed 2:55 the pyramid-like thing. really easy solution that shows how much you have to not overthink at problems like that
Since we're supposed to add up 1, 2 and 3-digit numbers together, the sum must have 3 digits too. Also, the most-significant digits of both the 3-digit addend and sum must be the same because all the digits are even numbers. abc de f agh c+e+f is either below 10 or above 19. If there's no 8 among them, at least one 0 is used: 0+2+6=8 0+0+6=6 0+0+2=2 If there's an 8: 0+0+8=8 8+8+6=22 (carry 2) 8+6+6=20 (carry 2) b+d can't exceed 9. d is at least 2, so b
30 year math teacher here. I'm so saddened as to what has happened to math instruction here in the US. Incomprehensible instructions are the rule, apparently. Mathematically incorrect procedures are also the norm. The big problem is that people teaching math typically had "math" as their worst subject when they were in school.
On the other hand, somewhat incomprehensible insructions is a nice way to teach children how to deal with such cases in our anyways imperfect world, full of poor instructions and ambiguities
I'm not from the US. In my experience, the teachers were all excelling at math, but usually horrible at communication. But maths is not just logic it's also its own, very unusual language and you need to excel at both logic and translation to teach it. It's a lot more than just memorising what addend means. Unfortunately maths geeks are so routined in this language they don't even realize. I remember trying to explain something abstract to a random person saying "imagine it as a mathematical function mapping positions to colors" or similar, and I was stopped mid-sentence with "what is a function?!" That's not just a hole in vocabulary, explaining that concept is harder than explaining what it was supposed to illustrate.
@@The14Some1 No, "trick" questions are NOT appropriate for young children. They do NOT teach kids to "think outside the box", they just confuse kids and put them off wanting to learn. Trick-questions should be reserved for later, maybe college. Elementary-school is for teaching basics and setting a foundation. I hate it when I see teachers trying to TRICK young children. 😒
Why are you assuming that this problem is from the US? The internet is worldwide! And even if it is from the US--so what? Part of learning math, and learning in general, is learning how to adapt your learning to different presentations or instructions. Life doesn't present problems to people in the form of cookie-cutter instructions. Sometimes you have to adapt your knowledge to the way the problem is presented to you. Inconsistent (/"incomprehensible") instructions are part of that.
What really helped me was how you drew up the boxes to show a blank "format". (3:50) Then after a couple of false starts, I had it. There are a lot of answers I can see. You just replace the numbers with one-another once you get the pattern.
This is insanely simple if it is made clear that you are allowed to rearrange the digits, which you usually aren't allowed to do in similar questions. Which btw is not mentioned anywhere in the question, and the unordered list of the digits would also imply that this is the case here as well Other than that, I don't see how this could pose any problems for anyone above 2nd grade
This is an example of a question as an exercise vs a question as a problem. Problems are intended to have singular solutions, or possibly several solutions, but the goal is to simply solve it. Exercises, on the other hand, are not just about doing some work. It’s something meant to challenge you to think through a question and see if you can figure it out. A problem is like assembling a Lego set according to the included instructions so that you build the thing that was intended to be built. An exercise is like using the same Lego set to see if you can build a building that meet certain criteria, using a certain set of rules such as which pieces you must or cannot use. Parents just want to help their kid find *the answer*. And many students also just want to get their homework done. Yet if we want quality, education thought exercises are probably at least as valuable if not more important than just repetition.
Majored in mechanical engineering, minored in math. I don't think I've ever seen the word "addend" in my life. The - symbols after 1, 2 and 3 also confused me.
This is what happens when art history majors teach math. They have no understanding of how rigorous math is and how ambiguity and vagueness are, for all intents and purposes, forbidden.
Addend, minuend, subtrahend, multiplicand, dividend, and radicand all have "rigorous" mathatical definitions, nor are they new words by any stretch. Most of those terms even appear in both mathematical journals and US tax laws. The only ambiguity in this question is not knowing what addend means.
@@matts.1352 The problem neither specifies the number of addends allowed, nor the number of digits which are permitted to be used. Yet, the way it is formulated implies it is exactly 3 addends and precicely all 9 digits. This is what makes the problem vague.
Always impressed. What I learned by watching this channel was that you don't actually need to do it the hard way but the smart way. I thought the equation wording was the catch, but didn't notice the trick to pairing the digits. Now I know. Those little things is what I tried to teach my little brother because the hard way is the pathway of highest electrical potential in my brain's medium. And we may entertain the thought, but isn't the way the scientific notation treats the zeros the standard?
My immediate thought was, “It says I have to use _all_ the digits shown, but not _only_ the digits shown, meaning there is an infinite amount of answers, as I can just add more numbers infinitely.”
The reason why i find this question hard at first was because i didn't understand it , it only took me a few minutes once i actually understood the question
My first thought was "What the hell is an 'addend'?"I couldn't even understand the question. I thought it involved addng up the 9 digits after right-padding some of them with 1, 2, or 3 digits. Maybe it would have made sense if I'd had the benefit of classroom context, but I didn't - so it didn't. Kudos to the mom who at least knew what was expected of her.
As long as it was presented to the kids as a brain-teaser, I think it's a pretty fun little puzzle. Better than pages of addition problems which is what I got in 2nd grade.
There's no way in hell this was assigned to 2nd graders unless it was extra-credit and nobody was really expected to get it. 2nd grade math is learning to add and subtract through tons and tons of repetition. This video poster does this all the time, he takes these problems that give the average high school math student a lot of problems and says that it was assigned to 8 year olds (usually he says "gifted" 8 year olds). He throws in a strong implication, "A bunch of kiddies got it, what's wrong with you?" Same sh!+, different day.
@@Skank_and_Gutterboy It requires both a knowledge of addition, and a flexibility of mind. I don't think 2nd graders lack either of those things, but they need to learn to use both and that's the great thing about brain-teasers.
3:51 Once I saw that the result was included in the digits used, I quickly saw that a valid solution is units, tens, and hundreds, with the result being a permutation of the distinct non-zero digits.
Nah, it's second grade alright, considering that it's a basic addition and, maybe, number positioning. If curriculum wasn't made dumber, third grade would have multiplication and division (basic fractions) and 4th grade - math operations on a three-digit numbers and a little bit of geometry.
For all.we know, this could be a bonus question for extra credit. We always had tricky problems at the bottom of the test/worksheet that wouldn't hurt our grade if we got it wrong, but help if we got it right.
I could see some students getting it if they had done similar questions in class and in their homework assignments. If this just came out of the blue, it would be way too hard imo.
In context of their classwork it is probably very simple. I imagine they have been learning to split up a number into hundreds, tens and units, eg 862 = 800 + 60 + 2. Creating any three digit number from different digits given in the question would then allow it to be split into hundreds, tens and units as an answer to the question.
When I read the question I understood it like one of those match stick puzzles where the digits have to stay in place and you're only allowed to add symbols inbetween. So I searched for a solution like 66+22=8+80+00. Then I watched the video and realized you're allowed to use the digits in any order you want, which makes it a lot easier.
I think I figured it out- "stretch your thinking" is code: it means, "0 doesn't have to be just one digit!" With that in mind, there's 6 potential solutions: 0+00+[one of 268, 286, 628, 682, 826, or 862] = 3-digit added
If we solve these kinds of problems, it will only SHRINK my brain, NOT STRETCH them What a complete waste of time ? Why is Presh posting such trivial problems ??
200+60+8, or 200+80+6, or 600+80+2, etc etc. A little bit of thought gets you there and a 7-year old might benefit from the exercise without Mom spreading math-panic
There are 2 of each number except the 0’s, which there are enough to express a multiple 10 and 100. A number with the digits ABC can be written as A00 + B0 + C. That uses each digit twice and three zeros, there are 6 possible solutions using this formula: 268=200+60+8 286=200+80+6 628=600+20+8 682=600+80+2 826=800+20+6 862=800+60+2 After the step where we figured out that the answer has to be a 3 digit number, I realized the three 0’s meant you could make any 3 digit number and break it into it’s expanded form
Nobody has math teachers at 7yo. Maybe you learn to count beans, or add and subtract. But math, no. That starts in most countries once you're a teenager.
@@JaneAustenAteMyCatI guess this depends on where you were raised and what you remember of what you learned as a child. All I can say is we learned those words in math in grade 1 or 2 when I was in school 40 years ago in Canada. (I still think the word subtrahend is weird!)
@@Misteribel Exactly, this problem was given to 2nd graders? BS. The vid poster does this all the time and likes to imply, "A bunch of 8 year olds got this, what's wrong with you?" In the 2nd grade, you're learning to add and subtract through A LOT of repetition. They're not throwing this at you. You don't do anything with equations until the 5th or 6th grade, up until 99% of what you do it simplifying expressions. You may dabble a little in inequalities, number bases, and set theory (which is totally worthless, probably just used as a filler because you can only do so much add/subtract/multiply/divide).
I recall being taught the names of the different parts of equations, but possibly when I was a little older than the local equivalent of 2nd grade. I would have been confused by the question at that age. Several decades later, it's still a bit of a challenge to stretch my thinking in a useful way for solving this kind of problem.
@@martinferrand4711 Because the problem 1) does not limit the number of addends to three, 2) does not limit the number of digits they contain (so long as the solution contains one-digit, two-digit, and three-digit addends), and 3) does not limit the digits used in the solution to those listed -- there isn't even a proper list of the digits which must be used.
@@rdbchase ok if you go under those rules I understand. It was under the impression that the list of number was mandatory and all numbers were to be taken from that list.
The 48th solution is at 11:01. 0+00+862=862. It has a green checkbox next to it. Then it runs through the remaining permutations and ends on something incorrect, but that's not #48.
I'll be honest, I tried this one for a bit and legitimately failed because I never stopped to think that the 1-digit addend might just be the last digit of the sum. Such a simple, obvious step, and I discarded it right from the get-go.
@@Inncubus-J "Addend is a word none of us were taught" "The wording is so confusing" "The phrasing of this question is busted" ^actual comments No, this is not people wishing they'd learned, this is people generalizing something that only applies to them
@@etymonlegomenon931 Certainly, or extrapolate from the context clues. Surely it's a concern though when people with PhDs and Maths degrees etc are saying they don't know it but 11 year olds are expected to; how was it missed from the curriculum for so many. To never have come up in the lives of so many of the commenters it is demonstrably a somewhat obscure word.
The problem doesn't appear to prohibit using decimal separators. Given that we have a 1-digit number as an addend, we can only add decimal separators between the ones and tens places. However, America uses a decimal point while Europe uses a decimal comma. So multiply the final answer by 3.
Not quite true. You can put the decimal point as: 60.0 + 2.0 + .8 = 62.8 or 6 + 0.2 + 0.08 = 6.28 or .6 + .02 + .008 = .628 etc. And since you're adding decimals, you can also add negative signs and come up with other creative solutions. Here's just one example: 6 + .28 + (-6.28) = 0.00
@@arandombard1197 Firstly, there are 9, not 10 given digits. But secondly, and more importantly, it is not stated that you are not allowed to use other digits, only that the listed gidits have to be used.
@@gabrielgrey2708 It doesn't say you can use other digits. It says you can use these digits. It then gives you the format that those digits must be used in. Pay attention.
@@arandombard1197 The problem states "use all of these digits", and my solution does use all of those digits. The format is just the preferred format of Presh, not a part of the original problem.
@@arandombard1197 Wrong -- you're making unstated assumptions. There are an infinite number of solutions to the problem stated, which does not preclude using digits other than those listed, does not restrict the number of addends to three, and does not limit the number of digits they contain (so long as the sum includes a one-digit, two-digit, and three-digit addend).
The problem is that the wording of the assignment is EXTREMELY vague. I am 69, have a bachelor's degree in math, and math was my best subject. I came up with one of the possible solutions (6 + 80 + 200 = 286), but only because I made assumptions as to the meaning of the assignment. Nowhere does it say that some of those digits are used in the sum. And when I was in 2nd grade, I never would have been able to infer the necessary assumptions.
I got 6 answers, but I didn't allow leading zeros, or even the number 0 by itself (a mistake on my part), and I didn't find the answer myself. I wrote a program to find the answer, and still screwed it up since I didn't allow 0 as a single number. It also took me longer than an hour. Kudos to any 2nd grader that answered this question.
After a few minutes of thinking I sadly gave up - the intented answer is actually trivial, but the question is so convoluted in it's message that I'm not suprised other adults can't figure this out
This feels like one of those questions the book author thought was so clever but in reality it was just a terrible idea that probably confused all but the smartest kids in the room.
Mr. Talwalkar, there are far more solutions than you listed, due to the wording of the question. It doesn't limit you to only the digits shown, it merely requires all of them to be used. It also merely requires at least three numbers to be added (at least one 1-digit number, at least one 2-digit, and at least one 3-digit), but it doesn't preclude others as well. So 2+60+800+1000=1862 is another of the tbousands of additional answers.
The only thing that confusing in that question at 0:34 is the word addend which I never come across before. But the fact there's 9 digits listed to be used and the fact that digits are repeated means they looking for an answer in the form of X+XX+XXX=XXX. So 6+20+800=826 you can swap the 2, 6 and 8 around.
I had 66 + 0 + 22 + 100 = 188. All required digits were used and to the first number a 1-digit, a 2-digit and a 3-digit are added. I read the question so that you would have a starting number and then you needed to add at least three times a number. You may ask why use two 1’s? Well, that’s because the problem doesn’t state you are restricted to the displayed numbers. The only requirement is that all of them are used. And it said “Stretch your thinking”, so that hinted me I should think outside of the box. So that makes that there is an infinite number of solutions.
My solution started from noting that that 1) there are no odd digits, so we can never carry a 1, and 2) there are only 2 8's, so if we ever do 2 non-zero digits (e.g. 6+2=8) in one column the other copies of those digits would be unusable (I missed the 22+66=88 angle). I also didn't allow leading 0's (which would also disqualify 0+22+066=088 permutations). That left me with 3 leading non-zero digits and 3 non-zeros in the answer and the 3 zeroes locked in as the non-leading digits in the addends - i.e. of the form a+b0+c00 =cba, yielding 6 permutations. I did neglect 0 as an option for the single digit addend, and allowing this yields answers of the form 0+ba+c00=cba and 0+b0+c0a=cba for a total of 18 permutations when leading 0's not allowed.
I didn't even understand the question until he explained but once I understood it took like 10 minutes to play with the numbers to figure it out then it made so much sense
Considering this is a 2nd grade question, it's very possible (and honestly likely) that this was intended to be a follow up or practice after learning about place values and how 0 holds a place without "giving it a value"
Among the great many previously published math puzzles people have come up with over the years, there are myriad examples containing phrases like "1-digit", "2-digit", "n-digit number", and the like. Notice that in nearly every case, it is implied, if not outright stated, that the numbers referred to are positive integers without leading zeros. Exceptions to this rule are rare. It is a longstanding convention that "00" does not count as a 2-digit number.
PS: "Addend" was the word I learned in school as the component of an addition problem, just like you have "multiplicands" for multiplication problems. Never heard of "summands" or "augends" before. So this is how I solved this (before watching the video): First, you have nine digits, and you have to use six of them in your addends, which mean only three are left for the sum. So your problem is in the form of: a bc + def ------- = ghi The first problem is finding digits a, c, and f that add up to i. The key here is the three zeroes-you have to use them all, and they can't be leading digits, which severely limits where you can place them. A little experimenting shows that the answer to the rightmost column is: 8 + 0 + 0 = 8. That leaves two 6's, two 2's, and a zero, and the zero has to go in the middle place of either the three-digit addend or the sum. There are only a couple of combinations possible here, and it should become clear that the middle column is 6 + 0 = 6, and the leftmost column is 2 = 2. Put it all together and you get: 8 60 + 260 ------- = 268
Answering before I hear the answer but my logic was that there are no odd numbers, so anything that involved carrying a 1 was invalid (8+2=10, etc). This means all columns had to add up to 8 or less. The 1s digit could not be 0 in the final solution since that would require 4 0s since we can't carry digits over. None of the other columns could result in 0 because that would mean one of the numbers on top would be invalid (6+62+020=088 would not have a true 3-digit number). 0s can't start a number and can't be part of the solution, so that left a triangle of A+B0+C00=DEF. If any column used 6+2=8, that would leave an additional 6 and 2 orphaned since each column needed 2 non-0 digits. That leaves any solution where A=F, B=E, and C=D using the notation I used. So 2+60+800, 6+20+800, 2+80+600, 8+20+600, 8+60+200, 6+80+200 are all valid
looking at it, I genuinely have no idea what the problem even is.
English is also not my mother tongue and I understand why you don't understand.
They throw in word words the kids should know, 99% of the time I get stuck on soemthing helping my kid, I ask, “how did you learn this” and they’ll show me a quick easy thing and it’ll click in my head, there’s always a random word for me that I have no idea what they mean lol. Like in this it was “addend” or whatever that word was, remove that word and I’m good hahahah
They never taught me the word 'addend' in school. They just say 'one of the two numbers which get added'.
@@موسى_7same
@@bebektoxic2136 Even with English tonguers, nobody knows what an Addend is.
I need to go back to 2nd grade English because I had no idea what the question even asked
Addend is a word none of us were taught
@@موسى_7Yeah, I'm pretty good at math, and I truly do not think I was ever taught the words "addend," "aguend," nor "summand." I know "term" and "sum," but not the others.
The wording of the question is confusing.
Haha, right. "Have a go at solving it?" I don't even know what the question is!
That's what my problem with the question was also. 😂 @@موسى_7
Honestly this feels more like a language comprehension question than a math question
If i were to construct the question i would write:
Use the following numbers to construct a valid equation by filling in the boxes below
2,2,6,6,8,8,0,0,0
[] [] [] + [] [] + [] = [] [] []
I will go with this... The original question was horribly constructed!
@@hillaryclinton1314 the original question used terms no 2nd grader ever heard.
@@scottmcshannon6821
Says who?
I'm sure that digit, equation, addition, and addend were all mentioned in math classes before.
@@jnharton Strangely I had never heard "addend" and had to look it up as an adult when I was writing some documentation.
Ohhh then it’s easy, it’s 800 + 60 + 2 = 862
The most difficult part of this problem was knowing what an "addend" was.
Why? You learn that in day 1 of school. Addend + Addend = Sum... Next you're going to cry about not knowing what a dividend is.
@@TraceguyRuneAugend + addend = sum.
But it does seem that "addend" is being used here to refer to either operand of an addition, rather than specifically referring to the second one.
@@TraceguyRune yeah... No you dont.
maybe my school system was just different but i never ever learned what an addend was. I learned term, and sum, but never addend or augend
same. but probably because english is not my first language.
The whole reason this is difficult is because you can overcomplicate the question
exactly, the equation can be written as my first answer (which is 6 + 20 + 800 = 826 aka I only used the digits listed in the question). The thing is, you can TECHNICALLY add more digits to your equation since the question never stated that you should ONLY use the digits listed in the question (for example: 6 + 20 + 800 + 826 = 1452, aka my second answer, nobody said I couldn't add a "1452" to my equation). This makes the question more complicated than what it's probably initially intended for (aka ONLY using the numbers listed to make an addition equation).
edit: I saw another viable solution that makes sense which also bends the supposed "rules" of the question, as nowhere in the question states that you ONLY need a 1-, 2-, and 3-digit addend, resulting in this addition equation: 8 + 68 + 206 + 0 + 0 = 828
The thing that stumps most people the most, however, is the fact that they have no idea what an addend is, and since English is a second language to most people in my country, I get it (lucky for me, I grew up speaking English AND we were taught about "addends", "subtractor/subtrahend", "factor", "dividend/divisor", etc. where I live so it's just an advantage for people like me).
And it's easy to overcomplicate because they used digits that add up to each other. Makes you think the two has to add to the six to make eight, or 2+8 to make a 0.
what's overly complicated about the question?
@@LtPowers I'm pretty sure that makes it much easier. anyone with half a brain would know that when you add 8+2 you don't just get zero, you also add 1 to the next column, which automatically means you can't have 8+2 in a column as there are no odd numbers.
I actually think the question is not specific enough. You must ONLY use a single 1-digit, a single 2-digit, and a single 3-digit addend and your equation and sum can ONLY contain the following list of numbers. Then it gets much more clear.
I am 68 and just learnt what addend is. I have never heard that word before. I have o and a level maths. But the problem is not the maths it is the English. How about arrange the above digits to form a 1 digit, a 2 digit and 3 digit number which when added together make a number formed of the remaining digits.. Simple!!
I agree that's much better wording. In fact I believe much of the problem so many people have with math and word problems is not the math, but the way the problems are written.
@@kmbbmj5857 A poor tradesman blames his tools. It's the not the fault of the question writer that you don't understand fundamental mathematics terminology - that obviously would have been taught in this class.
Understanding these kinds of wordings is part of the training.
@@beng4186It maybe now it wasn't then or probably when the mother was at school. Not sure it is a term used in the UK now.
Plain English. No technical pedantic language in primary school. Too obvious I guess.
The 3 zeroes are the key. Once you realize there are only 2 of everything else, you understand that everything that appears in the addends also has to appear in the sum, and there are enough zeroes to make that happen. There are no odd numbers available to do any kind of carry logic. It's actually probably easier for a second grader, who doesn't have a lot of experience carrying digits forward yet, so they see the obvious solution right away.
Exactly. If you avoid the carrying then it is simple.
Simple, but I wonder what practical use it has. Just realizing that adding a 0 with a digit (an integer in the range [0,9]) yields the digit being added?
Exactly! What a neat question!
No, you have misinterpreted the problem.
@@barahoupt7849 Exactly wrong -- you all rejected the problem and solved a different one without even realizing it.
I really like the compliment to her for trying for an hour before asking for help. And I fully agree! Giving it a proper try *and* asking for help once you’re sure you need it are both amazing habits
Primary school homework should never take more than 30 min. and it should be practice and nothing else. Go have 3 kids and put 3h in every week day. ffs.
@@Fred-yq3fs 1. I agree that her spending half an hour on the question would’ve already been enough
2. One problem taking an hour once isn’t even bad as long as they’re typically much shorter
3. I can commend her habits without thinking it should take that long
@@Fred-yq3fsI'm stumped...ffs?
@@smellydeadcat2178 ffs means “for fucks sake”
I really doubt she tried. Look how easy it was to stumble into a valid answer.
The question should have stated, "using only this complete set of digits." Nothing in the problem statement prevents you from adding more digits.
I wonder if this is the intention? It makes the math of the problem MUCH easier, and that kind of logic, while not something most of us were taught in second grade, is something that I think a second grader could grasp, especially if they're already being taught what an equation is. I mean, I mostly remember second grade math focusing on doing basic addition quickly, and they probably don't have to spend nearly as much time on that in the "you DO keep a calculator in your pocket at all times" era.
just what I thought, also with the amount of addends so 6+22+680+800=1508 is a solution.
exactly.
This is only possible if you also have an additional addend (which is also not specified, so the question is still underspecified).
If you have 1 more digit, it has to go somewhere - and if your addends are defined, you'll need a 4 digit sum (so you can fit all the given digits and your new one).
A+BB+CCC=DDDD requires the 4 digit sum to start with a 1, since a 1 digit number + a 2 digit number + a 3 digit number is at most 9+99+999=1107. Since 1 is not part of the given digits, it must be the new digit you added (assuming no leading 0s). So to get this you need to use 6 of the given digits to add together to a 4 digit number.
However, the largest of the given digits is an 8, and 8+88+888 < 1000, so you cannot create a 4 digit sum using the given digits, so the total number of digits matches the number of given digits.
That was my first thought
I get why people might be confused, but probably just because the wording and phrasing is rough for people who have been out of school for a long time and don't do math regularly. It took me a minute to see what the teacher's intent was but I think it's pretty fair for second graders who were just learning it in class that week.
A student in that class would be introduced to the Wording before these questions.
Once they know these words, the question can "make sense" for them.
The poor parents, who learned the "old" language, won't know what is being asked.
@@hrayz That's a problem in and by itself. There is no "new wording" to be had, especially not in primary school. It's basic knowledge. it's thousands of years old. No need to make it new every 2 years... except for the bottom line of text book editors of course.
@Fred-yq3fs This is the old language. I was taught this in grade 2 about 40 years ago.
@@SC-gs8dc Not in the UK. Never heard of 'addend' before. It's not used when teaching numeracy here.
@@JaneAustenAteMyCat English is my second language, but I since i know the word addition I could make it out with no problem.
I am 58 UK born and I have never heard of or seen or even been told of the word addend before
46 iowan me too
Yes me too… which country is this that uses this word ??
lol me too! Ireland here.
...but it didn't take much to have a decent guess what it meant....what else could it have meant?
I'm 70, American engineer and I had never heard of this (or an "augend") before now, either!
Took me longer to figure out what the problem wanted me to do than to solve it.
It's asking for us to use those 9 digits to make a valid addition problem: 3 digits to make one of the addends, 2 to make another, 1 to make a 3rd, and then the last 3 to make the total.
Took me 5 minutes to work that out and 1 minute to come up with 600 + 20 + 8 = 628.
Had never heard the words "addend" and "augend" before -- I got up to multivariable calculus in college. Learned something new today.
I'm a PhD student in engineering and I was equally confused by those terms!
If you have a phd you can GUESS what an addend is.
2 + 60 + 800 = 862 ?
or any such variation yeah.
Ya, I did 8+20+600=628
There are 3 0s for a reason...
Good one- here's what I did: 0+0+[permutation of 2, 6, and 8]=[3-digit number] (I thought "stretch your thinking" meant "0 doesn't have to be a single digit.")
Yes. The kids are probably learning or reviewing place values. The context makes the intended answer more obvious.
Solved it in 30 seconds in my head, but I harbor no illusions that it would be within reach of most second graders.
You mean finding out there were 48 solutions?
Yeah, I got a correct answer quickly but most of my problem was seeing if I even understood the problem correctly.
@@sanamite the sufficiency case was one solution, as it would have been for the second graders. I intuited several solutions by digital permutation but didn’t go to the trouble to count them.
That’s always the hype title for these kinds of videos “third grade Chinese math problem stumps physics professors”
All they needed to say is create a equation that adds a 1-digit number, a 2-digit number and a 3-digit number with these digits included
It is most probable that the question was set as homework in order to reinforce the lesson taught in class that day. Before you help your child with their homework it is a good idea to ask them what they were taught, and to show you the relevant pages in their work books. This will often guide you towards the sort of answers required.
That's a good point. I definitely remember being taught in elementary school how to break numbers down using their place values, such as:
135 = 100 + 30 + 5
So if that was the lesson taught, it would be obvious the answer would be in the form:
a00 + b0 + c = abc, where a, b, c have values 2, 6, 8 in some order.
The books suck ass.
that is a very good question to ask.. I remember this Fox Trot cartoon decades ago. He was in either in elementary school doing a normal word problem or maybe Algebra at worst... But he solves the problem using Calculus... :)
Farmer Joe wants to build a fence that is 10 by 20 feet what is the area of that fenced in area... and he sets up an integral of x going from 0 to 10 for 20 dx. The last panel the teacher returns the quiz or test from the previous week its 1 foot tall of stacked papers.
@@ericbaer9089 you can use calc to find something like the minimum length of fence or maximum area fenced in, but you wouldn't set up the equation that way.
“use all the following digits to create an addition equation that adds up a 1-digit, a 2-digit, and a 3-digit number.”
Guessing was never a permitted part of math classes, not even when estimation was taught. We had to learn the teacher’s way of solving problems and be able to duplicate it in any problem we encountered.
Inspection is a very important to learn in math, particularly in Calc II and Differential equations.
200+60+8=268? You can also move the numbers around for at least 6 solutions.
Every time it's "student's math problem stumps parents" I guarantee it's something the teacher already explained in class but the student wasn't paying attention.
Or the parents haven't bother to ask the question what did the teacher teach you today.
Neither did the parents, and they even lack the basic deductive skills to find that "addend" probably means one of the numbers being *add*ed. I'm a non-native English speaker on the verge of failing English literature, but it only took me about 30 seconds to figure this one out. And no, I haven't seen that word once in my life.
@@shadesoftime Same crap. We use the word "слагаемое" and it took me exactly 11 seconds to deduce what addend means.
And it's not like you can google it and have the wiki page of pretty much any mathemical operation contain the table listing, specifically, names of the operations or terms involved.
Which gives really unfortunate implications about how your average Joe is completely helpless when doing even the basic "research", and expects everything to be chewed out and spoonfed to them. Really makes you think.
Last I checked, there is no maths requirement to procreate. But to be less glib, a generation or two has been taught socially relative "math" that is intentionally opaque to anyone that knows real math.
2:24 I've lived in the US for most of my life and this is the first time I am hearing of "addend", "augend", or "summand".
The problem didn’t state that you should only use the given digits, just that they must all be used, so adding extra terms would open up a huge number of additional solutions.
"What's wrong?"
The meta-answer is to look at the child's curriculum.
"Decomposing parts of numbers using the positional system" is the key.
First of all, once I did a search to find out what an "addend" was, it was quite easy for me to find a solution. And, like many others, I had never had a math teacher, professor, etc. ever use the term "addend".
Secondly, using "02", etc. and "002", etc. as two and three-digit numbers is invalid - the only times I've ever seen such a notation was when teachers or textbooks used it to explain the addition of numbers with a different number of digits (as in the problem in this video).
Maybe the operating systems / spreadsheet programs / etc. are smarter about it these days, but I remember computers having trouble with alphabetical sorting of things like file names with letters and numbers in them where you might get "file100" sorted out of what we'd expect to be the logical order so it gets slipped in front of "file10" (or something like that, it's not set up to recognize numbers within the string of characters so it's just sorting based on the ASCII values of each character in the string), so as a workaround you get used to a convention of including leading zeroes to avoid any potential issues like that (even if you end up never actually naming that many files anyway) because the computer will correctly sort "file010" earlier than "file100". My example is completely off topic for the subject of this video though.
14 years of math including 2 years of calculus and I don't remember being taught the word addend, but if I replace it with number, I come up with
600 + 20 + 8 = 628.
the trick of this question is context: i'd say that this exercise is in a chapter in the school textbook probably teaches about "tens, hundreds, thousands", and/or how to write and manipulate summations with "carry over", what to do with leading zeroes, etc
this exercise is training the students'ability to comprehend and interpret the text, but is also to help the _teacher_ discern the individual students' abilities
1) the student that goes for the low effort answer: 0+00+268=268 (or permutations)
2) the student that struggles to find an answer, whether they do it or not - most of them will be in this category
3) the student that finds a couple of answers or possibly a _pattern_ in those answers
and i guess a 4th category would be *you,* the obviously-not-a-second-grader
You missed solutions with a different pattern: 60 + 208 = 260 + 8, 20 + 806 = 820 + 6, etc.
Those aren't really addition equations. They are equations, but from what I can find addition equation means two or more numbers added together with the sum on the other side of the equals sign. If you have anything but just the sum over there it isn't an addition equation..
@@corvididaecorax2991 Whoa, there's an official definition of "addition equation"? >_
@@HarvardHeinous Honestly I just Googled it. Some websites listed that as a definition. I'm not sure how official it is, but I didn't find anything that gave any other definition.
But it is Mathematics. Everything has definitions.
I also considered the possibility of a compound sum on the right hand side. But, second grade, probably not.
Not a solution, since the problem stated "a 1, a 2 and a 3 digits *addend* ".
I think a part of these “super hard” problems is knowing what the person is learning at the time. Assuming they were probably learning about how 862 is 8 100’s plus 6 10’s plus 2 1’s, it feels more intuitive
Exactly. As with any of these viral "impossible" homework problems, they only become "impossible" if you fail to take into account that when 7 year olds get set mathematics homework, it's about consolidating the stuff they've been learning in class. They will already have been exploring and solving this kind of question with their teacher.
And the inclusion of three zeroes is undoubtedly not a coincidence, because that means easy solutions like 200+60+8 = 268 are available. Solutions like that show us that this is really just a question about understanding place value (units, tens, hundreds), and place value is a completely normal thing for 7 year olds to be learning about.
It took me like a minute to understand what the question is asking but then I got the answer in just 10 seconds
I don't think I even knew the meaning of the word 'equation' back in 2nd grade.
The real question is more "what does this question mean?" I thought the sum wasn't supposed to be part of the digits. So my answer was
006+062+822=890 which is a stretch to the definition of an "n digit number".
Same. I never even considered that the answer HAD to be from within the remaining digits and therefore couldn't solve it. Although that is a failure on my part since the question didn't state otherwise either
The key is in the word "equation". With that word, the problem is telling you it's needed to write on both sides of the equal sign
No, a teacher would not accept a number with leading zeros to use up the otherwise unused zeros.
You used 4 zeroes, 3 twos and a number not even in the question. Are you sure you got it?
The way I see it, there are 216 separate solutions. You can’t include leading zeros but you can count 200+80+6=286, 80+6+200=286, and 286=200+80+6 as three separate valid responses. Just because the responses are equivalent doesn’t make them redundant.
I had to look up what an addend was but after that I realized this was a question about understanding digit placements.
I see 108 solutions, once an initial candidate is found:
- 6 column assignment combinations for the 3 non-zero pairs,
- 6 row arrangements for the 1, 2, and 3 digit numbers, and
- 3 arrangements for the last column (assuming that 0 counts as a stand-alone 1-digit number).
(I did not allow leading zeros beyond the lone zero.)
IM0, using 0 as an addend is acceptable, but 00 or a number with a leading zero is not as that's not how numbers are typically described. Yes, 00 is 0 and is valid, but I think most teachers would flag that. Also, the answer should not have a leading zero.
eg: 8+60+200=268
I honestly found it ridiculously easy once I figured out where to put the zeros. Took me about 5 minutes in total. Hats off to anyone who can find any solutions with two non-zero numbers in the same column with no leading zeros.
I messed with that avenue for a while, but realized there were roadblocks. Can't carry a one, because no odd numbers. Can only carry a two from the first column (6+6+8), but then run out of sixes and nothing else works. Presh's simulation of all possible combos shows the range of answers is all of similar types. Nothing exotic turned up.
Literally 90s of thinking is enough to get 2 + 60 + 800 = 862
Or it can be any permutation of 2, 6 and 8
i was stunned a first and tried to figure it out while you were explaining, it clicked in my brain as soon as you showed 2:55 the pyramid-like thing. really easy solution that shows how much you have to not overthink at problems like that
Flipping "6" to "9" is not enough. Why not rotating "8" 90° and turning it into ♾️ ? 😮😨
Or cutting the 8 into two small 0s or two 3s.
Since we're supposed to add up 1, 2 and 3-digit numbers together, the sum must have 3 digits too. Also, the most-significant digits of both the 3-digit addend and sum must be the same because all the digits are even numbers.
abc
de
f
agh
c+e+f is either below 10 or above 19. If there's no 8 among them, at least one 0 is used:
0+2+6=8
0+0+6=6
0+0+2=2
If there's an 8:
0+0+8=8
8+8+6=22 (carry 2)
8+6+6=20 (carry 2)
b+d can't exceed 9. d is at least 2, so b
You have a good principled answer. Ruling out the carries first is the way to go if you approach it as a maths problem.
30 year math teacher here. I'm so saddened as to what has happened to math instruction here in the US. Incomprehensible instructions are the rule, apparently. Mathematically incorrect procedures are also the norm. The big problem is that people teaching math typically had "math" as their worst subject when they were in school.
On the other hand, somewhat incomprehensible insructions is a nice way to teach children how to deal with such cases in our anyways imperfect world, full of poor instructions and ambiguities
I'm not from the US. In my experience, the teachers were all excelling at math, but usually horrible at communication. But maths is not just logic it's also its own, very unusual language and you need to excel at both logic and translation to teach it. It's a lot more than just memorising what addend means. Unfortunately maths geeks are so routined in this language they don't even realize. I remember trying to explain something abstract to a random person saying "imagine it as a mathematical function mapping positions to colors" or similar, and I was stopped mid-sentence with "what is a function?!" That's not just a hole in vocabulary, explaining that concept is harder than explaining what it was supposed to illustrate.
@@The14Some1 No, "trick" questions are NOT appropriate for young children. They do NOT teach kids to "think outside the box", they just confuse kids and put them off wanting to learn. Trick-questions should be reserved for later, maybe college. Elementary-school is for teaching basics and setting a foundation. I hate it when I see teachers trying to TRICK young children. 😒
Why are you assuming that this problem is from the US? The internet is worldwide!
And even if it is from the US--so what? Part of learning math, and learning in general, is learning how to adapt your learning to different presentations or instructions. Life doesn't present problems to people in the form of cookie-cutter instructions. Sometimes you have to adapt your knowledge to the way the problem is presented to you. Inconsistent (/"incomprehensible") instructions are part of that.
Once I figured out what an addendum was and saw the columns, I got it immediately. Your set up was really logical and easy follow, thanks.
This is not a problem about math this is a problem about definitions. I can guarantee the kids were taught what to do
What really helped me was how you drew up the boxes to show a blank "format". (3:50) Then after a couple of false starts, I had it. There are a lot of answers I can see.
You just replace the numbers with one-another once you get the pattern.
This is insanely simple if it is made clear that you are allowed to rearrange the digits, which you usually aren't allowed to do in similar questions. Which btw is not mentioned anywhere in the question, and the unordered list of the digits would also imply that this is the case here as well
Other than that, I don't see how this could pose any problems for anyone above 2nd grade
This is an example of a question as an exercise vs a question as a problem. Problems are intended to have singular solutions, or possibly several solutions, but the goal is to simply solve it. Exercises, on the other hand, are not just about doing some work. It’s something meant to challenge you to think through a question and see if you can figure it out. A problem is like assembling a Lego set according to the included instructions so that you build the thing that was intended to be built. An exercise is like using the same Lego set to see if you can build a building that meet certain criteria, using a certain set of rules such as which pieces you must or cannot use. Parents just want to help their kid find *the answer*. And many students also just want to get their homework done. Yet if we want quality, education thought exercises are probably at least as valuable if not more important than just repetition.
Majored in mechanical engineering, minored in math.
I don't think I've ever seen the word "addend" in my life.
The - symbols after 1, 2 and 3 also confused me.
I really like this problem. It’s the kind that seems hard, then when you figure it out it seems simple.
This is what happens when art history majors teach math. They have no understanding of how rigorous math is and how ambiguity and vagueness are, for all intents and purposes, forbidden.
Addend, minuend, subtrahend, multiplicand, dividend, and radicand all have "rigorous" mathatical definitions, nor are they new words by any stretch. Most of those terms even appear in both mathematical journals and US tax laws. The only ambiguity in this question is not knowing what addend means.
@@matts.1352 The problem neither specifies the number of addends allowed, nor the number of digits which are permitted to be used. Yet, the way it is formulated implies it is exactly 3 addends and precicely all 9 digits. This is what makes the problem vague.
Just a silly idea, but if we decide we can rotate digits...
2 + 26 + 600 + 0 + ∞ = ∞
And, of course, lots of variations.
You have replaced the 8's by something that is not a digit
I think this is the most clever answer
that has 5 addends, not 3
@gorak9000 It requires 1, 2, and 3 digit addends, but doesn't specifically limit itself to those.
This is correct answer, and those presented in the video are not. The instruction clearly says "stretch your thinking". Bravo!
I am 60. Until today I have never seen the word "addend" used in a math question for 7 year olds.
It is a very poorly formatted question.
I did a math minor in college. Had to look up the word "addend."
Good for whinge though Ted! can't pass those by.
@@fritzhenning1 You said it.
Touché.
Always impressed. What I learned by watching this channel was that you don't actually need to do it the hard way but the smart way. I thought the equation wording was the catch, but didn't notice the trick to pairing the digits. Now I know. Those little things is what I tried to teach my little brother because the hard way is the pathway of highest electrical potential in my brain's medium. And we may entertain the thought, but isn't the way the scientific notation treats the zeros the standard?
My immediate thought was, “It says I have to use _all_ the digits shown, but not _only_ the digits shown, meaning there is an infinite amount of answers, as I can just add more numbers infinitely.”
The reason why i find this question hard at first was because i didn't understand it , it only took me a few minutes once i actually understood the question
this question feels like its easy but has the most absurd wording ever, i have never once heard 'addend' in my entire life
My first thought was "What the hell is an 'addend'?"I couldn't even understand the question. I thought it involved addng up the 9 digits after right-padding some of them with 1, 2, or 3 digits. Maybe it would have made sense if I'd had the benefit of classroom context, but I didn't - so it didn't. Kudos to the mom who at least knew what was expected of her.
As long as it was presented to the kids as a brain-teaser, I think it's a pretty fun little puzzle. Better than pages of addition problems which is what I got in 2nd grade.
There's no way in hell this was assigned to 2nd graders unless it was extra-credit and nobody was really expected to get it. 2nd grade math is learning to add and subtract through tons and tons of repetition. This video poster does this all the time, he takes these problems that give the average high school math student a lot of problems and says that it was assigned to 8 year olds (usually he says "gifted" 8 year olds). He throws in a strong implication, "A bunch of kiddies got it, what's wrong with you?" Same sh!+, different day.
@@Skank_and_Gutterboy It requires both a knowledge of addition, and a flexibility of mind. I don't think 2nd graders lack either of those things, but they need to learn to use both and that's the great thing about brain-teasers.
3:51 Once I saw that the result was included in the digits used, I quickly saw that a valid solution is units, tens, and hundreds, with the result being a permutation of the distinct non-zero digits.
I am suprised people found this difficult, but tthis being for grade 2s is insane. Maybe grade 4s or 5s
Nah, it's second grade alright, considering that it's a basic addition and, maybe, number positioning.
If curriculum wasn't made dumber, third grade would have multiplication and division (basic fractions) and 4th grade - math operations on a three-digit numbers and a little bit of geometry.
For all.we know, this could be a bonus question for extra credit. We always had tricky problems at the bottom of the test/worksheet that wouldn't hurt our grade if we got it wrong, but help if we got it right.
3:28 when it's written like this it is suddenly so painfully simple.
For a 2nd grade student this is nuts
it honestly doesn't look too bad. There are so many solutions, just some guesswork and a little thinking should easily stumble you into an answer
I could see some students getting it if they had done similar questions in class and in their homework assignments. If this just came out of the blue, it would be way too hard imo.
In context of their classwork it is probably very simple. I imagine they have been learning to split up a number into hundreds, tens and units, eg 862 = 800 + 60 + 2.
Creating any three digit number from different digits given in the question would then allow it to be split into hundreds, tens and units as an answer to the question.
The most difficult part is understanding the question (does a 7-year old know what an "addend" is?). Once understood, it is pretty easy to an answer.
The problem with some of these is the way they are worded. They can be ambiguous and confusing and neglect to clarify just what is wanted.
When I read the question I understood it like one of those match stick puzzles where the digits have to stay in place and you're only allowed to add symbols inbetween. So I searched for a solution like 66+22=8+80+00. Then I watched the video and realized you're allowed to use the digits in any order you want, which makes it a lot easier.
I think I figured it out- "stretch your thinking" is code: it means, "0 doesn't have to be just one digit!" With that in mind, there's 6 potential solutions: 0+00+[one of 268, 286, 628, 682, 826, or 862] = 3-digit added
those 6 solutions are already included in the answer of 36
@@NihaarB I hadn't even *watched* the video when this solution hit me!
@@wyattstevens8574 👍
The question didn't say you couldn't use additional digits not in the list, it just said you had to use those.
If we solve these kinds of problems, it will only SHRINK my brain, NOT STRETCH them
What a complete waste of time ? Why is Presh posting such trivial problems ??
Heres a problem with a trivial proof, that almost no-one seems able to do:
Prove that people who work for government pay no tax.
Someone : i couldn't solve a 2nd grade problem even with an hour help
This guy : here are 48 ways to show you that you failed
200+60+8, or 200+80+6, or 600+80+2, etc etc. A little bit of thought gets you there and a 7-year old might benefit from the exercise without Mom spreading math-panic
There are 2 of each number except the 0’s, which there are enough to express a multiple 10 and 100. A number with the digits ABC can be written as A00 + B0 + C. That uses each digit twice and three zeros, there are 6 possible solutions using this formula:
268=200+60+8
286=200+80+6
628=600+20+8
682=600+80+2
826=800+20+6
862=800+60+2
After the step where we figured out that the answer has to be a 3 digit number, I realized the three 0’s meant you could make any 3 digit number and break it into it’s expanded form
This problem baffles only those who have not listened to their Math Teachers.
Well, no. It baffles those who have never heard of an 'addend' because it's a new word. It's definitely not a word I or my children have heard
Nobody has math teachers at 7yo. Maybe you learn to count beans, or add and subtract. But math, no. That starts in most countries once you're a teenager.
@@JaneAustenAteMyCatI guess this depends on where you were raised and what you remember of what you learned as a child. All I can say is we learned those words in math in grade 1 or 2 when I was in school 40 years ago in Canada. (I still think the word subtrahend is weird!)
@@SC-gs8dc it must do. It's not a word used in the UK, I'm fairly certain.
@@Misteribel
Exactly, this problem was given to 2nd graders? BS. The vid poster does this all the time and likes to imply, "A bunch of 8 year olds got this, what's wrong with you?" In the 2nd grade, you're learning to add and subtract through A LOT of repetition. They're not throwing this at you. You don't do anything with equations until the 5th or 6th grade, up until 99% of what you do it simplifying expressions. You may dabble a little in inequalities, number bases, and set theory (which is totally worthless, probably just used as a filler because you can only do so much add/subtract/multiply/divide).
I recall being taught the names of the different parts of equations, but possibly when I was a little older than the local equivalent of 2nd grade. I would have been confused by the question at that age. Several decades later, it's still a bit of a challenge to stretch my thinking in a useful way for solving this kind of problem.
Not buying double zero as a two digit number, but solid framework for solving the problem. Still, I think it's way too hard for a 2nd grader.
You don't have to
600+20+8=628
You can swap the digits around no problem
@@martinferrand4711 You can use all the digits and addends of any length too -- as stated, the problem has an infinite number of solutions.
@@rdbchase that I don't get, there is a finite amount of digit so how can you construct an infinite amount of solution?
@@martinferrand4711 Because the problem 1) does not limit the number of addends to three, 2) does not limit the number of digits they contain (so long as the solution contains one-digit, two-digit, and three-digit addends), and 3) does not limit the digits used in the solution to those listed -- there isn't even a proper list of the digits which must be used.
@@rdbchase ok if you go under those rules I understand. It was under the impression that the list of number was mandatory and all numbers were to be taken from that list.
I have no idea what the question is even asking. This is yet one more reason why people grow up to believe they can't "do" maths
11:02 The 48th solution seem to be incorrect 🤔
The 48th solution is at 11:01. 0+00+862=862. It has a green checkbox next to it. Then it runs through the remaining permutations and ends on something incorrect, but that's not #48.
@benjaminmorris4962 0 + 00 + 886 = 622... is it correct?!
I'll be honest, I tried this one for a bit and legitimately failed because I never stopped to think that the 1-digit addend might just be the last digit of the sum. Such a simple, obvious step, and I discarded it right from the get-go.
i will solve a math problem for every like this gets
Go ahead do it
Solve Eighteen math problems
I solve a problem have math every one gets one. Thank you.
I quite literally have a BS in math, a Master's in Ed, and even taught HS math for 3.5 years and I have never heard the word "addend" before.
Why are people acting like addend is such an obscure word that no student should even be *taught* it.
I was definitely taught the meaning of all those words in elementary school. Don't have an issue with the question.
...or you could view it as horrified we weren't when we should have been.
@@Inncubus-J Why would you be horrified? Use a dictionary
@@Inncubus-J "Addend is a word none of us were taught"
"The wording is so confusing"
"The phrasing of this question is busted"
^actual comments
No, this is not people wishing they'd learned, this is people generalizing something that only applies to them
@@etymonlegomenon931 Certainly, or extrapolate from the context clues. Surely it's a concern though when people with PhDs and Maths degrees etc are saying they don't know it but 11 year olds are expected to; how was it missed from the curriculum for so many. To never have come up in the lives of so many of the commenters it is demonstrably a somewhat obscure word.
The problem doesn't appear to prohibit using decimal separators. Given that we have a 1-digit number as an addend, we can only add decimal separators between the ones and tens places. However, America uses a decimal point while Europe uses a decimal comma. So multiply the final answer by 3.
Only some places in Europe. Please don't group us all together. We're hardly homogenous.
Not quite true. You can put the decimal point as:
60.0 + 2.0 + .8 = 62.8
or
6 + 0.2 + 0.08 = 6.28
or
.6 + .02 + .008 = .628
etc.
And since you're adding decimals, you can also add negative signs and come up with other creative solutions. Here's just one example:
6 + .28 + (-6.28) = 0.00
Too generalised. Some of Europe uses commas but by no means all.
6+62+288+1000 = 1356. Nowhere is it stated that only the given digits can be used.
Except it does. You're given 10 digits to use.
@@arandombard1197 Firstly, there are 9, not 10 given digits. But secondly, and more importantly, it is not stated that you are not allowed to use other digits, only that the listed gidits have to be used.
@@gabrielgrey2708 It doesn't say you can use other digits. It says you can use these digits. It then gives you the format that those digits must be used in. Pay attention.
@@arandombard1197 The problem states "use all of these digits", and my solution does use all of those digits. The format is just the preferred format of Presh, not a part of the original problem.
@@arandombard1197 Wrong -- you're making unstated assumptions. There are an infinite number of solutions to the problem stated, which does not preclude using digits other than those listed, does not restrict the number of addends to three, and does not limit the number of digits they contain (so long as the sum includes a one-digit, two-digit, and three-digit addend).
The problem is that the wording of the assignment is EXTREMELY vague. I am 69, have a bachelor's degree in math, and math was my best subject. I came up with one of the possible solutions (6 + 80 + 200 = 286), but only because I made assumptions as to the meaning of the assignment. Nowhere does it say that some of those digits are used in the sum. And when I was in 2nd grade, I never would have been able to infer the necessary assumptions.
I’m not sure what you mean, it seemed to me like it was implied that you had to use those digits in the sum
The heck is an addend?
deduce it from the context.
Something those students would have been taught before being given the question.
I got 6 answers, but I didn't allow leading zeros, or even the number 0 by itself (a mistake on my part), and I didn't find the answer myself. I wrote a program to find the answer, and still screwed it up since I didn't allow 0 as a single number. It also took me longer than an hour. Kudos to any 2nd grader that answered this question.
After a few minutes of thinking I sadly gave up - the intented answer is actually trivial, but the question is so convoluted in it's message that I'm not suprised other adults can't figure this out
I struggled to understand the question as it was written. Once i understood the question, I found an answer quickly
I'm glad I learned arithmetic before "new math".
This feels like one of those questions the book author thought was so clever but in reality it was just a terrible idea that probably confused all but the smartest kids in the room.
Mr. Talwalkar, there are far more solutions than you listed, due to the wording of the question. It doesn't limit you to only the digits shown, it merely requires all of them to be used. It also merely requires at least three numbers to be added (at least one 1-digit number, at least one 2-digit, and at least one 3-digit), but it doesn't preclude others as well. So 2+60+800+1000=1862 is another of the tbousands of additional answers.
*Thousands* of additional answers? It’s actually infinite.
Copilot understood the question as it was resolved in the video and generated a Python script for me.
@@rainmannoodles not for second-graders
The only thing that confusing in that question at 0:34 is the word addend which I never come across before.
But the fact there's 9 digits listed to be used and the fact that digits are repeated means they looking for an answer in the form of X+XX+XXX=XXX. So 6+20+800=826 you can swap the 2, 6 and 8 around.
I had 66 + 0 + 22 + 100 = 188. All required digits were used and to the first number a 1-digit, a 2-digit and a 3-digit are added. I read the question so that you would have a starting number and then you needed to add at least three times a number.
You may ask why use two 1’s? Well, that’s because the problem doesn’t state you are restricted to the displayed numbers. The only requirement is that all of them are used. And it said “Stretch your thinking”, so that hinted me I should think outside of the box. So that makes that there is an infinite number of solutions.
My solution started from noting that that 1) there are no odd digits, so we can never carry a 1, and 2) there are only 2 8's, so if we ever do 2 non-zero digits (e.g. 6+2=8) in one column the other copies of those digits would be unusable (I missed the 22+66=88 angle). I also didn't allow leading 0's (which would also disqualify 0+22+066=088 permutations). That left me with 3 leading non-zero digits and 3 non-zeros in the answer and the 3 zeroes locked in as the non-leading digits in the addends - i.e. of the form a+b0+c00 =cba, yielding 6 permutations. I did neglect 0 as an option for the single digit addend, and allowing this yields answers of the form 0+ba+c00=cba and 0+b0+c0a=cba for a total of 18 permutations when leading 0's not allowed.
I didn't even understand the question until he explained but once I understood it took like 10 minutes to play with the numbers to figure it out then it made so much sense
It's actually interesting how the question is made intentionally with the zeros in mind.
I don’t really get why this was hard for people, you just do 0 + 00 + some combination of 628 and make that equal the same combination
Bro just put salt by finding not 1 but 48 solutions, 😂
Considering this is a 2nd grade question, it's very possible (and honestly likely) that this was intended to be a follow up or practice after learning about place values and how 0 holds a place without "giving it a value"
Among the great many previously published math puzzles people have come up with over the years, there are myriad examples containing phrases like "1-digit", "2-digit", "n-digit number", and the like. Notice that in nearly every case, it is implied, if not outright stated, that the numbers referred to are positive integers without leading zeros. Exceptions to this rule are rare. It is a longstanding convention that "00" does not count as a 2-digit number.
PS: "Addend" was the word I learned in school as the component of an addition problem, just like you have "multiplicands" for multiplication problems. Never heard of "summands" or "augends" before.
So this is how I solved this (before watching the video):
First, you have nine digits, and you have to use six of them in your addends, which mean only three are left for the sum. So your problem is in the form of:
a
bc
+ def
-------
= ghi
The first problem is finding digits a, c, and f that add up to i. The key here is the three zeroes-you have to use them all, and they can't be leading digits, which severely limits where you can place them. A little experimenting shows that the answer to the rightmost column is: 8 + 0 + 0 = 8. That leaves two 6's, two 2's, and a zero, and the zero has to go in the middle place of either the three-digit addend or the sum. There are only a couple of combinations possible here, and it should become clear that the middle column is 6 + 0 = 6, and the leftmost column is 2 = 2. Put it all together and you get:
8
60
+ 260
-------
= 268
Answering before I hear the answer but my logic was that there are no odd numbers, so anything that involved carrying a 1 was invalid (8+2=10, etc). This means all columns had to add up to 8 or less. The 1s digit could not be 0 in the final solution since that would require 4 0s since we can't carry digits over. None of the other columns could result in 0 because that would mean one of the numbers on top would be invalid (6+62+020=088 would not have a true 3-digit number). 0s can't start a number and can't be part of the solution, so that left a triangle of A+B0+C00=DEF. If any column used 6+2=8, that would leave an additional 6 and 2 orphaned since each column needed 2 non-0 digits. That leaves any solution where A=F, B=E, and C=D using the notation I used. So 2+60+800, 6+20+800, 2+80+600, 8+20+600, 8+60+200, 6+80+200 are all valid