The last one (without the answer) is based on compression algorithms. The sequence is just saying what you see in the previous element. describing how many of each recurring digit So: 1 is just a single One ie One one (11) 11 is Two Ones. (21) 21 is One 2 followed by One one (1211) 1211 is One one followed by One two followed by two Ones (111221) 111221 is Three ones, followed by Two twos, followed by One one( 312211) So the next in the sequence would be 13112221 Simple
I agree, the obvious answer is 25%. The given solution answers the question "Solve x/2 = 50%." Which *could* be read "What is 50% (when) divided by 2" but they ommit such clarifying words. Sure it isn't strictly necissary, but it's omition heavily implies another meaning. "Evaluate x = 50% / 2." The statement is deliberately subversive.
That 50% question is legitimately incorrect. This is why language literacy is just as important as mathematics literacy when participating in doing math.
Yeah. They answered “50% / (1/2)”. The question was what is “50% / 2”. They converted divided by 2 into 1/2, but forgot to change the division sign to a multiplication sign,
I guess if you REALLY want to you can still justify that the answer is 1. The question is "what is 50% divided by 2 ?" If you interpret it as "what is 50 per (cent divided by 2) ?" (which you have no reason to do, of course) you do get 1 as the answer.
The last pattern is the “look and say sequence”, starting at 1… The number after 312211 is 13112221, because there’s 1 3, 1 1, 2 2, 2 1… but they didn’t ask for the next number, they asked for the *last* number in the sequence… The last digits will alternate between 11 and 21, so this sequence never ends, so there is no “last number”… unless you take 312211 as the last number they gave you…
So the correct answer would be 1? Because they didn't read the sequences as big numbers, but rather a sequence of one digit numbers without spaces. And the last number (digit) of the last sequence (of 1 digit numbers) of the infinite whole sequence, is 1 because it always is 1 and it can't be anything else than 1.
But they not ask for the number (btw a Conway sequence), but "Can you figure out ...". So the answer must be "yes" when you can, otherwise "no" when you can't.
#3 they clearly got wrong too. In mathematical writing it is completely standard that a formula surrounded by text is treated as a whole. You never have a part of the formula interact with the text, and then with the rest of the formula. So the answer is unequivocally 2.
My instinct was that the answer was 2, but realised it was too obvious, so re-read it to come up with the 'right' answer. But it just didn't 'seem' to look right, but I couldn't understand why. Sure, if you follow BODMAS, the answer is 3, but as I read the question, I couldn't see whatever seemed wrong with it. Your explanation makes it so clear, so thank you for putting me out of my misery!
Is there a rule of the internet that "there's an XKCD for that?" Because I entirely agree with what I think is Tom's main complaint and the same as Randall Monroe voiced 18 years ago in XKCD 169: "communicating badly and then acting smug when you're misunderstood is not cleverness."
And for my less TL;DR commentary: #2: The order of operations "riddles" are so common online that this should be pretty easy. Note that it also highlights why BODMAS (or PEMDAS) doesn't even work: after M, you have 3+9-3+3; applying A next gives 12-6, which is 6. To get 12 you have to either use BODMSA or group as BO[DM][AS] or PE[MD][AS], applying addition and subtraction together. #3: I got "2, but they're going to tell me it's 3" because I think embedding maths notation implicitly groups that apart from the operations in the English text. At best, it's ambiguous (unlike #2, which is well-defined because it's all written in symbols). #5: The answer just straight-up lied about what the question was, so the video can *&^% right off with that one. #6: I see Tom missed the extra instruction "all you can use is addition" because it was spoken but not on the board. Which actually helps because the only thing you could use and then pretend is nothing is writing multiple 8s as one number. And then there's barely enough time to say "888 leaves 112, so plus 88 and plus however many are left as singles and I hope that works." #8: Tom's attempt imaginines extra '+' signs between the lines. I got to "do they want to ignore the first two lines and get 2 or join them into 1+1+1+1+11+1+1+1+11+1×0+1 = 30?" #9: The Look And Say Sequence is pretty instantly recognisable to sequence fans. Find it as OEIS A005150.
@@peterb5 The part about only using addition was the only way I got it quickly. You need 5 8's in the units column to make 0, carry 4. Then 2 more 8's in the tens column for 0, carry 2. Then 1 more 8 in the hundreds column for 0, carry 1.
@@peterb5 Oh damn... Yeah, really glossed over that one... I'm used to encountering variations of this question with a pretty standard stipulation that the four basic operators are allowed. I was mostly watching for the commentary anyway, though, since these types of questions are usually irritatingly trivial or just badly phrased.
I really dislike these as a concept. Not the riddles themselves, but the whole "thing" around the riddles. The poorly written prompts, grammatical errors, taunting phrasing. Everything about these riddles feels like they're designed to prey on people who are easily influenced. They fish for engagement with every single aspect of their presentation.
for 1+1+1+1+1 question, there is no operation between the lines (no hanging +), so they are different independent statements and have no bearing on the last statement. The last question is a description of the digits in the previous number in the sequence. 1 is described as "a single one" aka "one one" aka 11. 11 is described as "two ones" aka 21, then "one two, one one" aka 1211, etc... Numberphile did a video on it.
I originally got 12, and then quickly changed my answer to 30 after I saw they had omitted the missing plus signs on the end of each line. I thought they maybe wanted you to concatenate them to make two 11s, but apparently not 😂
There are no symbols that join them in a vector. But in any case, it looks vertical, it would be a matrix with 3 rows and 1 column. my answer was 5 5 ...=2 No connection seen between each row.
18:16 Well, on that one, they aren't very clearly part of the equation. There are not math operators linking the first two lines to the last. The answer I got was a 5, another 5, and a 2.
You're missing the point. Due to the lack of rigor in all of the previous problems, you simply can't determine what the person who created the problem intends, because anything is acceptable if it leads to more people getting the answer wrong.
@@weirdlyspecific302 What the person intends is not relevant to my comment. Tom says the numbers are "very clearly part of the equation" and I'm saying that, because of the very lack of rigor you refer to, they are *not* _very clearly_ part of the equation.
The last question - key is to read the numbers aloud to get the next number - the first number is one one - 11 (which is second number) - so the third number is two ones or 21 - which is one two then one one etc
I've seen #8 multiple times online, and there they say that since there is no + in between the 1 at the end and the beginning of a row, its 11. So you basically add 4 + 11 + 3 + 11 + 0 + 1 = 30. But yeah.
You can't just ignore the carriage return. How does that in any way make sense? It's clearly 3 unrelated lines, specifically 2 expressions, and 1 equation that you need to finish.
The final one is just a matter of reading out and counting the numbers of the previous sequence. The first is one 1 (written as 11), next is 2 ones (written as 21), then one 2 and one 1 (1211), and so on. So the answer is 13112221. It's actually an interesting analogy to file compression algorithms :)
For problem #2 the same applies in programming. Programing languages have well-defined operator precedence rules which define the order of the operations, however adding parenthesis/brackets around the groups makes it easier to read/follow, especially for complex equations or logic checks.
The only thing that surprised me was the reaction to bodmas. Can you imagine doing algebra without bodmas? 5 + 3x would equal 8x if you just go from left to right. Having to write 8 + (3x) would be so stupid. And if algebra becomes tedious and difficult without it, every other part of maths would too because it is literally built on algebra.
When I first noticed these 'order of operation' type riddle short videos, they were almost always about fighting over notation; as if there somehow was ONE correct interpretation. Often the parties arguing genuinely did not know better, as they had their particular 'correct' notation drilled into them at school over and over again (and had eventually given up resisting). Now we have math professors join in and tell what we (the non-resigned) knew all along: The notation means what we agree the notation means, and if there is doubt we should really agree ahead of time. So, rejoice, math fans, we won! (thank you Tom).
The thing about any expression is that it is attempting to express something. So the correct answer to "3+3x3-3+3" and its friends is always "Express yourself more clearly!"
@@peterbrockway5990 I find that often there is some context present, like a particular computer language or a particular math model problem, that will make the expression fairly well-defined (I guess 'fairly well-defined' is an oxymoron). The 'fun' or 'riddle' part is to some extent that the context is removed. Would it help if I go, say, "(3 + (3x3) - 3) + 3"? I am happy to go along with "3+3x3-3+3" when I feel I know the context. Are you more stringent, to the point, where you would still go "express yourself more clearly" even if you think you might be able to guess from the context? To me the win in this video is that WHEN the context might not be clear, or maybe entirely missing, THEN the expression defaults to largely undefined (or "bad notation" in Tom's words).
There is actually a fairly interesting bit of mathematics related to the "look-and-say" sequence. John Conway showed that the ratio between adjacent terms approaches a constant, and gave a polynomial with integer coefficients, of which said constant is a root.
@@remischmitt9308 This is not true. The sequence grows (asymptotically) exponentially forever. The only starting number which results in a sequence that doesn't grow infinitely is 22, since that stays at 22.
@@remischmitt9308it's provably nonrepeating in the strict sense, i.e. it's nonperiodic. sure you'll see the same patterns reappear, but they will forever do so somewhat randomly.
There is something so pleasing about seeing a maths professor get as frustrated with these videos as me! 😂 I also made the exact same mistake as you on #6…
50% divided by 2 can't be 1, since they never say that it's 50% of 1. So since it's not 50% of anything specific, but 50% in general, the answer is 25% of that thing that we don't know of. If we were to accept that it's 1/2, we get 1/2 divided by 2, which is 1/2*1/2 = 1/4 Also, it's not 1/2/2, but rather
They want you to assume that it is already half of 100% so it is already divided by 2. This question is written wrong for the type of answer they are looking for.
I didn't see any comments on puzzle #8 but the first 2 lines are not part of the equation because they don't have a plus sign in the end. Completely legit, very subtle trick.
have you ever seen numbers written on multiple lines? Like long expansions of decimals of PI where you continue the digits on the next line because there isn't enough space on the first? 1 + 1 + 1 + 1 + 11 + 1 + 1 + 1 + 11 + 1 * 0 + 1 = 30, those pesky 11's clearly take up so much space on the blackboard they had to be split on multiple lines, much like PI.
20:24 It is the “look and say” sequence (it’s called something like that) and the next term is given by saying the number of a certain digit in order so the next one will be 13112221
I'm MSc math and do not always respond correctly to riddles, even though I've constructed some crazy (correct) proof's over the years. Now I feel better.
For anyone curious, the trick to the last riddle is to express the previous term in words and interpret that worded expression literally as the next term in the sequence: 1 - first term 11 - "1" has one 1 (one 1 = 11) 21 - "11" has two 1's (two 1 = 21) 1211 - "21" has one 2 followed by one 1 (one 2, one 1 = 1211) 111221 - "1211" has one 1 followed by one 2 followed by two 1's (one 1, one 2, two 1 = 111221) 312211 - "111221" has three 1's followed by two 2's followed by one 1 (three 1, two 2, one 1 = 312211) So the next term would be 13112221 because "312211" has one 3 followed by one 1 followed by two 2's followed by two 1's (one 3, one 1, two 2, two 1 = 13112221)
As a PhD. from Oxford (or Cambridge) you should know that there is a convention about precedence of operations: multiplication precedes addition: a+b*c = a+(b*c) and not (a+b)*c, this is not left to what one "wants to do".
Oh, I at first thought he meant that (a+b)c=ac+bc. I mean (a+b)c is equivalent to doing addition first and then multiplication, and ac+bc is equivalent to doing multiplication first and then addition. On the other hand, this property has little to do with the example in the video, so you’re probably correct 😅
He should have known that but I also agree that when you are communicating maths you wouldn't write it in that way precisely because it confuses rather than illuminates what you are trying to convey.
I have found the answer for the question left opened. And i have a Formula in getting what i got The answer is 13122111 And the cornerstone of the sequence is 21 And my formula i used to get my answer which proves the results of the previous group of series before the expectant is binomial triangle method but with a little bit of complexity in it.
Hey Tom! Idk if you’d be interested in this but the LSAT just removed their “logic games” section from the test, which tested lots of conditional logic. Would you consider doing an LSAT Logic Games section? Think it would be really cool to see! Keep up the good work on the vids
I already learned the trick to the last question but... Every time I see a question like this it reminds me that any finite series of numbers can represent the values of a carefully-chosen polynomial. Which values? Could be solutions for P(x)=0 or P(1),P(2),etc..
Okay so question 3 doesn't make sense. By order of operations, you do parenthesis first, and switching notation (from linguistic to mathematical notation) it's grammatically implied to be separated ideas
The 1+1+1… turned out to be 30… the lines wrapped around and there were two elevens in the middle of the list. One of the 1’s was multiplied by 0 so it disappeared. If I subtotaled, it would look like 4+11+3+11+1.
#3 depends on how you read the problem. If you pause after "half of" then in constant speed say "2 + 2" then the answer is 2. But if you pause after "half of 2" then and "+ 2" then the answer is 3. The problem with word problems in math is that they are ambiguous and depends much on both context and how it is interpreted.
Bodmas doesn’t apply to a sentence - it applies to mathematical notation. Once you describe the problem in words, the rules of verbal interpretation apply.
the one with all the ones is definitely 2 after looking back because at the end and beginning of each line there is no function so they can't be a apart of the same equation
For the 50% question, I think what they did is that since 50% is (50/100), they divided that by 2, i.e. 50/100/2 and the 50/100= 1/2 and since there was a 2 dividing (50/100) it would go in to the numerator making the eq look something like (1/2)×2, the two in numerator will cancel the 2 in denominator resulting in 1.
Omg, i can't believe they don't have answer to #9. It's one of my favorites. It's 13112221. You almost had it when you said counting the ones. Each is count the amount of numbers in the previous. One, one one, two ones, one two and one one, One one and one two and two ones, Three ones and two twos and one one, Etc
For problem #8 you have to ignore the two first rows because there are no functions between them. Even if you don't want to ignore them, you don't know if your supposed to add, subtract multiply or divide or what you're supposed to do, cant just assume that you're supposed to add it when it doesn't say so.
Riddles, when applied to certain disciplines, are frustrating. "Math riddles" are meant to trick you into applying that mindset to it. Question 8 uses it well. "The indented portion wasn't part of the equation." Where plenty of others have stated that's not normal mathematical practice.
To be fair to the question with multiple lines, there wasn't an addition sign to connect each line so I believe it was fair to say it wasn't part of the equation
My guess for #8 was 10. I knew _something_ was up without the plus signs, but from there, it was impossible to guess exactly what we were supposed to do. Since two numbers next to each other typically means multiply, I assumed the 1 from the previous row was supposed to be multiplied by the 1 from the next row, which going by PEMDAS, would equal 10. So yeah, there's no way to get that right without either getting lucky or being a mind reader, because even noticing the missing plus signs, I wasn't sure what the cartoon teacher wanted us to _do_ with that information.
Tom, with question 8, you failed to notice that there were no addition signs at the end of the first to lines to connect the three lines together as one equation. Hence, the video was correct with that question. I do, however, agree with you regarding question 5, he clearly said "divided by 2" not "divided by half".
I can accept that at the "puzzle" level Roman numerals are used and even a vague operation like "take" (removing a symbol) is an option. But, reciprocally and for consistency, I hope that all my answers that use these tricks will be accepted as valid. That is, I have the freedom to solve in other numerical bases, in other arithmetics (modular for example) in other languages, operate according to the meaning of the dictionary... and in general, jump freely between different rules that were not specified.
Is it half of 2... plus 2 (three). But I clearly heard "What is half... of 2+2" (two). These kind of interpretive questions are REALLY maddening because both answers can be correct depending on how you ask the question.
YES. thank you. I strongly agree with your take on order of operations. As a programmer there's strict rules, but even then if you have to look up the rules you should probably rewrite it with more brackets! Still good to know the rules, however, as sometimes you get code written by a worse programmer than yourself.
For 6, I think you missed only addition. With that restriction, it’s a bit easier. I got this in 15 s using trial and error with a kind of recursive algorithm. I just figured 888 is close to 1000, so makes sense to start there. That leaves 112 to make up and 5 8’s remaining, so apply the same reasoning, 88 is closest to 112, leaving 24 and 3 8’s which obviously add to 24. This was the only I felt I actually had to use some strategy on.
Problem 2 is a matter of operator precedence rather than order. All operators with the same precedence can be evaluated in any order. In this context, infix operators are assumed. Polish and Reverse would be much better : bracket free.
I'd say only the '50% question' is a legitimate logically wrong question, the rest are valid. Since it's riddles and not straightforward questions, the roman numerals question is definitely valid. And the one where they said the first 2 rows aren't the part of the equation is also correct since they didn't have any symbol at the end of the lines or at the start of them. About the last one, I'd say the answer is infinity since they said 'the last number in this sequence' and the sequence is divergent.
#8 you could argue 2 solutions Either consider that the first 2 lines are not part of the equation since there's no + sign at the end, which results in 2. Another way to look at this problem is the coding grammar where spaces within an equation are first trimmed and we get 1+1+1+1+11+1+1+1+1+11+1+1x0+1= 32
I actually got #6, but wasn’t 100% certain I was right in the time. They said using only addition, so I figured concatenation had to be legal. We were never going to get anywhere near it if we didn’t do 888. This leaves us a bit over 100 away, and they told us it was 8 8s, so I figured it was 888 + 88 + 8 + 8 + 8, because 888 + 88 + 88 + 8 would over shoot, but I was still working out if it was exactly 1000 when time ended.
For the 1+1+1+1+1etc question, i assumed that the 5th and 6th, and 10th and 11th 1's were actually an 11 since there was no sign noted between them. Doing this I got an answer of 30. 1+1+1+1+11+1+1+1+11+1×0+1=30
For #8, even if you consider the first two lines part of the equation, it's still not 12. There is no operation between the end of each line and the beginning of the next. So yes, they are trying to trick you, but also no, it is not clearly one equation.
#7 first two lines are not part of the equation because there are no connecting operator between line 1 to line 2 and from line 2 to line 3. If you are a sharp computer programmer you would notice this immediately because what is written on the board would give a syntax error.
About thirty years ago there was an (Associated Examinations Board?) advanced-level English GCE that came with directions along the lines of 'Answer 4 questions in-all - 3 from section A and 2 from section B'. But the candidates didn't expect a mathematics test
This isn't a math riddle video, it's just a "let's see if we can phrase it in a way that will make people make a mistake" type video. Fuck this, it's not about checking your math skills, it's checking whether you are following their stupid exact phrasing to the latter to find out the crooked answer their mind concocted.
Riddle 2# how the hell you mess it up your brain must really have gotten fried from Harvard math and all of that bs university to make you forget basic math.
he was right about the last problem if you say each number individually it reads the previous problem which I think when he said counting should be right
In the next to the last one, what's the operator between the first and second rows, and the second and third rows? There isn't one, hence they aren't part of the equation... I agree with your sentiments though. I really dislike "math" problems like these.
The 1+1 and so on-equation is very clearly 2. There's no mistake, just confusion. On the new lines it doesn't start with '+'. That's a dead giveawey. The last one are just the look-and-say numbers.
For #8, I was taught at school that if you have to change lines in an equation you need to say what are you doing next and follow it to the next line. Like in this case: 1+1+1+1+1+ +1+1+1+1+1+ 1+1x0+1 If it would be written like this then 12 is the correct answer. At least from what I was taught
That would double the plus signs. Now for plus signs this doesn't pose problems, but it would if you do this with minus signs. 4- -2 is actually 6, because it says 4 - -2. If you continue a line, just write the operator at the end of the first line: 1+1+1+1+1+ 1+1+1+1+1+ 1+1*0+1 or, preferably, at the start of the next line: 1+1+1+1+1 +1+1+1+1+1 +1+1*0+1 The last is prefered because here too, if the line were broken at a subtraction, then the minus sign would be close to the subtracted number.
So here is my thought for #5.... if you divide any number by 2 then it means that what we will be getting is the half of that number.... For example if you divide 10 by 2 then its the half of 10 i.e 5. But i guess they rather divided it by 1/2 thinking that it would give half of 50% but they actually had to multiply it by 1/2. that's where they got it wrong... what do y'all think
RE: order of operations The order we have exists because algebra is easier to do if you don't need brackets everywhere to make it clear 3X+5 means (3×X)+5 rather than the unintuitive 3×(X+5). Their teaching as a rule to kids who don't understand the reasoning is IMO part of the problem with the whole education there. No one writes such problems with numbers for anyone over 8 or 9 because by that time you're getting introduced to the basics of algebra and it stops being an issue.
6:00 when i was a wee little lad in school they taught me PEMDAS or BEMDAS (their quite similar) parenthesis exponents multiplication division addition subtraction.
Watch the original video from Bright Side here: th-cam.com/video/r5P-f5arPXE/w-d-xo.html
Your video is very nicely done
Better than theirs lol
The last one (without the answer) is based on compression algorithms. The sequence is just saying what you see in the previous element. describing how many of each recurring digit So:
1 is just a single One ie One one (11)
11 is Two Ones. (21)
21 is One 2 followed by One one (1211)
1211 is One one followed by One two followed by two Ones (111221)
111221 is Three ones, followed by Two twos, followed by One one( 312211)
So the next in the sequence would be
13112221
Simple
u need pre-school 4 cheating :)
@@KenFullman ha nice
try solving IOQM exam from India
Waiiiiiiit whattt?! #5 says 50% divided by 2, not 50% divided by 1/2, they’re so gaslighting us!
This is not just annoying, its crazy! They _are_ wrong!
its 1/4 or 25%
50% is 1/2 and deviding it by 2 means 1/2 * 1/2
95% of people don't understand percentages, so they easily get away with it.
Almost fooled Tom as well ;-)
I agree, the obvious answer is 25%.
The given solution answers the question
"Solve x/2 = 50%."
Which *could* be read
"What is 50% (when) divided by 2"
but they ommit such clarifying words.
Sure it isn't strictly necissary, but it's omition heavily implies another meaning.
"Evaluate x = 50% / 2."
The statement is deliberately subversive.
Xd how you messed up Question 2? 😅 @@mlloser8318
A great example of "writing my 'riddles' ambiguously to make the reader feel like a donkey".
😂😂
That 50% question is legitimately incorrect. This is why language literacy is just as important as mathematics literacy when participating in doing math.
it was probably also incorrect on purpose to drive engagement in the comments
@@MegaOoga That is the problem. This gives birth to Terrance Howard's of the future
Yeah. They answered “50% / (1/2)”. The question was what is “50% / 2”. They converted divided by 2 into 1/2, but forgot to change the division sign to a multiplication sign,
I guess if you REALLY want to you can still justify that the answer is 1.
The question is "what is 50% divided by 2 ?"
If you interpret it as "what is 50 per (cent divided by 2) ?" (which you have no reason to do, of course) you do get 1 as the answer.
that video is
95% childhood trauma
4% gaslight sold as “thinking out of the box”
1% maths
The last pattern is the “look and say sequence”, starting at 1…
The number after 312211 is 13112221, because there’s 1 3, 1 1, 2 2, 2 1… but they didn’t ask for the next number, they asked for the *last* number in the sequence…
The last digits will alternate between 11 and 21, so this sequence never ends, so there is no “last number”… unless you take 312211 as the last number they gave you…
Yes, I also recognized the John Conway sequence from the Numberphile video.
@@thomashoglund5671 The Conway sequence is the look-and-say sequence starting with a 3, specifically, instead of a 1.
Thank you "please don't touch anything" for introducing me to this sequence
So the correct answer would be 1? Because they didn't read the sequences as big numbers, but rather a sequence of one digit numbers without spaces. And the last number (digit) of the last sequence (of 1 digit numbers) of the infinite whole sequence, is 1 because it always is 1 and it can't be anything else than 1.
But they not ask for the number (btw a Conway sequence), but "Can you figure out ...". So the answer must be "yes" when you can, otherwise "no" when you can't.
#3 they clearly got wrong too. In mathematical writing it is completely standard that a formula surrounded by text is treated as a whole. You never have a part of the formula interact with the text, and then with the rest of the formula. So the answer is unequivocally 2.
My instinct was that the answer was 2, but realised it was too obvious, so re-read it to come up with the 'right' answer. But it just didn't 'seem' to look right, but I couldn't understand why. Sure, if you follow BODMAS, the answer is 3, but as I read the question, I couldn't see whatever seemed wrong with it.
Your explanation makes it so clear, so thank you for putting me out of my misery!
Yup
Is there a rule of the internet that "there's an XKCD for that?" Because I entirely agree with what I think is Tom's main complaint and the same as Randall Monroe voiced 18 years ago in XKCD 169: "communicating badly and then acting smug when you're misunderstood is not cleverness."
And for my less TL;DR commentary:
#2: The order of operations "riddles" are so common online that this should be pretty easy. Note that it also highlights why BODMAS (or PEMDAS) doesn't even work: after M, you have 3+9-3+3; applying A next gives 12-6, which is 6. To get 12 you have to either use BODMSA or group as BO[DM][AS] or PE[MD][AS], applying addition and subtraction together.
#3: I got "2, but they're going to tell me it's 3" because I think embedding maths notation implicitly groups that apart from the operations in the English text. At best, it's ambiguous (unlike #2, which is well-defined because it's all written in symbols).
#5: The answer just straight-up lied about what the question was, so the video can *&^% right off with that one.
#6: I see Tom missed the extra instruction "all you can use is addition" because it was spoken but not on the board. Which actually helps because the only thing you could use and then pretend is nothing is writing multiple 8s as one number. And then there's barely enough time to say "888 leaves 112, so plus 88 and plus however many are left as singles and I hope that works."
#8: Tom's attempt imaginines extra '+' signs between the lines. I got to "do they want to ignore the first two lines and get 2 or join them into 1+1+1+1+11+1+1+1+11+1×0+1 = 30?"
#9: The Look And Say Sequence is pretty instantly recognisable to sequence fans. Find it as OEIS A005150.
For #6, I did 8+8+8+8+8+8+8+8+936. They never said we have to ONLY use 8.
I did (8 × 8 × 8) + (8 × 8 × 8) - (8 + 8 + 8), then realised I used nine 8s. Degree in pure maths and I can't count to nine, apparently.
@@hughcaldwell1034 ((8*8*8)-8)*((8+8)/8)-8
@@hughcaldwell1034or hear either apparently, it says you can only use addition😂
@@peterb5 The part about only using addition was the only way I got it quickly. You need 5 8's in the units column to make 0, carry 4. Then 2 more 8's in the tens column for 0, carry 2. Then 1 more 8 in the hundreds column for 0, carry 1.
@@peterb5 Oh damn... Yeah, really glossed over that one... I'm used to encountering variations of this question with a pretty standard stipulation that the four basic operators are allowed. I was mostly watching for the commentary anyway, though, since these types of questions are usually irritatingly trivial or just badly phrased.
I do agree with Toms statement that riddles like these abuse math to wrongly make people think math is hard, and that this is a bad thing.
I really dislike these as a concept. Not the riddles themselves, but the whole "thing" around the riddles. The poorly written prompts, grammatical errors, taunting phrasing. Everything about these riddles feels like they're designed to prey on people who are easily influenced. They fish for engagement with every single aspect of their presentation.
I think there's a bigger mistake these riddles make: the answer to a riddle should be fun even if you got it wrong.
for 1+1+1+1+1 question, there is no operation between the lines (no hanging +), so they are different independent statements and have no bearing on the last statement. The last question is a description of the digits in the previous number in the sequence. 1 is described as "a single one" aka "one one" aka 11. 11 is described as "two ones" aka 21, then "one two, one one" aka 1211, etc... Numberphile did a video on it.
Wrong. No hanging + means concatenation is implied hence 2 eleven and the answer is 30.
I'm pretty sure the answer for #8 is a vector (5 5 2) since there are no symbols uniting the lines
I originally got 12, and then quickly changed my answer to 30 after I saw they had omitted the missing plus signs on the end of each line. I thought they maybe wanted you to concatenate them to make two 11s, but apparently not 😂
But you have no = signs after the first two lines, so clearly you are not supposed to give an answer to these.
@@general_isaac I did the same thing, 30.
@@general_isaac forgot the x0?
There are no symbols that join them in a vector. But in any case, it looks vertical, it would be a matrix with 3 rows and 1 column.
my answer was
5
5
...=2
No connection seen between each row.
18:16 Well, on that one, they aren't very clearly part of the equation. There are not math operators linking the first two lines to the last. The answer I got was a 5, another 5, and a 2.
You're missing the point. Due to the lack of rigor in all of the previous problems, you simply can't determine what the person who created the problem intends, because anything is acceptable if it leads to more people getting the answer wrong.
I understood it as the last one from one line and the first line from the next line as 11, so the answer as 30
@@weirdlyspecific302 What the person intends is not relevant to my comment. Tom says the numbers are "very clearly part of the equation" and I'm saying that, because of the very lack of rigor you refer to, they are *not* _very clearly_ part of the equation.
@@GeekRedux you are right.
The last question - key is to read the numbers aloud to get the next number - the first number is one one - 11 (which is second number) - so the third number is two ones or 21 - which is one two then one one etc
you’re a fucking genius my friend. bes wishes buddy you going far for real
Yes. However I don't think there's a clear end via this algorithm.
I've seen #8 multiple times online, and there they say that since there is no + in between the 1 at the end and the beginning of a row, its 11. So you basically add 4 + 11 + 3 + 11 + 0 + 1 = 30. But yeah.
That's what I got.
You can't just ignore the carriage return. How does that in any way make sense? It's clearly 3 unrelated lines, specifically 2 expressions, and 1 equation that you need to finish.
@@TahgtahvWell it makes sense if you just run out of space and have to continue somewhere.
You can interpret the question "can you take 1 from 19 to make 20" as "make a correct expression out of 19 - 1 = 20". You could say 19 - 1(i^2) =20
The final one is just a matter of reading out and counting the numbers of the previous sequence.
The first is one 1 (written as 11), next is 2 ones (written as 21), then one 2 and one 1 (1211), and so on. So the answer is 13112221. It's actually an interesting analogy to file compression algorithms :)
For problem #2 the same applies in programming. Programing languages have well-defined operator precedence rules which define the order of the operations, however adding parenthesis/brackets around the groups makes it easier to read/follow, especially for complex equations or logic checks.
The only thing that surprised me was the reaction to bodmas. Can you imagine doing algebra without bodmas? 5 + 3x would equal 8x if you just go from left to right. Having to write 8 + (3x) would be so stupid. And if algebra becomes tedious and difficult without it, every other part of maths would too because it is literally built on algebra.
When I first noticed these 'order of operation' type riddle short videos, they were almost always about fighting over notation; as if there somehow was ONE correct interpretation. Often the parties arguing genuinely did not know better, as they had their particular 'correct' notation drilled into them at school over and over again (and had eventually given up resisting). Now we have math professors join in and tell what we (the non-resigned) knew all along: The notation means what we agree the notation means, and if there is doubt we should really agree ahead of time. So, rejoice, math fans, we won! (thank you Tom).
The thing about any expression is that it is attempting to express something. So the correct answer to "3+3x3-3+3" and its friends is always "Express yourself more clearly!"
@@peterbrockway5990 I find that often there is some context present, like a particular computer language or a particular math model problem, that will make the expression fairly well-defined (I guess 'fairly well-defined' is an oxymoron). The 'fun' or 'riddle' part is to some extent that the context is removed. Would it help if I go, say, "(3 + (3x3) - 3) + 3"?
I am happy to go along with "3+3x3-3+3" when I feel I know the context. Are you more stringent, to the point, where you would still go "express yourself more clearly" even if you think you might be able to guess from the context?
To me the win in this video is that WHEN the context might not be clear, or maybe entirely missing, THEN the expression defaults to largely undefined (or "bad notation" in Tom's words).
Last one was especially non-math, the answer is 13112221: the previous number has one 3, followed by one 1...
There is actually a fairly interesting bit of mathematics related to the "look-and-say" sequence. John Conway showed that the ratio between adjacent terms approaches a constant, and gave a polynomial with integer coefficients, of which said constant is a root.
The sequence ends in a repeat: the same number will start appearing because it describes itself
@@remischmitt9308 This is not true. The sequence grows (asymptotically) exponentially forever. The only starting number which results in a sequence that doesn't grow infinitely is 22, since that stays at 22.
@@remischmitt9308it's provably nonrepeating in the strict sense, i.e. it's nonperiodic. sure you'll see the same patterns reappear, but they will forever do so somewhat randomly.
There is something so pleasing about seeing a maths professor get as frustrated with these videos as me! 😂
I also made the exact same mistake as you on #6…
12:29 The Oxford math professor outsmarts the Bright side writers, that is what I came here to watch!
50% divided by 2 can't be 1, since they never say that it's 50% of 1. So since it's not 50% of anything specific, but 50% in general, the answer is 25% of that thing that we don't know of.
If we were to accept that it's 1/2, we get 1/2 divided by 2, which is 1/2*1/2 = 1/4
Also, it's not 1/2/2, but rather
They want you to assume that it is already half of 100% so it is already divided by 2. This question is written wrong for the type of answer they are looking for.
I didn't see any comments on puzzle #8 but the first 2 lines are not part of the equation because they don't have a plus sign in the end. Completely legit, very subtle trick.
have you ever seen numbers written on multiple lines? Like long expansions of decimals of PI where you continue the digits on the next line because there isn't enough space on the first? 1 + 1 + 1 + 1 + 11 + 1 + 1 + 1 + 11 + 1 * 0 + 1 = 30, those pesky 11's clearly take up so much space on the blackboard they had to be split on multiple lines, much like PI.
Thanks Tom, these daft problems seem to pop up more and more regularly.
20:24 It is the “look and say” sequence (it’s called something like that) and the next term is given by saying the number of a certain digit in order so the next one will be 13112221
I'm MSc math and do not always respond correctly to riddles, even though I've constructed some crazy (correct) proof's over the years. Now I feel better.
For anyone curious, the trick to the last riddle is to express the previous term in words and interpret that worded expression literally as the next term in the sequence:
1 - first term
11 - "1" has one 1 (one 1 = 11)
21 - "11" has two 1's (two 1 = 21)
1211 - "21" has one 2 followed by one 1 (one 2, one 1 = 1211)
111221 - "1211" has one 1 followed by one 2 followed by two 1's (one 1, one 2, two 1 = 111221)
312211 - "111221" has three 1's followed by two 2's followed by one 1 (three 1, two 2, one 1 = 312211)
So the next term would be 13112221 because "312211" has one 3 followed by one 1 followed by two 2's followed by two 1's (one 3, one 1, two 2, two 1 = 13112221)
I always pause the video and then feel like a genius when I get the answer in 20 minutes, lol
The original video being reacted to should have been called "How to make a mathematician salty in nine easy steps"
Tom , do we have Oxford university mathematical papers from previous decades, centuries ??
18:00 the answer is actually 30! Notice how the second and third row end and start with a 1 respectively. same thing with first and second row
The last one is the Conway sequence, I had a coding test on it a few days ago so I definitely remember it :)
Brightside came up on my feed and was blocked after watching a video. I appreciate you doing this. Their videos are crap.
As a PhD. from Oxford (or Cambridge) you should know that there is a convention about precedence of operations: multiplication precedes addition: a+b*c = a+(b*c) and not (a+b)*c, this is not left to what one "wants to do".
Exactly I’m still in high school and it baffled me how he got this wrong.
A pHD student is not going to waste their time with arithmetic rules. Tom probably hasn’t done a calculation like that in years!
Oh, I at first thought he meant that (a+b)c=ac+bc.
I mean (a+b)c is equivalent to doing addition first and then multiplication, and ac+bc is equivalent to doing multiplication first and then addition.
On the other hand, this property has little to do with the example in the video, so you’re probably correct 😅
He should have known that but I also agree that when you are communicating maths you wouldn't write it in that way precisely because it confuses rather than illuminates what you are trying to convey.
@@lustrous3846thats bs. Its basic math, you dont need to do exercise
19:37 it was not part of the equation because the second and third line did not start with pluses, neither the 1st and 2nd lines ended with it
I have found the answer for the question left opened.
And i have a Formula in getting what i got
The answer is
13122111
And the cornerstone of the sequence is 21
And my formula i used to get my answer which proves the results of the previous group of series before the expectant is binomial triangle method but with a little bit of complexity in it.
I'm surprised Tom (nor the video) did not know about the "look and say sequence" (studied by Conway) which provides the answer to the last question.
Hey Tom! Idk if you’d be interested in this but the LSAT just removed their “logic games” section from the test, which tested lots of conditional logic. Would you consider doing an LSAT Logic Games section? Think it would be really cool to see! Keep up the good work on the vids
I already learned the trick to the last question but... Every time I see a question like this it reminds me that any finite series of numbers can represent the values of a carefully-chosen polynomial. Which values? Could be solutions for P(x)=0 or P(1),P(2),etc..
When he said a little bit beneath us it was 3 brown 1 blue.(Really good one at that)😂😂😂
"This golden rule of math always works."
Terrance Howard doesn't agree.
Okay so question 3 doesn't make sense. By order of operations, you do parenthesis first, and switching notation (from linguistic to mathematical notation) it's grammatically implied to be separated ideas
The 1+1+1… turned out to be 30… the lines wrapped around and there were two elevens in the middle of the list. One of the 1’s was multiplied by 0 so it disappeared. If I subtotaled, it would look like 4+11+3+11+1.
#3 depends on how you read the problem. If you pause after "half of" then in constant speed say "2 + 2" then the answer is 2. But if you pause after "half of 2" then and "+ 2" then the answer is 3.
The problem with word problems in math is that they are ambiguous and depends much on both context and how it is interpreted.
Bodmas doesn’t apply to a sentence - it applies to mathematical notation. Once you describe the problem in words, the rules of verbal interpretation apply.
the one with all the ones is definitely 2 after looking back because at the end and beginning of each line there is no function so they can't be a apart of the same equation
50% divided by 2 is 1 if you look at it like (1/2)/2 which gives you 1 after moving the bottom “2” to the top
For the 50% question, I think what they did is that since 50% is (50/100), they divided that by 2, i.e. 50/100/2 and the 50/100= 1/2 and since there was a 2 dividing (50/100) it would go in to the numerator making the eq look something like (1/2)×2, the two in numerator will cancel the 2 in denominator resulting in 1.
Nah bro ur dumb
Omg, i can't believe they don't have answer to #9.
It's one of my favorites.
It's 13112221.
You almost had it when you said counting the ones. Each is count the amount of numbers in the previous.
One,
one one,
two ones,
one two and one one,
One one and one two and two ones,
Three ones and two twos and one one,
Etc
they have the answer, they just say it like that to bait people to engange in comments since it helps the video
17:28
Bro that sucks I got 30 because i saw it as 1 + 1 + 1 + 1 + 11 + 1 + 1 + 1 + 11 + 0 + 1
For problem #8 you have to ignore the two first rows because there are no functions between them. Even if you don't want to ignore them, you don't know if your supposed to add, subtract multiply or divide or what you're supposed to do, cant just assume that you're supposed to add it when it doesn't say so.
So this is basically just ‘what am I thinking’ making you feel stupid when you can’t answer their stupidly worded questions.
Riddles, when applied to certain disciplines, are frustrating. "Math riddles" are meant to trick you into applying that mindset to it. Question 8 uses it well. "The indented portion wasn't part of the equation." Where plenty of others have stated that's not normal mathematical practice.
To be fair to the question with multiple lines, there wasn't an addition sign to connect each line so I believe it was fair to say it wasn't part of the equation
My guess for #8 was 10. I knew _something_ was up without the plus signs, but from there, it was impossible to guess exactly what we were supposed to do. Since two numbers next to each other typically means multiply, I assumed the 1 from the previous row was supposed to be multiplied by the 1 from the next row, which going by PEMDAS, would equal 10. So yeah, there's no way to get that right without either getting lucky or being a mind reader, because even noticing the missing plus signs, I wasn't sure what the cartoon teacher wanted us to _do_ with that information.
Tom, with question 8, you failed to notice that there were no addition signs at the end of the first to lines to connect the three lines together as one equation. Hence, the video was correct with that question. I do, however, agree with you regarding question 5, he clearly said "divided by 2" not "divided by half".
13112221. Read the numbers. There’s 1#3 1#1 2#2’s 2#1’s.
Go back to the lines starting from any eg 1211 next is 1#1 1#2 2#1= 111221
I can accept that at the "puzzle" level Roman numerals are used and even a vague operation like "take" (removing a symbol) is an option.
But, reciprocally and for consistency, I hope that all my answers that use these tricks will be accepted as valid.
That is, I have the freedom to solve in other numerical bases, in other arithmetics (modular for example) in other languages, operate according to the meaning of the dictionary... and in general, jump freely between different rules that were not specified.
For number 8: They aren't just arbitrarily ignoring the first 2 lines. There's no addition sign connecting the first 2 lines to the equation.
Is it half of 2... plus 2 (three). But I clearly heard "What is half... of 2+2" (two). These kind of interpretive questions are REALLY maddening because both answers can be correct depending on how you ask the question.
YES. thank you. I strongly agree with your take on order of operations. As a programmer there's strict rules, but even then if you have to look up the rules you should probably rewrite it with more brackets! Still good to know the rules, however, as sometimes you get code written by a worse programmer than yourself.
For 6, I think you missed only addition. With that restriction, it’s a bit easier. I got this in 15 s using trial and error with a kind of recursive algorithm. I just figured 888 is close to 1000, so makes sense to start there. That leaves 112 to make up and 5 8’s remaining, so apply the same reasoning, 88 is closest to 112, leaving 24 and 3 8’s which obviously add to 24. This was the only I felt I actually had to use some strategy on.
Can you solve ted ed riddles?
Problem 2 is a matter of operator precedence rather than order. All operators with the same precedence can be evaluated in any order. In this context, infix operators are assumed.
Polish and Reverse would be much better : bracket free.
This was hilarious, thanks Tom 👍
for problem 6 i got
sqrt(sqrt((8+8+8+8)^8))-8-8-8
That’s John Conways see and say sequence. Count the number of each different digit and say it for the next number in the sequence
I'd say only the '50% question' is a legitimate logically wrong question, the rest are valid. Since it's riddles and not straightforward questions, the roman numerals question is definitely valid. And the one where they said the first 2 rows aren't the part of the equation is also correct since they didn't have any symbol at the end of the lines or at the start of them.
About the last one, I'd say the answer is infinity since they said 'the last number in this sequence' and the sequence is divergent.
😂😂😂 your reaction to them having an error in the video was so funny
#8 you could argue 2 solutions
Either consider that the first 2 lines are not part of the equation since there's no + sign at the end, which results in 2.
Another way to look at this problem is the coding grammar where spaces within an equation are first trimmed and we get
1+1+1+1+11+1+1+1+1+11+1+1x0+1= 32
That "what is 50% divided by 2" one was stupid. They blundered - no marks to them for that one. A good time to exit.
17:55 you could get another answer
Those 2 1 can become 11
So it could be 30 as an answer
I actually got #6, but wasn’t 100% certain I was right in the time. They said using only addition, so I figured concatenation had to be legal. We were never going to get anywhere near it if we didn’t do 888. This leaves us a bit over 100 away, and they told us it was 8 8s, so I figured it was 888 + 88 + 8 + 8 + 8, because 888 + 88 + 88 + 8 would over shoot, but I was still working out if it was exactly 1000 when time ended.
Thank you, Tom.
In its own way fascinating.
the#5 may have something wrong, because 50% decided by 2 is obviously = 0.25(25%)in any way although 50%=1/2 and we use 1/2/2 =1/2*1/2 =0.25
For the 1+1+1+1+1etc question, i assumed that the 5th and 6th, and 10th and 11th 1's were actually an 11 since there was no sign noted between them. Doing this I got an answer of 30.
1+1+1+1+11+1+1+1+11+1×0+1=30
For #8, even if you consider the first two lines part of the equation, it's still not 12. There is no operation between the end of each line and the beginning of the next. So yes, they are trying to trick you, but also no, it is not clearly one equation.
18:10 There is no operation sign between last "1" in a row and the first "1" in the next row. You assumed there is an addition
In fairness the 1+1+1+1+1
Has no continuing operation after the fifth one on the first line or the second line
All the tatoo ink, all the piercings, won't hide the fact that you're a math nerd of the geekiest order.
Thanks for making this vids the fault isn’t on you, If I did these problem I’ll be more angry it not math anyway, your math skill is really great.
#7 first two lines are not part of the equation because there are no connecting operator between line 1 to line 2 and from line 2 to line 3. If you are a sharp computer programmer you would notice this immediately because what is written on the board would give a syntax error.
About thirty years ago there was an (Associated Examinations Board?) advanced-level English GCE that came with directions along the lines of 'Answer 4 questions in-all - 3 from section A and 2 from section B'. But the candidates didn't expect a mathematics test
This isn't a math riddle video, it's just a "let's see if we can phrase it in a way that will make people make a mistake" type video. Fuck this, it's not about checking your math skills, it's checking whether you are following their stupid exact phrasing to the latter to find out the crooked answer their mind concocted.
Riddle 2# how the hell you mess it up your brain must really have gotten fried from Harvard math and all of that bs university to make you forget basic math.
#8 the top 2 lines are =10 but there’s not addition symbol to indicate that they are adding to the bottom line. I think it was just a tricky spot
he was right about the last problem if you say each number individually it reads the previous problem which I think when he said counting should be right
In the next to the last one, what's the operator between the first and second rows, and the second and third rows? There isn't one, hence they aren't part of the equation... I agree with your sentiments though. I really dislike "math" problems like these.
The eight 8s was gettable if you heard the voiceover say to only use addition, given that 1000/8 is 125, and 1+2+5 is 8
maybe I'm missing something but what does anything of the last part you wrote have to do with the solution?
The 1+1 and so on-equation is very clearly 2. There's no mistake, just confusion. On the new lines it doesn't start with '+'. That's a dead giveawey.
The last one are just the look-and-say numbers.
13112221.
Each number describes the previous number. 1 has one 1. 11 has two 1s. 21 has one 2 and then one 1. 1211 has one 1, one 2, and two 1s. etc.
For #8, I was taught at school that if you have to change lines in an equation you need to say what are you doing next and follow it to the next line.
Like in this case:
1+1+1+1+1+
+1+1+1+1+1+
1+1x0+1
If it would be written like this then 12 is the correct answer.
At least from what I was taught
That would double the plus signs. Now for plus signs this doesn't pose problems, but it would if you do this with minus signs.
4-
-2
is actually 6, because it says 4 - -2.
If you continue a line, just write the operator at the end of the first line:
1+1+1+1+1+
1+1+1+1+1+
1+1*0+1
or, preferably, at the start of the next line:
1+1+1+1+1
+1+1+1+1+1
+1+1*0+1
The last is prefered because here too, if the line were broken at a subtraction, then the minus sign would be close to the subtracted number.
So here is my thought for #5....
if you divide any number by 2 then it means that what we will be getting is the half of that number....
For example if you divide 10 by 2 then its the half of 10 i.e 5.
But i guess they rather divided it by 1/2 thinking that it would give half of 50% but they actually had to multiply it by 1/2.
that's where they got it wrong... what do y'all think
Tom doing %50/2=%25 is utter nonsense
%50= 50/100 which is 1/2
1/2 divided by 2 is= 1
RE: order of operations
The order we have exists because algebra is easier to do if you don't need brackets everywhere to make it clear 3X+5 means (3×X)+5 rather than the unintuitive 3×(X+5).
Their teaching as a rule to kids who don't understand the reasoning is IMO part of the problem with the whole education there. No one writes such problems with numbers for anyone over 8 or 9 because by that time you're getting introduced to the basics of algebra and it stops being an issue.
6:00 when i was a wee little lad in school they taught me PEMDAS or BEMDAS (their quite similar) parenthesis exponents multiplication division addition subtraction.
love how number three frogets proper grammar tho
That half of 2 + 2 got me hangry for a while 😅
Problem number 3 is absolute trash the way he said it meant that he wanted you to mess up