People often send me puzzles they see on social media. They love these videos because learning how to solve them helps builds their confidence in math. What can hurt their confidence, and turn people away from learning math, is seeing negative comments about things they enjoy, or being told something is easy. Everyone agrees negativity is hurting math education, so we need to be extra positive to cancel them out!
MindYourDecisions I completely agree. This is actually the first puzzle on this channel that I was able to solve on my own without waiting for you to explain. I wouldn't say it was too simple. It was enough to challenge me and get me thinking for a minute or two, yet it wasn't so hard I couldn't solve it myself. This is the exact purpose of puzzles like these. To stimulate the brain and to get you thinking. It is very encouraging when you're able to solve one of these on your own.
I like these puzzles, they give me ideas to design my own. Not just the "math" part, the "use colored circles to represent numbers" part as well. A easy change is to change the "answer" to three white circles.
Given the history of your questions, where the "plus" and "equals" signs do not have their original definitions; and given that there is no specific set of rules other than establishing a "pattern"... You could say that red is 3.. and the answer is only adding up the balls in the columns... while the number on the ball is irrelevant.... so gray and blue can be any digit other than 3; and other than each other.. This still provides the possible solutions to a vague question. in fact, they could all be 3's, because it is not stated that different colors represent different digits; it was only assumed. They could all be 3, meaning 3:00 o'clock; while the different colors are days of the week... and red being tuesday- the 3rd day of the week..... and the answer being red just represents 3 days of each month. in fact, its my pay schedule... Check please. This is the problem with having real symbols that do not adhere to their correct definitions in your past questions; it starts to not be math anymore.
I just quickly used process of elimination on the red and found only 5 worked. From there it was the same process for blue and silver. Only one number added 3 times had a 5 as the last digit, which was 8. Then a 2 was carried over from the 3 eights so the final digit had to be a 1. It was much quicker than any formulaic method, at least for me it was
What I did was much simpler. I started with the final sum, a 3-digit number where every digit is the same. There are only ten possibilities, and we can quickly rule out 000, 111, 222, 333, 666, and 999. Among those remaining, only 555 ends with the same digit after being divided by 3.
Every digit d can be represented (a,b), where a = d mod 2, and b = d mod 5. Then, from the problem statement, we get 3x = x (mod 10), meaning 2x = 0 (mod 10), meaning x is a zero divisor. Since 2 = (0,2), then x must equal (y, 0), because (0,2)*(y,0) = (0*y, 2*0) = (0,0) = 0. There are two possibilities for y: y = 0, or y = 1. Using the Chinese remainder theorem, we get that either x = 0 or 5 (mod 10). Due to requiring each digit be different, then it must be that x = 5 (mod 10), and therefore, x = 555/3 = 185.
Making this comment before watching the video to see if I used the same method you did. Red + Red + Red must have Red as ones. The only single digits where 3x has x as the ones is 0 and 5. Since RRR is the overall solution, we can eliminate 0. Therefore, Red is 5. The total Sum is 555, and 555 / 3 = 185. So Blue is 1 and Grey is 8.
a=1 b=8 c=5 This is the only one I've ever gotten right on this channel. I just used basic logic to find out the value of "c" can only possibly be 5. From there, I divided 555 by 3 and got 185. As simple as this is, I feel so smart and accomplished after figuring it out.
Yes. One of the very few problems that I could solve on this channel. At first I was very happy to be able to solve it. But when I looked at the comments, I realised that I’m just a normal person after all. But, I Still feel proud about myself for being able to solve it! LOL
E. Lau Don't sell yourself too short; the audience on this channel is not your average TH-camr, and anything shy of a nasty calculus problem is likely to be followed by dozens of comments complaining about how easy the question was.
This was a very interesting puzzle! I hope everyone felt satisfied when they solved it, especially the younger people who have not t taken any algebra classes. It’s surprising how little actual math is needed to solve this; just logic.
185? The red must be 5 or 0, it can't be 000 -> red's 5 The white must be one less than a multiple of 5 and it must be divisible by 3, so 24 -> white's 8. The blue must be two less than a multiple of 5 and it must be divisible by 3, so 3 -> blue's 1 Edit: Didn't even take a minute but apparently I made it a lot more convoluted than I had to
After the realization that you have 555 in the end, you could just divide by three, because 3abc=555 Edit: apparently, it is the method used by Presh to solve this "mastemind" puzzle
Yeah, that’s kind of how I solved it too. 5 was the only one that made sense for red then there was a remainder of 1 so you needed 3 numbers that added together gave you something with a 4 in the ones column. 8 worked because it gave you 24. Then you had a remainder of 2 and since you know red is 5 you subtract the 2 and it left you with three meaning that the blue had to be 1.
Funny, I ignored the fact that I could divide the final number by three and continued to solve for the 10's place digit and 100's place digit. I guess tunnel vision happens sometimes.
Same here - which meant I'd found the solution before Presh finished saying to pause the video and continue once you'd solved it. Thinking about other possible solution paths to find the shorter one would have taken longer...
I was looking at the thumbnail and solved it pretty fast. The way I did it is that since the answer was all red I asked my self what three numbers add up to the last digit being the same number being added and got 5. Since the answer is 555 and 5x3=15, I subtracted 15 from 555 and was left with 540. I then divided 540 by 3 and got 180. Since I subtracted 15 from the total I added 5 to 180 and got 185.
Everyone in the comments are always bragging and complaining about getting the answer in 10 seconds or it being too easy, but can no one appreciate the effort Presh is putting into actually making the videos, rather than complaining it’s too easy?
I do appreciate the effort, and I never suggest that Presh making a video on an easy problem is bad or unworthy. And I never rag on people who barely solve it. But there's a whole nother class of problems that Presh posts sometimes that I find much more interesting, and not just for the challenge.
I am doing MSc and this is totally opposite to the mathematics I have! *Please post something for us as well because I know you are highly qualified for that.*
abc + abc + abc = ccc so the units digits of c*3 = c just quickly go through in your head which numbers work 0 * 3 = 0 yes 1 * 3 = 3 no 2 * 3 = 6 no 3 * 3 = 9 no 4 * 3 = 12 no 5 * 3 = 15 yes 6 * 3 = 18 no 7 * 3 = 21 no 8 * 3 = 24 no 9 * 3 = 27 no so c is either 0 or 5, but since 000 is not a valid answer (by common sense), ccc = 555 555/3 = 185 a = 1 b = 8 c = 5
Just to add a little challenge: Presh never said what base this puzzle was in. I never like to assume decimal. Let's look at a few other bases. Base 2: Not enough digits for the colors. Base 3: Multiplying by 3 gives all zeroes, already ruled out. Base 4: Red*3 = red (mod 4), so red = 2. This gives us 222 (base 4) / 3, which is 42 / 3 (decimal), which gives 032 (base 4) Base 5: red*3 = red (mod 5) -> the empty set. No solution is possible. More generally, for a value to satisfy red*3=red (mod N), red*2 must divide N. This is only possible for even N, and red always = N/2. Base 6: red * 3 = red (mod 6) -> red = 3, which gives 129 / 3, which is 43. But this doesn't satisfy: Presh tells us that each color corresponds to a unique digit, but 43 = 111 (base 6). Base 8: red = 4, so it's 444 (base 8) or 292 (decimal). This is not divisible by 3. So for bases up to 10, there are only two solutions, 032 (base 4) and 185 (decimal).
I think about this puzzle for 5 minutes. But i could not found any answer. Then i realize that i can make computer program to find this answer. So then i make a C++ program. And its answer me that the number is 185. Thank u sir for such an amazing puzzle.
The only values for C are 0, 5, and 6 because only those multiplied by three end in the original digit. 0 cannot be the answer (QED), so C is either 5 or 6 and the carry from the 1s is 1. A must be 1 because if A = 2, then B = (C-1)/3 which cannot be an integer. A>=3 is a four digit number. If C = 6, the carry from the tens must be 3, but the largest carry of three digits is 2 (9+9+9), so C = 5. The carry from the tens must be 2, and the only 3B+1 that ends in 5 is 8. Ergo. 185+185+185=555.
I enjoyed many videos and thus subscribed to the channel. Two recent videos just irritated me. I get it, the channel is meant to popularize Maths to all audiences. Just please avoid having these misleading titles such as "only mastermind/genius can solve this" or "95 % failed" on viral social media problems...
I think the reference to "mastermind" is to the game en.wikipedia.org/wiki/Mastermind_(board_game) - not particularly misleading and in fact I found it a nice joke.
For a short solution, we have 3c = c mod 10. Therefore c can't have an inverse mod 10, so c must be a zero divisor and must be either 2 or 5. 2*3=6 which is not equal to 2 mod 10. 5*3 = 5 mod 10, so c=5. Then divide 555 by 3 to get a and b.
People here are complaining how easy it is! But the funny thing is i couldn't even solve it even after watching this video. I found most of the sums of this channel easy except this one. I mean how do you know that C can only be 5.? Rest i understood. Plz help
Wow I'm a mastermind!! Good to know.Point to self: Never look at the comments after you've actually solved a question on this channel. Most of it is filled with people exclaiming how easy the problem was which pretty much ruins the feeling of being super smart you get after solving the question.
Second way can be just to try each 3 same digit number and divide it by 3. Bruteforce but in this case works as well ;) Also since we know we have same digit under the line we can assume it needs to be a digit that multiplied 3x will give same number in last place and probably some rest to carry to the next row. So in this case 5 seems to be natural.
Honestly I think you made this too complicated. All you had to so was substitute 111,222, etc into the bottom and divide by 3 to find which one gave a 3 digit number with 3 different digits. Thats how I did it and it took like 30 seconds.
(100B + 10W + R)3 = 100R + 10R + R. The only number that has its own value in the ones digit when multiplied by 3, is 5. Substituting 5 into the above equation gives you 10B + W = 18. The only 2 numbers that work are 1 and 8.
You mean you don't already know that 111 = 3*37? -> 555/3 = 5*37 = 10* (37/2) = 10*18.5 = 185... Actually, I found 185 by finding c=5, -> b=4/3(mod 10) = 8 -> a=3/3=1 because that was faster than taking the time to think about what would be a shorter method of solution after finding c...
This seemed a little easier than the title would lead you to believe. There are only two digits which can be added three times and get the same value - 0 and 5. Since the leftmost digit can't be zero, the red is 5 by process of elimination. Then just divide 555 by 3 to get the correct answer for the blue and white digits.
185? I didn’t watch the answers yet. Edit: yess! This is actually a very easy question. I’ll explain it in my 13 year old mind: So I know the answer has the same numbers for each digit. So, 000,111,222,333...999 could be all possible answers. Next, I took out all the numbers that when divided by 3, the make the same digits. For example: 333 divided by 3 is 111. This breaks the rule, because blue circle, grey circle and red circle must have different digits. So, now we’re left with 111,222,444,555,777,888. Now, I took turns dividing each by 3 until I got to 555. 555 divided by 3 makes 185. Since the last digit must be the same numbers as the answer, it must be 185. No other triple digits ended with the same number. :)
This is actually very easy. First you need a number that when trippled produces a sum who's last digit is equal to that number. The only possible number is five, which produces 15. Since 1 gets carried over to the next column, we need a number that when trippled the last digit is equal to 4, the only possible number is 8, which sums to 24, and 2 is carried over. This means that the blue collumn must sum to 3, and 1 is the only number which satisfies it. So blue is 1, white is 8, and red is 5.
Really lmao I don’t usually solve your stuff but this was easy, the red must be 5 because it’s the only number when multiplied by 3 (besides 0) to give it’s self, hence the answer is 555, and 555/3 is 185
Before watching the solution: jotted down 1 thru 9 in one column and what they equal when multiplied times 3 in the next. Whichever the red circle could be any line where the 1s column matched. This was 5 and 15. Filled in 5s for red and carried the 1. For white, the 1s digit had to be a 4 since the 1 carried. That made the whites 8, carrying the 2, and the only solution for blue then had to be 1. However, once we work out red is 5, we can also just divide 555 by 3 to get the same solution. In the same vein, we could just divide each of 111, 222, 333, 444, 555, 666, 777, 888, and 999 by 3 and see if we get any solutions where the 1s column is the same digit as the original number, getting 555 again.
Could maths be universal because it is based on a universal geometrical process: (E=ˠM˳C²)∞ with energy ∆E equals mass ∆M linked to the Lorentz contraction ˠ of space and time. The Lorentz contraction ˠ represents the time dilation of Einstein’s Theory of Relativity. We have energy ∆E slowing the rate that time ∆t flows as a universal process of energy exchange or continuous creation. Mass will increase relative to this process with gravity being a secondary force to the electromagnetic force. The c² represents the speed of light c radiating out in a sphere 4π of EMR from its radius forming a square c² of probability. We have to square the probability of the wave-function Ψ because the area of the sphere is equal to the square of the radius of the sphere multiplied by 4π. This simple geometrical process forms the probability and uncertainty of everyday life and at the smallest scale of the process is represented mathematically by Heisenberg’s Uncertainty Principle ∆×∆pᵪ≥h/4π. In such a theory we have an emergent future unfolding photon by photon ∆E = hf with the movement of charge and flow of EM fields. This gives us a geometrical reason for positive and negative charge with a concaved inner surface for negative charge and a convexed outer surface for positive charge. The brackets in the equation (E=ˠM˳C²)∞ represent a dynamic boundary condition of an individual reference frame with an Arrow of Time or time line for each frame of reference. The infinity ∞ symbol represents an infinite number of dynamic interactive reference frames that are continuously coming in and out of existence. At the smallest scale the Planck constant ħ=h/2π is a constant of action in the dynamic geometrical process that we see and feel as the passage of time.
My method may be a bit convoluted but it worked. The original problem can be represented as 3(100a + 10b + c) = 100c + 10c + c = 111c = 3(37c) 100a + 10b + c = 37c 100a + 10b = 36c 10(10a + b) = 36c ==> 36c is a multiple of 10 ==> c = 5 10(10a + b) = 180 10a + b = 18 a = 1, b = 8
*5* is the only digit that when multiplied by 3 results in a number that ends in 5. So, red is 5. *8* is the only digit that when multiplied by 3 results in a number that ends in 4, So, grey is 8. *1* is the only digit that when multiplied by 3 results in a 3. So, blue is 1. P.S. We need the sum of the second column to end in a 4 because we carried the one from the first column (because 5x3=15). And we need a 3 in the last column because we carried the 2 (because 8x3+1=25).
Zero K the ones digit has to be itself and once it is multiplied by 3. In this case, only 0 and 5 work. And obviously we cant accept 0 because this makes others dots have to be 0
I just wrote down the multiplication table for 3: 0 · 3 = 0 1 · 3 = 3 2 · 3 = 6 3 · 3 = 9 4 · 3 = 12 5 · 3 = 15 6 · 3 = 18 7 · 3 = 21 8 · 3 = 24 9 · 3 = 27 I then started from units (red circle), as did you. I checked where the units of the product is the same as the multiplier, and its in the cases of 0 and 5. I noticed the same problem with zero as you did, so the red circle must me 5. One is carried to the grey circles.
I then proceeded to the grey circle, which had one carried from the red circles. I checked when the units of the product is one less than the 5. 8 · 3 = 24, and 1 + 24 = 25, so that's the only number that fits in there. 2 is carried to the blue circles. And now I just have 2 + 3 · BLUE = 5, which gives me the number 1 to the blue circles.
185 Simple puzzle, solved in under 1 minute: Red must be a number that when multiplied by 3 has itself as the last digit. This means red must either be 0 or 5. If red = 0, then both grey and blue would have to equal 3.33333... That means red is 5, and 3x5 = 15. 3 x grey must have a final digit of 4, so that when it is added to the carried 1, that digit = 5. That means grey = 8, and 3x8=24. Blue must fulfill 2 requirement to meet the puzzle conditions. When multiplied by 3, the product must be a single digit, and that product must also equal 3, so when it's added to the carried 2, that sum equals 5. Therefore, blue = 1.
Two comments: 1. I saw the gray circles as white circles that were lit from above, but yes, they are actually gray and who wants to relive the blue/white dress again, and 2. Presh mentioned said only a “mastermind” can solve the problem because the puzzle looks like the Mastermind board game not because it is difficult so everyone can now get off their high horse.
Had it immediately. The red ones can only be 0 or 5 (as multiplying each number between 0 and 9 gives a result that ends in something different, except 0 and 5). However, no three same numbers (other than 000) added give 000. But 000 would be equal to 000 so all of the marbles would need to be red. So it must be 555. Which means the answer must be xy5 + xy5 + xy5 = 555. Which is easily solved by 555 divided by 3. So 185 is the solution.
So, in part due to your past videos showing me a notation for writing the abstract: I see 300a+30b+3c-111c=0; the ones digit is ONLY influenced by c, and the only puzzle is c itself, and since 111-3=108, the only choices for c are 0 and 5, and with the three digits being unique the conclusion is c=5 and [abc]=555/3=185
300a+30b+3c=111c => 300a+30b=108c => 50a+5b=18c => 5(10a+b)=18c Since 18 is not a multiple of 5, we must have c=0 or c=5. c cannot be 0 because this would imply a=b=c=0 and we assumed the digits are different. Thus, c=5 which leads us to 10a+b=18. If a>1 then 10a+b>18 which gives us that a=0 or a=1. If a=0 then b=18 which is impossible since b is a digit. Thus a=1. Now, we get 10+b=18 and therefore, b=8. Hence, the number is 185!
The only single digit (excluding 0), if added by itself 3 times or multiplied by 3 that results to have same digit in ones column is 5. Therefore, Red is equal to 5. Thus, this would have a total of 555 When divided by 3 would result to 185. Answer: Blue=1, Gray=8, Red=5.
RED: 0 or 5, not 0, 5. 15 Carry the 1. WHITE: must end with 4, so 8. 24+1 carry the 2. BLUE: must end with 3 and total less than 8, so 1. 3+2. 1, 8, 5.
I solved it a bit different. ~Noticed that each colour was a single digit multiplication of 3 higher than 0 (as x+y+0≠0) and wrote them down. ~ Next, I looked at the red and looked at which solutions ended in the multiplier, isolating 5, meaning Red=5 ~Third, I looked up which ones ended in the solution to 5 - the careied number for the next two colours.
It can b solved using algebra also. Let no. be abc. Value of no. = 100a+10b+c. Result is 100c+10c+c i.e. 111c. Now 3(100a+10b+c) = 111c or 100a+10b = 36c. Minm value of LHS is 110. So, find next multiple of 36 divisible by 10. Which means RHS=180 or 360. Taking RHS = 180 i.e c=5. We get a=1 and b=8. Hence no. is 185. 185x3 = 555
The sum of the three values, each with a red circle as the last digit, gives a last digit that is also represented by a red circle, and so the red circle can only be 5. And so we already know that the sum of the three values is 555, and so the value formed by the blue circle, white circle and red circle is (555 / 3 =) 185, and so blue circle = 1 and white circle = 8.
I may have two solutions For 3x's last number to be equal to x and x>10, 5 and 0 are the only numbers that follow these rules (3(5)=15 and 3(0)=0). This leads to two solutions 1) 5 is indivisible by 3 (5/3=1.666…), so it must be that 15-1 is divisible by 3, but 14 isn't divisible by 3, making this solution faulty 2) No matter how many times you add 0 to itself, nothing happens, so R=0, W=0 and B=0 Easy
1 8 5. Trial and error. The only number other than 0 that works for red is 5, I assumed all numbers were single digits. If the red is 5, then you will be carrying a 1 to the "10's column". Again, with trial and error I substituted the various numbers and came up with 8, which when you add the carried 1, makes 25. Carrying the 2 and needing to end in a 5 made it easy, as 1 works. I am sure that Presh will have a far more elegant solution. Now to watch.
Without a pad of paper, I believe that I have solved it. Verified with my calculator. The solution is 185 time 3. Approach (for xyz): For red, z times 3 equals z, z must be 5 or 0. And z is obviously not 0. For blue, x times 3 plus 0, 1 or 2, equals 5, x must be 1 (plus 2). For grey, y times 3, plus 1 (i.e., 3 times 8 plus 1 equals 25) equals 5. y must be 8. For xyz, must be 185, QED (I hope). Should I mention my age of 76, my 3 degrees, or my numerous strokes (i.e., dead brain cells)? Very entertaining. Thank you for your efforts. May you and yours stay well and prosper. Terry
The last digit in each number is either 5 or 0, however, if the colors equal distinct digits, this summation cannot equal 000, so the total is 555. Dividing by 3, we get our magic number of 185.
Alexa has an incontrovertible proof in court that her boyfriend was murdered by her sister. The judge declares, “This is the strangest case I’ve ever seen. Though it’s a cut-and-dried case, this woman cannot be punished.” How can this possibly be?
Blue is 1, white is 8 and red is 5. 5 is the only digit that tripled give something ending with itself. So, 5 and carry 1. The second column must end with a 4 + 1 = 5. Only 8 x 3 ends with a 4. So, 24 +1 = 25. Put a 5 and carry 2. Lastly, a digit time 3 must be 3 without any carry. So, 1 is the only possibility. 185
Assuming every colour is a digit then red is 5 because that's the only digit that leaves unit 5 when multiplied by 3 which gives 15, so the sum should be 555. Then with the white you do 1 (from 15) +3x=5y and whenever you get a whole number you know that y=8 which gives 25, then you do 2+3x=5 and get x=1.
Very easy. Let ABC + ABC + ABC = CCC. We are adding three C's and the units digit of our sum is also C. We can easily check that only one digit can do this and that is C = 5. (Note that 1+1+1 has unit digit 3, 2+2+2 has unit digit 6, and so on). Thus, AB5 + AB5 + AB5 = 555. If A => 2, then our sum on the left yields a number > 600 so that is impossible. Thus, A = 1. Then 1B5 + 1B5 + 1B5 = 555. Adding the units digits yields 15 so our sum has a unit digit of 5 and the 1 carries over to the tens digit. Then 1 + B + B + B must have a unit digit of 5. Note that the hundred's digits is 1 + 1 + 1 but the sum is showing a 5. Thus, we need a 2 to carry over from the tens digit. That occurs when 1 + B + B + B = 25. Thus, B = 8. Therefore, our solution is 185. Note that 185 + 185 + 185 = 185 * 3 = 555
This is trivial. 1) red added together 3 times is red. So R+R+R=X*10+R. So R+R=X*10. R is a single digit so we can't have X>=2. So X=1 leaving us with R+R=10. (Or R=0 bu this requires othr digits to be 0 as well and they should be different.) So R=5 2) Gray digits in the middle give us G+G+G+1=X*10 + 5. Substract 1 from both sides and get G+G+=X*10+4. Here X*10+4 needs to be a multiple of 3. And a criteria for any number being a multiple of 3 is having its digits to add up to a multiple of 3. So X+4=6+3*Y. Or X=2+3*Y. However G being a single digit requires 0
This is so easy, figure out what each digit times 3 is that ends in the same digit. only option is 5 = number is 555 - 15 (because of 5*5) = 540, figure out what digit * 3 ends on 4 = 8 = 24 = 240 because of the 0 540 - 240 = 300, 1*3 = 3 = 185
It took me two minutes , if not less (doesn't require a mastermind) 185 x 3 =555. first what digit when multiplied by 3 gives the same digit and that is 5(as multiplication is the same as addition), so you will have 1 left to add to the other digit, then what digit when multiplied by 3 would give 4 since you know will need to add 1 to that digit and that of course is 8 and 3 times 8 is 24, then what digit when multiplied by 3 would leave 3 since you need to add to the 2 from the 24 to it and that of course is 1, so the answer is 185, the blue =1 gray = 8 and red =5
We know that there are only 9 possible combinations for the total, 111, 222,... 999. We can skip the 000 as this would result in all the digits being the same. Since all the numbers are the same, all that we need to do is to divide the total by 3. 111 / 3 = 037 222 / 3 = 074 ... 555 / 3 = 185
I just said that the only possible last number would be 5, because if it were 0, then the sum is 000, and 5 is the only other number that when added to itself 3 times, the resulting sum is 15, and it’s ones digit is 5, so it works, then I thought about what numbers resulted in a ones digit of 4 when added to itself 3 times, and I came up with 8, 3*8=24, and then the last digit is just n+2=5. The answer I got is 185
The red is 5. It is the only single digit # that if multiplied by 3 the product is still ending with 5. So since the red is 5, therefore the 3 digit sum is 555. Just divide 555 by 3 and you will get 185.
I did it in a very, very, VERY inefficient way. My first step, for C, was actually ok: 3C must end in C, and the only nonzero digit that meets that is 5, coming to 15. After that is when I did things terribly inefficiently. I wrote the 555, but instead of dividing by 3, I said "Well, 3A must be either 5 or less than 5 if there is any carry over. Only A = 1 does that." Once that was set up, I solved for B using decimal expansion: 300 + 30B + 15 = 555 means B = 8. I have no idea why I did it that roundabout way... but it worked, I guess.
The three fives were easy, I just kinda jumped to 15 because it wasn't likely any number times 3 would have itself as the last digit except 5. I would've felt more wound in 'proving' it if I had come up with those equations though. The 8 and 1 I just used the process of elimination knowing the tens place of each sum would get carried over, and that they'd always result in a 5. Dividing 555 by 3 would've been the better route.
There is a famous puzzle that I just realized has a problem with. There is a band with 7 people in it, yet they keep losing their insterments. Their manager is sick and tired of it. He tells them that there instruments are each in the next room, inside 7 labeled boxes, the catch is that no instrument is in a box labeled with it's own name. Each person only has 3 chances to find their own insterment. If less than half of them find their instruments in 3 tries then he will kill them all. The solution we are given is that each person looks in the box with their instrument, the drummer looks in the box with the drums and finds the base, so he looks in the box with the base and finds the drums. Then the keyboard player opens the keyboard box to find a microphone, then opens the microphone box and finds a trombone, then opens the trombone box to find the tambourine. The problem comes when the base player comes in and opens the base box to find it empty. He knows that it either had the drums or the keyboard. If he opens the drums box then he finds the base and wins, yet if he opens the keyboard box then he finds the microphone and can't find his base. Next the singer comes looking for her microphone, opens that box and trombone, opens the trombone box and finds the trombone. The next time someone comes to an empty box, was this the box that had the drums, the keyboard or the base?
It has to be a 3 digit number where all three digits are the same number, and when it's divided by three it equals a whole number ending with the original number. So just divide them by 3 starting with 444, because 333 divided by 3 is 111, and that and 222 divided by 3 are two digit numbers. You only have to do two calculations if you're working upward from 444 before you get your answer
Solutions I found: Base 9++ (decimal): 3 × 185 = 555 Base F++ (hexadecimal): 3 × 2D8 = 888 Base L++: 3 × 3IB = BBB Base R++: 3 × 4NE = EEE I am starting to see a pattern. There seems to be a solution in every base A+6n (every sixth base starting from decimal).
It was easy. 3 R = R + Carry. Carry can be 0/10/30. Hence 2R = 0 or 10 or 20 .. and R = 0, 5, or 10. R cannot be 10, and it cannot be 0 (unless everything is 0 as the sum would be 000). If R is 5, the answer is 555. Divide by 3 and we get 185.
This is by far the easiest puzzle that I had seen in this channel. I don't understand why its title says that only a masternind can solve it. My approach is this: take 000, 111, 222... through 999 and divide each number by 3 and only 555 satisfy the conditions. It took me 30 seconds to make myself a mastermind.
The book "Sideways Arithmetic from Wayside School" has a good number of problems like this, where words are added together, and you have to deduce which digit each letter represents. For example, egg + egg = page, or seed + iced = spice.
Most of the problems on this channel are pretty tough, but this was really really easy. 185. you just figure out the last digit by doing 3 times every number between 1 and 9 and checking equivalence mod 10, it's 3*5=15. Then divide 555 by 3. By making it so easy to get the sum, and having the summed numbers be the same, the problem becomes trivial.
The only numbers that added to themselves three times result in a number that ends in themselves are 0 and 5. 000 is not a legitimate sum, so red is 5. From there its a simple matter of dividing 555 by 3. Blue = 1 Gray = 8 Red = 5
Alternative route: our goal is to solve for either x or y. 111*x = 3 * y, 37 x = y notice that we need 7x mod 10 = x. Only 1 digit satisfies this property so x must be 5, and now we can solve for y.
Mmm, I did it in my head in about 15sec, but differently. 3u has u in its digits/units place, so can only be 0 or 5, and 000 won't work, so red must be 5, for 555. After carrying the 1 (15), 3t must have 4 in the tens place, 04 and 14 don't fit, so 24, and white must be 8. Same, carry the 2 (24), so 3h must be 3, so blue is 1. Thus 185. Yeah, dividing by 3 would work, but I like going through the steps.
3 * c = c means that they must end with same digit and so as a result to do this with same number is only solution of c = 5 That means the total is 555 and since all the numbers are same, 3x = 555 == > x = 185 so a...b....c = 185 which means that the values are a = 1, b = 8 and c = 5
People often send me puzzles they see on social media. They love these videos because learning how to solve them helps builds their confidence in math. What can hurt their confidence, and turn people away from learning math, is seeing negative comments about things they enjoy, or being told something is easy. Everyone agrees negativity is hurting math education, so we need to be extra positive to cancel them out!
MindYourDecisions I completely agree. This is actually the first puzzle on this channel that I was able to solve on my own without waiting for you to explain. I wouldn't say it was too simple. It was enough to challenge me and get me thinking for a minute or two, yet it wasn't so hard I couldn't solve it myself. This is the exact purpose of puzzles like these. To stimulate the brain and to get you thinking. It is very encouraging when you're able to solve one of these on your own.
Yes, this is to learn and have fun, not to brag or be negative. Cheers.
I like these puzzles, they give me ideas to design my own. Not just the "math" part, the "use colored circles to represent numbers" part as well.
A easy change is to change the "answer" to three white circles.
4 out of 3 people on social media don't like math.
Given the history of your questions, where the "plus" and "equals" signs do not have their original definitions; and given that there is no specific set of rules other than establishing a "pattern"...
You could say that red is 3.. and the answer is only adding up the balls in the columns... while the number on the ball is irrelevant.... so gray and blue can be any digit other than 3; and other than each other..
This still provides the possible solutions to a vague question.
in fact, they could all be 3's, because it is not stated that different colors represent different digits; it was only assumed.
They could all be 3, meaning 3:00 o'clock; while the different colors are days of the week... and red being tuesday- the 3rd day of the week..... and the answer being red just represents 3 days of each month.
in fact, its my pay schedule... Check please.
This is the problem with having real symbols that do not adhere to their correct definitions in your past questions; it starts to not be math anymore.
TH-cam has confirmed I am a mastermind. I'm putting that on my resume.
I just quickly used process of elimination on the red and found only 5 worked. From there it was the same process for blue and silver. Only one number added 3 times had a 5 as the last digit, which was 8. Then a 2 was carried over from the 3 eights so the final digit had to be a 1. It was much quicker than any formulaic method, at least for me it was
Did that same thing too, way easier than highschool-ahh math
Me too
Me too
Did the same to start, but once you solve red you can just divide 555 by 3 to get the other 2 digits.
same here
What I did was much simpler. I started with the final sum, a 3-digit number where every digit is the same. There are only ten possibilities, and we can quickly rule out 000, 111, 222, 333, 666, and 999. Among those remaining, only 555 ends with the same digit after being divided by 3.
Only A Mastermind Can Divide 555 By 3.
Wolfram Stahl no everyone can If he/she knows divisibilty rule of 3
Every digit d can be represented (a,b), where a = d mod 2, and b = d mod 5. Then, from the problem statement, we get 3x = x (mod 10), meaning 2x = 0 (mod 10), meaning x is a zero divisor. Since 2 = (0,2), then x must equal (y, 0), because (0,2)*(y,0) = (0*y, 2*0) = (0,0) = 0. There are two possibilities for y: y = 0, or y = 1. Using the Chinese remainder theorem, we get that either x = 0 or 5 (mod 10). Due to requiring each digit be different, then it must be that x = 5 (mod 10), and therefore, x = 555/3 = 185.
manjeet, I think the OP's point was that once you realize that red is 5, the rest of the solution is perhaps too obvious.
Tehom you could also just brute force it in a fraction of the time by doing 111/3, 222/3.... 999/3 piece of cake
literally solved this in 20 seconds, and ill admit i'm far from a mastermind
Solved from the thumnail! Much fun :-)
Hey X are you here too?
here we see a wild xisumavoid spotted doing recreational maths...
a common past time for this species.
Omg the derp's here for maths!
literaly as easy as breathing...
Solved in 2 mins from thumbnail
185
Making this comment before watching the video to see if I used the same method you did. Red + Red + Red must have Red as ones. The only single digits where 3x has x as the ones is 0 and 5. Since RRR is the overall solution, we can eliminate 0. Therefore, Red is 5. The total Sum is 555, and 555 / 3 = 185. So Blue is 1 and Grey is 8.
*"There are so many masterminds in the world that now we need to search for the common people."*
a=1
b=8
c=5
This is the only one I've ever gotten right on this channel. I just used basic logic to find out the value of "c" can only possibly be 5. From there, I divided 555 by 3 and got 185. As simple as this is, I feel so smart and accomplished after figuring it out.
Thomas Steward Nice job! Solving math problems, even simple ones, can be very satisfying.
ToadStar100 thank you. It was very satisfying.
Yes. One of the very few problems that I could solve on this channel. At first I was very happy to be able to solve it. But when I looked at the comments, I realised that I’m just a normal person after all.
But, I Still feel proud about myself for being able to solve it! LOL
E. Lau Don't sell yourself too short; the audience on this channel is not your average TH-camr, and anything shy of a nasty calculus problem is likely to be followed by dozens of comments complaining about how easy the question was.
Jason Patterson Agree, everyone can learn something from these "easy" problems.
This was a very interesting puzzle! I hope everyone felt satisfied when they solved it, especially the younger people who have not t taken any algebra classes. It’s surprising how little actual math is needed to solve this; just logic.
185?
The red must be 5 or 0, it can't be 000 -> red's 5
The white must be one less than a multiple of 5 and it must be divisible by 3, so 24 -> white's 8.
The blue must be two less than a multiple of 5 and it must be divisible by 3, so 3 -> blue's 1
Edit: Didn't even take a minute but apparently I made it a lot more convoluted than I had to
After the realization that you have 555 in the end, you could just divide by three, because 3abc=555
Edit: apparently, it is the method used by Presh to solve this "mastemind" puzzle
Or if you already know that red's 5, you know the final answer (red red red) will be 555 and you can divide that by 3
Yeah, that’s kind of how I solved it too. 5 was the only one that made sense for red then there was a remainder of 1 so you needed 3 numbers that added together gave you something with a 4 in the ones column. 8 worked because it gave you 24. Then you had a remainder of 2 and since you know red is 5 you subtract the 2 and it left you with three meaning that the blue had to be 1.
Or you could just divide 555 by 3
Yea once I got red was 5 I just divided 555 by 3
It is 185 and this is easy. It is a good mind teaser for like 30 seconds.
Presh, you need to get back to the really difficult stuff.
yeah i solved it in literally 15 seconds
Site needs to be marketable for everyone, not just the know-it-all. Some easy, some difficult.
FlagDUDE08 yes, but he should make two separate channels.
FlagDUDE08 my thoughts exactly.
Making two separate channels dilutes the fan-base, thereby lower ratings, and lower "monetization" (assuming this hasn't been hit by Adpocalypse).
Funny, I ignored the fact that I could divide the final number by three and continued to solve for the 10's place digit and 100's place digit. I guess tunnel vision happens sometimes.
me too... still easy though
Samee but didn't take me more than 2 minutes
Same here - which meant I'd found the solution before Presh finished saying to pause the video and continue once you'd solved it. Thinking about other possible solution paths to find the shorter one would have taken longer...
Boris Pelgrum you took that long?
I did the same at first, before realising the much quicker solution!
I was looking at the thumbnail and solved it pretty fast. The way I did it is that since the answer was all red I asked my self what three numbers add up to the last digit being the same number being added and got 5. Since the answer is 555 and 5x3=15, I subtracted 15 from 555 and was left with 540. I then divided 540 by 3 and got 180. Since I subtracted 15 from the total I added 5 to 180 and got 185.
Scooby Roo yeah me 2
So you did it the hard way? :-)
(Instead of just dividing 555 by three.)
Scooby Roo Sup
This channel always has me feeling like a mastermind. Keep posting the easy questions!!!
"Only a Mastermind Can Solve This"
Meanwhile 13yr old me solving it by looking at the thumbnail:
Not only did I solve in less than a minute, but I used the same process as Presh! Today is a good day!
Same!
Everyone in the comments are always bragging and complaining about getting the answer in 10 seconds or it being too easy, but can no one appreciate the effort Presh is putting into actually making the videos, rather than complaining it’s too easy?
Lux Legend good point but then again he said mastermind.
I do appreciate the effort, and I never suggest that Presh making a video on an easy problem is bad or unworthy. And I never rag on people who barely solve it.
But there's a whole nother class of problems that Presh posts sometimes that I find much more interesting, and not just for the challenge.
they claim they can all easily solve it but they can't actually formulate the proper mathematical equations to solve it.
I am doing MSc and this is totally opposite to the mathematics I have! *Please post something for us as well because I know you are highly qualified for that.*
3*(100*B + 10*W + R) = R*100 + R*10 + R
300B + 30W + 3R = 111R
EQ1 => 300B + 30W - 108R = 0
3R = R + 10*C1
C1 = 0.2R
3W + C1 = R + 10*C2
3W + (0.2R) = R + 10*C2
C2 = (3W - 0.8R)*0.1
C2 = 0.3W - 0.08R
3B + C2 = R
3B + (0.3W - 0.08R) - R = 0
EQ2 => 3B + 0.3W - 1.08R = 0
EQ3 => (3R)%10 = R
R = 5
3B + 0.3W - 1.08*5 = 0
3B + 0.3W - 5.4 = 0
W = (5.4 - 3B)/0.3
300B + 30W - 108R = 0
300B + 30*((5.4 - 3B)/0.3) - 108(5) = 0
300B + 30*((18 - 10)) - 540 = 0
300B + 540 - 300 - 540 = 0
B = 1
W = (5.4 - 3B)/0.3
W = (5.4 - 3(1))/0.3
W = 8
Blue = 1
White = 8
Red = 5
I am a mastermind because when I got this kind of problem I checked it out Google 🤣🤣🤣😂😂
Me also😂🤣
I too do the same😄
Me also😂😂😂
Me too
Me too😅
Oh, no. I am a Mastermind.
*LOL.* Me too.
You are a wizard Bill Y.
y͙e͙s͙ m͙e͙ t͙o͙o͙😆🤣🤣🤣
Meagamind
lol, to check if you are a genius. You need to visit #PuzzleAdda
abc + abc + abc = ccc
so the units digits of c*3 = c
just quickly go through in your head which numbers work
0 * 3 = 0 yes
1 * 3 = 3 no
2 * 3 = 6 no
3 * 3 = 9 no
4 * 3 = 12 no
5 * 3 = 15 yes
6 * 3 = 18 no
7 * 3 = 21 no
8 * 3 = 24 no
9 * 3 = 27 no
so c is either 0 or 5, but since 000 is not a valid answer (by common sense), ccc = 555
555/3 = 185
a = 1
b = 8
c = 5
Just to add a little challenge: Presh never said what base this puzzle was in. I never like to assume decimal. Let's look at a few other bases.
Base 2: Not enough digits for the colors.
Base 3: Multiplying by 3 gives all zeroes, already ruled out.
Base 4: Red*3 = red (mod 4), so red = 2. This gives us 222 (base 4) / 3, which is 42 / 3 (decimal), which gives 032 (base 4)
Base 5: red*3 = red (mod 5) -> the empty set. No solution is possible. More generally, for a value to satisfy red*3=red (mod N), red*2 must divide N. This is only possible for even N, and red always = N/2.
Base 6: red * 3 = red (mod 6) -> red = 3, which gives 129 / 3, which is 43. But this doesn't satisfy: Presh tells us that each color corresponds to a unique digit, but 43 = 111 (base 6).
Base 8: red = 4, so it's 444 (base 8) or 292 (decimal). This is not divisible by 3.
So for bases up to 10, there are only two solutions, 032 (base 4) and 185 (decimal).
Tehom yeah, good idea. this at least makes the puzzle a bit harder
Best comment of this lot!
Haha, I started with base 16 and got 2d8 -> 888
To me, if the base is not stated, then it is base 10, by definition!
I think about this puzzle for 5 minutes. But i could not found any answer. Then i realize that i can make computer program to find this answer. So then i make a C++ program. And its answer me that the number is 185. Thank u sir for such an amazing puzzle.
Using that to find the solution is probably more impressive than the method used in the video, so congrats!
U just need to find the red
And its very easy cuz
Red+red+red=.. Red
So the red must be 5
5+5+5=1"5" (15)
555 : 3 = 185
thank u
The only values for C are 0, 5, and 6 because only those multiplied by three end in the original digit.
0 cannot be the answer (QED), so C is either 5 or 6 and the carry from the 1s is 1.
A must be 1 because if A = 2, then B = (C-1)/3 which cannot be an integer. A>=3 is a four digit number.
If C = 6, the carry from the tens must be 3, but the largest carry of three digits is 2 (9+9+9), so C = 5.
The carry from the tens must be 2, and the only 3B+1 that ends in 5 is 8.
Ergo. 185+185+185=555.
I enjoyed many videos and thus subscribed to the channel. Two recent videos just irritated me. I get it, the channel is meant to popularize Maths to all audiences. Just please avoid having these misleading titles such as "only mastermind/genius can solve this" or "95 % failed" on viral social media problems...
I think the reference to "mastermind" is to the game en.wikipedia.org/wiki/Mastermind_(board_game) - not particularly misleading and in fact I found it a nice joke.
petran HQ 35790
Zn Zn
For a short solution, we have 3c = c mod 10. Therefore c can't have an inverse mod 10, so c must be a zero divisor and must be either 2 or 5. 2*3=6 which is not equal to 2 mod 10. 5*3 = 5 mod 10, so c=5. Then divide 555 by 3 to get a and b.
The easiest problem in this channel.
185
3x5=15
8x3+1=25
1x3+2=5
There have been easier problems.
How ??
If you love solving puzzles, visit.
#PuzzleAdda
Fun puzzle. Took about 2 minutes in my head, no writing down, charting, etc. Just a bit of simple logic.
This one must have been easy, I normally can't figure these out while sitting at my computer. This one I did. Thanks for throwing us mortals a bone.
People here are complaining how easy it is! But the funny thing is i couldn't even solve it even after watching this video. I found most of the sums of this channel easy except this one. I mean how do you know that C can only be 5.? Rest i understood. Plz help
So true
Wow I'm a mastermind!! Good to know.Point to self: Never look at the comments after you've actually solved a question on this channel. Most of it is filled with people exclaiming how easy the problem was which pretty much ruins the feeling of being super smart you get after solving the question.
Second way can be just to try each 3 same digit number and divide it by 3. Bruteforce but in this case works as well ;) Also since we know we have same digit under the line we can assume it needs to be a digit that multiplied 3x will give same number in last place and probably some rest to carry to the next row. So in this case 5 seems to be natural.
Thanks for briefly letting me feel like I'm slightly intelligent.
b, g, and r are non-negative decimal digits, and none of them have the
same value
% for mod
300b+30g+3r=100r+10r+r
b
Honestly I think you made this too complicated. All you had to so was substitute 111,222, etc into the bottom and divide by 3 to find which one gave a 3 digit number with 3 different digits. Thats how I did it and it took like 30 seconds.
(100B + 10W + R)3 = 100R + 10R + R.
The only number that has its own value in the ones digit when multiplied by 3, is 5.
Substituting 5 into the above equation gives you 10B + W = 18. The only 2 numbers that work are 1 and 8.
Honestly? This is considered mastermind abilities? It's child's play.
185+185+185=555
It's odd that the way you explained it you would need to divide 555/3, which most people can not do in their heads.
Most people can't divide 555 by 3 in their heads? you just count up, 100 makes 300, and for 255 you just do 80 for 240 and 15 makes 5....185
You mean you don't already know that 111 = 3*37? -> 555/3 = 5*37 = 10* (37/2) = 10*18.5 = 185...
Actually, I found 185 by finding c=5, -> b=4/3(mod 10) = 8 -> a=3/3=1 because that was faster than taking the time to think about what would be a shorter method of solution after finding c...
lightdark00 master if puppets
lightdark00 I think the reference is to the game Mastermind, which is visually similar.
This seemed a little easier than the title would lead you to believe. There are only two digits which can be added three times and get the same value - 0 and 5. Since the leftmost digit can't be zero, the red is 5 by process of elimination. Then just divide 555 by 3 to get the correct answer for the blue and white digits.
I don't know why this would be considered difficult. Most of Presh's problems take me a long time, but this took me less than a minute.
The answer is simple.
185
+185
+185
=555.
Thanks for the minds boggling question. Upload tricky videos about questions related to log.
185?
I didn’t watch the answers yet.
Edit: yess! This is actually a very easy question. I’ll explain it in my 13 year old mind:
So I know the answer has the same numbers for each digit. So, 000,111,222,333...999 could be all possible answers.
Next, I took out all the numbers that when divided by 3, the make the same digits. For example: 333 divided by 3 is 111. This breaks the rule, because blue circle, grey circle and red circle must have different digits. So, now we’re left with 111,222,444,555,777,888. Now, I took turns dividing each by 3 until I got to 555. 555 divided by 3 makes 185. Since the last digit must be the same numbers as the answer, it must be 185. No other triple digits ended with the same number. :)
i solved it even before clicking on video
Answer 1 8 5
Same here
This is actually very easy. First you need a number that when trippled produces a sum who's last digit is equal to that number. The only possible number is five, which produces 15. Since 1 gets carried over to the next column, we need a number that when trippled the last digit is equal to 4, the only possible number is 8, which sums to 24, and 2 is carried over. This means that the blue collumn must sum to 3, and 1 is the only number which satisfies it. So blue is 1, white is 8, and red is 5.
Nope, zero is still a number.
Really lmao I don’t usually solve your stuff but this was easy, the red must be 5 because it’s the only number when multiplied by 3 (besides 0) to give it’s self, hence the answer is 555, and 555/3 is 185
Before watching the solution: jotted down 1 thru 9 in one column and what they equal when multiplied times 3 in the next. Whichever the red circle could be any line where the 1s column matched. This was 5 and 15. Filled in 5s for red and carried the 1. For white, the 1s digit had to be a 4 since the 1 carried. That made the whites 8, carrying the 2, and the only solution for blue then had to be 1. However, once we work out red is 5, we can also just divide 555 by 3 to get the same solution. In the same vein, we could just divide each of 111, 222, 333, 444, 555, 666, 777, 888, and 999 by 3 and see if we get any solutions where the 1s column is the same digit as the original number, getting 555 again.
Could maths be universal because it is based on a universal geometrical process: (E=ˠM˳C²)∞ with energy ∆E equals mass ∆M linked to the Lorentz contraction ˠ of space and time. The Lorentz contraction ˠ represents the time dilation of Einstein’s Theory of Relativity. We have energy ∆E slowing the rate that time ∆t flows as a universal process of energy exchange or continuous creation. Mass will increase relative to this process with gravity being a secondary force to the electromagnetic force. The c² represents the speed of light c radiating out in a sphere 4π of EMR from its radius forming a square c² of probability. We have to square the probability of the wave-function Ψ because the area of the sphere is equal to the square of the radius of the sphere multiplied by 4π. This simple geometrical process forms the probability and uncertainty of everyday life and at the smallest scale of the process is represented mathematically by Heisenberg’s Uncertainty Principle ∆×∆pᵪ≥h/4π. In such a theory we have an emergent future unfolding photon by photon ∆E = hf with the movement of charge and flow of EM fields. This gives us a geometrical reason for positive and negative charge with a concaved inner surface for negative charge and a convexed outer surface for positive charge. The brackets in the equation (E=ˠM˳C²)∞ represent a dynamic boundary condition of an individual reference frame with an Arrow of Time or time line for each frame of reference. The infinity ∞ symbol represents an infinite number of dynamic interactive reference frames that are continuously coming in and out of existence. At the smallest scale the Planck constant ħ=h/2π is a constant of action in the dynamic geometrical process that we see and feel as the passage of time.
An artist theory on the physics of 'Time' as a physical process. Quantum Atom Theory Yes
no
Damn
LOL
How much spare time do you have
My method may be a bit convoluted but it worked. The original problem can be represented as
3(100a + 10b + c) = 100c + 10c + c = 111c = 3(37c)
100a + 10b + c = 37c
100a + 10b = 36c
10(10a + b) = 36c ==> 36c is a multiple of 10 ==> c = 5
10(10a + b) = 180
10a + b = 18
a = 1, b = 8
0,0,0 easy
Presh did say that the colors stood for distinct numerals.
Tehom what if he/she is color blinded...😏
Can't be 0 0 0 because you would then have all colours = zero so no sum.
*5* is the only digit that when multiplied by 3 results in a number that ends in 5. So, red is 5.
*8* is the only digit that when multiplied by 3 results in a number that ends in 4, So, grey is 8.
*1* is the only digit that when multiplied by 3 results in a 3. So, blue is 1.
P.S. We need the sum of the second column to end in a 4 because we carried the one from the first column (because 5x3=15). And we need a 3 in the last column because we carried the 2 (because 8x3+1=25).
i thought it was 777 then abc is 259
Zero K So 9=c=7?
Zero K the ones digit has to be itself and once it is multiplied by 3. In this case, only 0 and 5 work. And obviously we cant accept 0 because this makes others dots have to be 0
I just wrote down the multiplication table for 3:
0 · 3 = 0
1 · 3 = 3
2 · 3 = 6
3 · 3 = 9
4 · 3 = 12
5 · 3 = 15
6 · 3 = 18
7 · 3 = 21
8 · 3 = 24
9 · 3 = 27
I then started from units (red circle), as did you. I checked where the units of the product is the same as the multiplier, and its in the cases of 0 and 5. I noticed the same problem with zero as you did, so the red circle must me 5. One is carried to the grey circles.
I then proceeded to the grey circle, which had one carried from the red circles. I checked when the units of the product is one less than the 5. 8 · 3 = 24, and 1 + 24 = 25, so that's the only number that fits in there. 2 is carried to the blue circles.
And now I just have 2 + 3 · BLUE = 5, which gives me the number 1 to the blue circles.
Bro xxxtentacion dead 😭😭😭😭😭
Claudiu Marciuc i couldnt watch this without thinking about x 😭😭😭 rip 😔❤️
lmfao
Xxxpired
Xxxtinct
Who?
Not used algebra - took me 3 minutes to figure out - quite happy with that.
185
Simple puzzle, solved in under 1 minute:
Red must be a number that when multiplied by 3 has itself as the last digit.
This means red must either be 0 or 5. If red = 0, then both grey and blue would have to equal 3.33333...
That means red is 5, and 3x5 = 15.
3 x grey must have a final digit of 4, so that when it is added to the carried 1, that digit = 5. That means grey = 8, and 3x8=24.
Blue must fulfill 2 requirement to meet the puzzle conditions. When multiplied by 3, the product must be a single digit, and that product must also equal 3, so when it's added to the carried 2, that sum equals 5. Therefore, blue = 1.
Two comments:
1. I saw the gray circles as white circles that were lit from above, but yes, they are actually gray and who wants to relive the blue/white dress again, and
2. Presh mentioned said only a “mastermind” can solve the problem because the puzzle looks like the Mastermind board game not because it is difficult so everyone can now get off their high horse.
Blue colour=1,white colour=8,red colour =5
Had it immediately. The red ones can only be 0 or 5 (as multiplying each number between 0 and 9 gives a result that ends in something different, except 0 and 5). However, no three same numbers (other than 000) added give 000. But 000 would be equal to 000 so all of the marbles would need to be red. So it must be 555. Which means the answer must be xy5 + xy5 + xy5 = 555. Which is easily solved by 555 divided by 3. So 185 is the solution.
So, in part due to your past videos showing me a notation for writing the abstract: I see 300a+30b+3c-111c=0; the ones digit is ONLY influenced by c, and the only puzzle is c itself, and since 111-3=108, the only choices for c are 0 and 5, and with the three digits being unique the conclusion is c=5 and [abc]=555/3=185
300a+30b+3c=111c =>
300a+30b=108c =>
50a+5b=18c =>
5(10a+b)=18c
Since 18 is not a multiple of 5, we must have c=0 or c=5.
c cannot be 0 because this would imply a=b=c=0 and we assumed the digits are different.
Thus, c=5 which leads us to 10a+b=18.
If a>1 then 10a+b>18 which gives us that a=0 or a=1.
If a=0 then b=18 which is impossible since b is a digit. Thus a=1.
Now, we get 10+b=18 and therefore, b=8.
Hence, the number is 185!
The only single digit (excluding 0), if added by itself 3 times or multiplied by 3 that results to have same digit in ones column is 5.
Therefore, Red is equal to 5.
Thus, this would have a total of 555
When divided by 3 would result to 185.
Answer: Blue=1, Gray=8, Red=5.
RED: 0 or 5, not 0, 5. 15 Carry the 1.
WHITE: must end with 4, so 8. 24+1 carry the 2.
BLUE: must end with 3 and total less than 8, so 1. 3+2.
1, 8, 5.
I solved it a bit different.
~Noticed that each colour was a single digit multiplication of 3 higher than 0 (as x+y+0≠0) and wrote them down.
~ Next, I looked at the red and looked at which solutions ended in the multiplier, isolating 5, meaning Red=5
~Third, I looked up which ones ended in the solution to 5 - the careied number for the next two colours.
It can b solved using algebra also. Let no. be abc. Value of no. = 100a+10b+c. Result is 100c+10c+c i.e. 111c. Now 3(100a+10b+c) = 111c
or 100a+10b = 36c.
Minm value of LHS is 110. So, find next multiple of 36 divisible by 10. Which means RHS=180 or 360.
Taking RHS = 180 i.e c=5. We get a=1 and b=8. Hence no. is 185. 185x3 = 555
I already answered it before watching the video 😆
Since 5 are the only numbers that is equal to itself by multiplying 3.
The proper way to solve it is not through trial and error. it's through actual algebraic equations. you have 3 unknowns, which means you need 3 equations to solve it. Here is the proper solution:
3*(100*B + 10*W + R) = R*100 + R*10 + R
300B + 30W + 3R = 111R
EQ1 => 300B + 30W - 108R = 0
3R = R + 10*C1
C1 = 0.2R
3W + C1 = R + 10*C2
3W + (0.2R) = R + 10*C2
C2 = (3W - 0.8R)*0.1
C2 = 0.3W - 0.08R
3B + C2 = R
3B + (0.3W - 0.08R) - R = 0
EQ2 => 3B + 0.3W - 1.08R = 0
EQ3 => (3R)%10 = R
R = 5
3B + 0.3W - 1.08*5 = 0
3B + 0.3W - 5.4 = 0
W = (5.4 - 3B)/0.3
300B + 30W - 108R = 0
300B + 30*((5.4 - 3B)/0.3) - 108(5) = 0
300B + 30*((18 - 10)) - 540 = 0
300B + 540 - 300 - 540 = 0
B = 1
W = (5.4 - 3B)/0.3
W = (5.4 - 3(1))/0.3
W = 8
Blue = 1
White = 8
Red = 5
The sum of the three values, each with a red circle as the last digit, gives a last digit that is also represented by a red circle, and so the red circle can only be 5. And so we already know that the sum of the three values is 555, and so the value formed by the blue circle, white circle and red circle is (555 / 3 =) 185, and so blue circle = 1 and white circle = 8.
Rather use hit and trial divide 444 by 3 =148 doesn't satisfy the conditions very next number 555 is the solution satisfying the conditions.
I may have two solutions
For 3x's last number to be equal to x and x>10, 5 and 0 are the only numbers that follow these rules (3(5)=15 and 3(0)=0). This leads to two solutions
1) 5 is indivisible by 3 (5/3=1.666…), so it must be that 15-1 is divisible by 3, but 14 isn't divisible by 3, making this solution faulty
2) No matter how many times you add 0 to itself, nothing happens, so R=0, W=0 and B=0
Easy
1 8 5. Trial and error. The only number other than 0 that works for red is 5, I assumed all numbers were single digits. If the red is 5, then you will be carrying a 1 to the "10's column". Again, with trial and error I substituted the various numbers and came up with 8, which when you add the carried 1, makes 25. Carrying the 2 and needing to end in a 5 made it easy, as 1 works. I am sure that Presh will have a far more elegant solution. Now to watch.
Without a pad of paper, I believe that I have solved it. Verified with my calculator. The solution is 185 time 3.
Approach (for xyz):
For red, z times 3 equals z, z must be 5 or 0. And z is obviously not 0.
For blue, x times 3 plus 0, 1 or 2, equals 5, x must be 1 (plus 2).
For grey, y times 3, plus 1 (i.e., 3 times 8 plus 1 equals 25) equals 5. y must be 8.
For xyz, must be 185, QED (I hope).
Should I mention my age of 76, my 3 degrees, or my numerous strokes (i.e., dead brain cells)?
Very entertaining. Thank you for your efforts. May you and yours stay well and prosper.
Terry
The last digit in each number is either 5 or 0, however, if the colors equal distinct digits, this summation cannot equal 000, so the total is 555. Dividing by 3, we get our magic number of 185.
Alexa has an incontrovertible proof in court that her boyfriend was murdered by her sister. The judge declares, “This is the strangest case I’ve ever seen. Though it’s a cut-and-dried case, this woman cannot be punished.” How can this possibly be?
Brainy Riddle what
manasser99
any ideas?)
Are Alexa and her sister conjoined twins?
It would be wrong to jail them both.
Blue is 1, white is 8 and red is 5.
5 is the only digit that tripled give something ending with itself. So, 5 and carry 1.
The second column must end with a 4 + 1 = 5. Only 8 x 3 ends with a 4. So, 24 +1 = 25. Put a 5 and carry 2.
Lastly, a digit time 3 must be 3 without any carry. So, 1 is the only possibility.
185
Tooooooo OSM..... Keeping going ji
Kindly, make more video.....
Assuming every colour is a digit then red is 5 because that's the only digit that leaves unit 5 when multiplied by 3 which gives 15, so the sum should be 555.
Then with the white you do 1 (from 15) +3x=5y and whenever you get a whole number you know that y=8 which gives 25, then you do 2+3x=5 and get x=1.
Very easy. Let ABC + ABC + ABC = CCC. We are adding three C's and the units digit of our sum is also C. We can easily check that only one digit can do this and that is C = 5. (Note that 1+1+1 has unit digit 3, 2+2+2 has unit digit 6, and so on). Thus, AB5 + AB5 + AB5 = 555. If A => 2, then our sum on the left yields a number > 600 so that is impossible. Thus, A = 1. Then 1B5 + 1B5 + 1B5 = 555. Adding the units digits yields 15 so our sum has a unit digit of 5 and the 1 carries over to the tens digit. Then 1 + B + B + B must have a unit digit of 5. Note that the hundred's digits is 1 + 1 + 1 but the sum is showing a 5. Thus, we need a 2 to carry over from the tens digit. That occurs when 1 + B + B + B = 25. Thus, B = 8. Therefore, our solution is 185. Note that 185 + 185 + 185 = 185 * 3 = 555
This one was rather simple, but I liked it quite a bit. Although there were some assuptions that needed to be considered. Thanks
15 seconds, but I had to use pen and paper to make sure I didn't forget carry digits...
This is trivial.
1) red added together 3 times is red. So R+R+R=X*10+R. So R+R=X*10. R is a single digit so we can't have X>=2. So X=1 leaving us with R+R=10. (Or R=0 bu this requires othr digits to be 0 as well and they should be different.)
So R=5
2) Gray digits in the middle give us G+G+G+1=X*10 + 5. Substract 1 from both sides and get G+G+=X*10+4. Here X*10+4 needs to be a multiple of 3. And a criteria for any number being a multiple of 3 is having its digits to add up to a multiple of 3. So X+4=6+3*Y. Or X=2+3*Y. However G being a single digit requires 0
This is so easy, figure out what each digit times 3 is that ends in the same digit. only option is 5 = number is 555 - 15 (because of 5*5) = 540, figure out what digit * 3 ends on 4 = 8 = 24 = 240 because of the 0 540 - 240 = 300, 1*3 = 3 = 185
It took me two minutes , if not less (doesn't require a mastermind) 185 x 3 =555. first what digit when multiplied by 3 gives the same digit and that is 5(as multiplication is the same as addition), so you will have 1 left to add to the other digit, then what digit when multiplied by 3 would give 4 since you know will need to add 1 to that digit and that of course is 8 and 3 times 8 is 24, then what digit when multiplied by 3 would leave 3 since you need to add to the 2 from the 24 to it and that of course is 1, so the answer is 185, the blue =1 gray = 8 and red =5
We know that there are only 9 possible combinations for the total, 111, 222,... 999. We can skip the 000 as this would result in all the digits being the same.
Since all the numbers are the same, all that we need to do is to divide the total by 3.
111 / 3 = 037
222 / 3 = 074
...
555 / 3 = 185
I just said that the only possible last number would be 5, because if it were 0, then the sum is 000, and 5 is the only other number that when added to itself 3 times, the resulting sum is 15, and it’s ones digit is 5, so it works, then I thought about what numbers resulted in a ones digit of 4 when added to itself 3 times, and I came up with 8, 3*8=24, and then the last digit is just n+2=5. The answer I got is 185
Blue is 1, gray is 8 and red is 5. 185x3 = 555
The red is 5. It is the only single digit # that if multiplied by 3 the product is still ending with 5. So since the red is 5, therefore the 3 digit sum is 555. Just divide 555 by 3 and you will get 185.
I did it in a very, very, VERY inefficient way. My first step, for C, was actually ok: 3C must end in C, and the only nonzero digit that meets that is 5, coming to 15. After that is when I did things terribly inefficiently. I wrote the 555, but instead of dividing by 3, I said "Well, 3A must be either 5 or less than 5 if there is any carry over. Only A = 1 does that." Once that was set up, I solved for B using decimal expansion: 300 + 30B + 15 = 555 means B = 8. I have no idea why I did it that roundabout way... but it worked, I guess.
The three fives were easy, I just kinda jumped to 15 because it wasn't likely any number times 3 would have itself as the last digit except 5. I would've felt more wound in 'proving' it if I had come up with those equations though.
The 8 and 1 I just used the process of elimination knowing the tens place of each sum would get carried over, and that they'd always result in a 5. Dividing 555 by 3 would've been the better route.
There is a famous puzzle that I just realized has a problem with.
There is a band with 7 people in it, yet they keep losing their insterments.
Their manager is sick and tired of it.
He tells them that there instruments are each in the next room, inside 7 labeled boxes, the catch is that no instrument is in a box labeled with it's own name.
Each person only has 3 chances to find their own insterment.
If less than half of them find their instruments in 3 tries then he will kill them all.
The solution we are given is that each person looks in the box with their instrument, the drummer looks in the box with the drums and finds the base, so he looks in the box with the base and finds the drums.
Then the keyboard player opens the keyboard box to find a microphone, then opens the microphone box and finds a trombone, then opens the trombone box to find the tambourine.
The problem comes when the base player comes in and opens the base box to find it empty. He knows that it either had the drums or the keyboard.
If he opens the drums box then he finds the base and wins, yet if he opens the keyboard box then he finds the microphone and can't find his base.
Next the singer comes looking for her microphone, opens that box and trombone, opens the trombone box and finds the trombone.
The next time someone comes to an empty box, was this the box that had the drums, the keyboard or the base?
It has to be a 3 digit number where all three digits are the same number, and when it's divided by three it equals a whole number ending with the original number. So just divide them by 3 starting with 444, because 333 divided by 3 is 111, and that and 222 divided by 3 are two digit numbers. You only have to do two calculations if you're working upward from 444 before you get your answer
r has to add up to number > 10 so that the 1s digit is r.
r = 3r - 10.
r = 5.
555/3 = 185.
b = 1 w = 8. r = 5
Solutions I found:
Base 9++ (decimal): 3 × 185 = 555
Base F++ (hexadecimal): 3 × 2D8 = 888
Base L++: 3 × 3IB = BBB
Base R++: 3 × 4NE = EEE
I am starting to see a pattern. There seems to be a solution in every base A+6n (every sixth base starting from decimal).
It was easy. 3 R = R + Carry. Carry can be 0/10/30. Hence 2R = 0 or 10 or 20 .. and R = 0, 5, or 10. R cannot be 10, and it cannot be 0 (unless everything is 0 as the sum would be 000). If R is 5, the answer is 555. Divide by 3 and we get 185.
This is by far the easiest puzzle that I had seen in this channel. I don't understand why its title says that only a masternind can solve it. My approach is this: take 000, 111, 222... through 999 and divide each number by 3 and only 555 satisfy the conditions. It took me 30 seconds to make myself a mastermind.
It is a play on the game mastermind.
The book "Sideways Arithmetic from Wayside School" has a good number of problems like this, where words are added together, and you have to deduce which digit each letter represents. For example, egg + egg = page, or seed + iced = spice.
Most of the problems on this channel are pretty tough, but this was really really easy. 185. you just figure out the last digit by doing 3 times every number between 1 and 9 and checking equivalence mod 10, it's 3*5=15. Then divide 555 by 3. By making it so easy to get the sum, and having the summed numbers be the same, the problem becomes trivial.
The only numbers that added to themselves three times result in a number that ends in themselves are 0 and 5. 000 is not a legitimate sum, so red is 5. From there its a simple matter of dividing 555 by 3.
Blue = 1
Gray = 8
Red = 5
Alternative route: our goal is to solve for either x or y.
111*x = 3 * y, 37 x = y
notice that we need 7x mod 10 = x.
Only 1 digit satisfies this property so x must be 5, and now we can solve for y.
Mmm, I did it in my head in about 15sec, but differently.
3u has u in its digits/units place, so can only be 0 or 5, and 000 won't work, so red must be 5, for 555.
After carrying the 1 (15), 3t must have 4 in the tens place, 04 and 14 don't fit, so 24, and white must be 8.
Same, carry the 2 (24), so 3h must be 3, so blue is 1. Thus 185.
Yeah, dividing by 3 would work, but I like going through the steps.
3 * c = c means that they must end with same digit and so as a result to do this with same number is only solution of c = 5 That means the total is 555 and since all the numbers are same, 3x = 555 == > x = 185 so a...b....c = 185 which means that the values are a = 1, b = 8 and c = 5