Logic And Intelligence Test – Solve For Each Color

Mind Your Decisions. I’m Presh Talwalkar. Solve for the value of each color
in the following arithmetic problem. Each color represents a different digit from 0 to 9. I thanks Lucas for suggesting this problem. It originally appeared as a Belgian Olympiad problem with the letters M, A, and T. Pause the video if you’d like to give this problem a try and when you’re ready, keep watching
to learn how to solve this problem. We’ll get started by focusing on the letter M. Suppose M equals 5. In that case, the sum will be at least 1500. And this is going to be too large of the value because we need the sum to be 1416. Therefore M equals 5 produces a sum that’s too large and it’s not possible. The same logic is true for M
greater than or equal to 5. We can eliminate all of these possibilities. What if M equals 3? In that case, the largest value of the sum will be 1197. And that’s too small because we need
the sum to be 1416. Therefore M equals 3 cannot be a possibility and M less than or equal to 3 can also be eliminated. What remains is M is equal to 4. This will simplify our calculation. If we substitute M is equal to 4 we know that just from the terms involving M we get a sum of 1204. We subtract those out we get the resulting sum of 212 and we have a new problem. We now need to solve for A and T. Let’s focus on T. In the unit’s column, T plus T can either equal 2 or it can equal 12. Consider the first case. If T plus T equals 2 then T is equal to 1. Which then means the entire problem has to be 10 A plus 10 A plus 1 plus 11 is equal to 212. This means 20 A equals 200 and A is equal to 10. But that’s not possible because A has to be
a single-digit from 0 to 9. Therefore we must have T plus T is equal to 12. This means T is equal to 6. And we can then go ahead and solve that A must be equal to 7. Therefore this is the answer to the problem. M is equal to 4, A is equal to 7, and T is equal to 6. And we can, in fact, verify this does work out. Thanks for making MindYourDecisions
one of the best channels on YouTube. As always thanks for watching
and thanks for your support.

100 thoughts on “Logic And Intelligence Test – Solve For Each Color”

• January 30, 2020 at 4:28 am

If this is a multiple choice question I will just verify it

• January 30, 2020 at 4:52 am

Got the same answer, but my process was different (used less equations and more process of elimination)-possibly due to not having a mathematics background. I'll just go through it.
1. I isolated the first column; the three M's equal 14. Since 14 is not divisible by 3, we know there's there's a carry-over number (which will be a 1 or a 2; anything higher then 2 is impossible since the highest possible number for the rest is 297), so I looked to the closest number less then 14 divisible by 3. That was 12. Divide 12 by 3, you get 4. This means (a) M = 4 and (b) there was a carry-over of 2.

2. Now that we've solved for M, we can remove the first column and focus on the second two. We know that one of the digits is 4 and that the total is equal to 216. We can see that the last column is 4+T+T=6 (or: 4+T(2)=6). There are 2 possible answers: T=1 and T=6. However, plug T=1 into the whole equation, and you can't get 216 (highest possible is 196), so by elimination, we get T=6.

3. And now, we can isolate the middle column. We know that A+A+6+1=21 (the one is carry over from the first column). Now, subtract 7 (6+1) from the 21 and we get A+A=14 (or 2(A)=14). Divide 14 by 2 and we get 7. As such A=7.

4. Finally, just to confirm the answer is correct, replace all the letters with numbers and see if it comes up with the right answer-and it did.

• January 30, 2020 at 5:48 am

ME: This is easy, I solve it in seconds. It is all about logic.
Exam: x+y+z=150 Please list all of the possibility of x,y,z.

• January 30, 2020 at 5:51 am

I solved it, T, M, then A. Your way is better and more logical. I was kinda like a chess computer just forcing my way to the answer.

• January 30, 2020 at 6:11 am

So, before i read this. I wanna say Red=1, Silver=10, and Blue=4. Ill respond after watching

• January 30, 2020 at 6:48 am

This is the second riddle I could solve

• January 30, 2020 at 7:46 am

This is the first time that i solve it.. And i do it mentally cuz getting a pen is too much work

• January 30, 2020 at 9:03 am

Which software you used for making videos ?

• January 30, 2020 at 9:39 am

Super easy… if you do it logically! Solve it from left to right and it comes quickly.

• January 30, 2020 at 10:01 am

Annoying edited in music. Chanel blocked. Bye.

• January 30, 2020 at 10:31 am

That was easy I didn't even use notes

• January 30, 2020 at 10:33 am

14/3 can't so it must be 12/3 so M =4
AAT is either 200 or 210 must be 20, then MTT must be 16 so (16-4)/2= 6 then (20-6)/2 is 7 solved

• January 30, 2020 at 10:37 am

4=blue
7=grey
6=red
474
+476
+466
——-
1416

• January 30, 2020 at 10:46 am

wow finally a problem I have succeed alone 😀

• January 30, 2020 at 10:58 am

M=10
T=1
A=10

• January 30, 2020 at 11:28 am

I solved it before watching the solution

• January 30, 2020 at 1:40 pm

I got the right answer, then I substituted them wrong, then I gave up

• January 30, 2020 at 1:43 pm

I had a lot of fun solving it 😍😍

• January 30, 2020 at 2:55 pm

Chuuhhh did it mentally

• January 30, 2020 at 2:59 pm

Before hearing the answer: M=4
A=10 and T=1

• January 30, 2020 at 3:09 pm

M=4, A=10, T=1 this is also correct…. please check and reply

• January 30, 2020 at 3:12 pm

M=4
A=10
T=1

• January 30, 2020 at 3:20 pm

Red = 6
White = 7
Blue = 4

• January 30, 2020 at 3:24 pm

I was very surprised I could wrote correct answer in legend mathematician test……
😍

• January 30, 2020 at 3:56 pm

This is satanic. You are a wizard.
If you were a woman you would be a witch… So you probably be burned.
Assume tha you are a woman…
BURN HER !!!!!!!

• January 30, 2020 at 4:00 pm

Easy

• January 30, 2020 at 4:44 pm

Solved it yay!

• January 30, 2020 at 4:47 pm

474+476+466=1416

• January 30, 2020 at 4:56 pm

Blue = 4, White = 7, Red = 6. I'm sure there's a way to do it algebraically but I used logic:

It's immediately obvious from the 1s column that blue must be even, since 2red+blue is even. This is helpful (though not necessary) to determine blue. Looking at the 100s column, we see that Blue < 5 otherwise the sum would be >1500. So that leaves only 2 and 4 as possibilities. But 2 is too low, there's no way that 2+2+2+carry could be 14. So Blue must be 4. Then we can go back to the 1s column to see that red must be either 1 or 6. But red cannot be 1 because we need 2white+red+possible carry= 21. So red must be 6. That means the carry from the 1s column is 1. 2white + 6+1 = 21. 2white = 14. White = 7.

• January 30, 2020 at 6:07 pm

Im genuinely turned on after watching this

• January 30, 2020 at 6:12 pm

red=6 , blue=4 , white= 7 😉

• January 30, 2020 at 6:16 pm

4 blue
1 red
10 grey

• January 30, 2020 at 7:01 pm

474+476+466=1416

• January 30, 2020 at 7:11 pm

this is my answer
M=4
A=7
T=6

question took me 30 minute to solve

• January 30, 2020 at 7:16 pm

Do harder questions, too many assumptions can be made from this and so I was able to do it in under 3 minutes.

• January 30, 2020 at 8:14 pm

bue=4 grey=7 red=6

• January 30, 2020 at 9:19 pm

Very nice video. Thanks. Now I know how to solve this type of problem.

• January 30, 2020 at 9:35 pm

1st , Use division by 3 at first to get approximate answer and value of M
Which is M = 4

2nd , you got the M correct , now guess a number that when you add it to himself and M value you will got 6 like in the answer .. we can chose 1 that 1+1+4 = 6 , but you will see when you try to get number 1 in total answer, the only way is by assuming A = 5
Thus it will be 5+5+1= 11
Overall total will be 1316
We go back to value of T and change it in order to get 6 in the total answer , therefore T = 6 , 4+6+6= 16 ,

We keep that additional 1 in mind .

3rd . Now we know T = 6 , and we have 1 number to add , and now we want to get A value ,with the total answer 1 and have 2 additional numbers so when we add M values + 2 we got 4+4+4+2= 14
Which is the last section of the total answer,

Keep in mind we have additional 1 from 2nd calculation , T=6 , the total answer must be 21 , what's the value of A ??
2A + 6 + 1 = 21
2A + 7 = 21
2A = 21 – 7
2A = 14
Divide both side by 2 to get A
Then A = 7

Another way
What's the number that if i add it to himself and to 6+1=7 will give me 21
7*3= 21 , A = 7

• January 30, 2020 at 9:35 pm

I did it!

• January 30, 2020 at 10:18 pm

What about B=4 R=1 AND W=10

• January 30, 2020 at 11:05 pm

From thumbnail
Red = 1
Blue = 4
White = 10

• January 31, 2020 at 12:33 am

301M+20A+12T=1416 …

• January 31, 2020 at 12:37 am

Took me under 30 seconds it wasn't hard try something more challenging next time I didn't even need to see the steps as long as you remember that numbers get carried over you can come to an easy conclusion

• January 31, 2020 at 2:09 am

Si construyó un ángulo x cualquiera del cual se todos los valores de las rectas con que lo construyó como hago para saber la medida del ángulo apartir del valor de estás líneas rectas con que lo construí
Pues si ya se los valores de sus líneas rectas no necesito funciones trigonométricas y debería ser suficiente saber el valor de las líneas rectas para hallar el valor del ángulo

• January 31, 2020 at 2:21 am

Unnecessary math.

• January 31, 2020 at 3:37 am

I solved, and i did it backwars

• January 31, 2020 at 7:54 am

Blue-4. White-7. Red – 6.

• January 31, 2020 at 10:40 am

I got it before watching the video…

B 4
G 7
R 6

• January 31, 2020 at 1:29 pm

I solve it just in 1min

• January 31, 2020 at 2:00 pm

Well, I found correct answer without this procedure

• January 31, 2020 at 4:02 pm

At 0:52 the first line should be 505, not 500 as MAM is equal to 505. Doesn't change the answer, it's just a typo. Thanks.

• January 31, 2020 at 4:29 pm

I took less than 30 seconds to find M, A and T.
Please give me more harder questions who never solved..

• January 31, 2020 at 5:21 pm

All those boastful comments… Like, ok, we get it, it's easy, nothing special. Human ego is one hell of a thing.

• January 31, 2020 at 6:22 pm

My solution:
Blue=x , Red=y , Grey=z
x+2y = 6,16,26 can't exceed that (3*9=27)
Thus, x is even.Also, 3x <= 14
Which gives x = 4
So carry from 2nd line must be 2.
=> 2z + y = 21,20 or 19 (as per carry from 1st line)

4 + 2y = 6,16 or 26
=> y = 1 or 6 (11 is not possible)
For, y = 1 , z = 10 BUT 10 is not possible.
Thus y = 6,
=> 2z + 6 = 20
=> z = 7

Ans: x = 4, y = 6, z = 7

I know it looks quite messy but it came to my mind very clear, it's just the fact that I expressed it badly.

• January 31, 2020 at 7:16 pm

I solved it in under 30 seconds with LUCK

• January 31, 2020 at 8:26 pm

I solved it in the same method

• January 31, 2020 at 10:50 pm

Wait it also works with blue = 4, grey = 10 and red = 1

• January 31, 2020 at 10:59 pm

4 7 6 ♧

• January 31, 2020 at 11:55 pm

Brute force for-loop with all combinations of M,A and T worked for me😁

• February 1, 2020 at 3:03 am

I thought it would be more complicated, where the 16 the one shifts above the second row. Where it becomes 7+7+6+1 from the 16..22. The 2 down 2 above the 4s

• February 1, 2020 at 5:51 am

Blue is an even number, so blue must be 4
Then red is either 1 or 6
If red is 1, white equals to 0 or 5
Red can't be 6 or white can't come
White must equal to >7
But it can't be possible
WHERE DID I GO WRONG?

• February 1, 2020 at 6:12 am

I looked at this and this and first tried blue=4 white=0 red=1. I saw 1 for red was two low hut knew the last number had to be a 6 so I put in red=6 because it had to be 12 because it was added to four. I saw 140 was missing and did white=7 and bame. Salved it in under a minute

• February 1, 2020 at 6:47 am

Blue 4
Gray 7

Red 6

4 7 4
4 7 6
4 6 6
_____
1416

• February 1, 2020 at 9:53 am

ok i think this is correct: m = 4 a = 10 t = 1. Solved it by saying ok 14 / by 3 =4.666 so the second numbers need to add up to 2 cuz u cant have a decimal in the first slot, cuz only one slot, and the highest integer is gonna be 4. and go from there. so then i look at a + a + t. well it needs to be 21. it is devidible by 4 to get a non decimal. but that would make 7 for each which doesnt work for the last one. well i just do 6 – 4 for the last one and i devide it by 2 cuz gonna be the same sumber for t and t. well its 1 for t so then i can just do 21 – 1 and then 20 / 2 and i get a to 10 and solved.

• February 1, 2020 at 10:52 am

I started by trying different values of 'T'. I solved it, but it was cumbersome. Anyways, I'm new to this. Thanks ♥️🧡

• February 1, 2020 at 11:11 am

I solved all colors and all colors were correct and I was only 12 years old :))

• February 1, 2020 at 12:08 pm

its same as solving 301M+20A+12T

• February 1, 2020 at 4:32 pm

Is he American

• February 1, 2020 at 5:30 pm

I figured it out in a few minutes just using common sense. It's not complicated.

• February 1, 2020 at 11:34 pm

More and more simple

• February 2, 2020 at 1:54 am

Solve it

• February 2, 2020 at 5:21 am

Solution before watching (only Thumbnail)
Red – 1
Grey – 10
Blue – 4

4+1+1=6
10+10+1='2'1
4+4+4+'2'=14

2nd Solution

Red – 6
Grey – 7
Blue – 4

4+6+6='1'6
7+7+6+'1'='2'1
4+4+4+'2'=14

• February 2, 2020 at 6:45 am

I was able to solve this
Blue-4
Red-6
Grey-7

• February 2, 2020 at 8:37 am

Can blue be 4, grey be 10 and red be 1. It works like this too….

• February 2, 2020 at 10:56 am

Pause at 15th second, background is white, lock your phone, unlock again, it turn into yellow, anyone else?

• February 2, 2020 at 12:16 pm

I got it! I usually don't. 🙂 But my way of getting there was not as elegant.

• February 2, 2020 at 4:48 pm

This video is π seconds long.

• February 2, 2020 at 8:32 pm

hello! how can i suggest a problem? i think it will be very interesting!

• February 2, 2020 at 8:40 pm

sqrt x + y = 11 x + sqrt y =7 i reach a point where i find a solution, and im left with a polynomial which has no roots, but i cant prove why this polynomial has no roots 😛

• February 3, 2020 at 12:09 am

Finally. A problem I was able to solve on my own! And I did it all in my head.

• February 3, 2020 at 12:12 am

You’re genius

• February 3, 2020 at 2:11 am

Blue=4, red=1 and grey=10 anyone else??

• February 3, 2020 at 2:57 am

Solution:- M=4,A=7,T=6

• February 3, 2020 at 9:21 am

Red 6
Blue 4
Grey 7

• February 3, 2020 at 11:30 am

Blue = 4
Red = 6
Gray = 7

• February 3, 2020 at 12:15 pm

first problem i actually solved on this channel, yay

• February 3, 2020 at 3:37 pm

the win

• February 3, 2020 at 11:48 pm

Thank you for video. Inspired by you I made first video for YouTube community.
https://youtu.be/aJnHDNiIa5w

• February 4, 2020 at 6:15 am

Pftt solved it in like 20 seconds pretty easy one

• February 5, 2020 at 12:18 am

Now let me pray a question like this doesn’t come for S.E.A this year 😇

• February 5, 2020 at 6:55 am

This one is easier than another

• February 5, 2020 at 2:37 pm

This one was easy

• February 7, 2020 at 11:29 pm

2:23 where did you get 10A + (10A + 1) + 11

• February 8, 2020 at 1:15 am

Blue 4
Gray 7
Red 6