Hey, this is Presh Talwalkar
I want to start this video by sharing an email
Hello, Presh. I presented one of your math questions to my maths teacher, and he couldn't solve it, haha
Before we go further in the email. I want to say thank you for showing your teacher my video
There are so many math teachers that are watching Mind Your Decisions videos
It's absolutely amazing, and I think we have the smartest community of subscribers over all of YouTube
But it's no big deal if your teacher could not solve the problem
Admittedly I cannot solve a lot of these puzzles either
The fun part is learning about hard problems,
learning the problem solving techniques, and then using them to solve future puzzles
So back to the email
Instead he gave me another one which I couldn't solve would you mind having a look and maybe put it out as a video
The question is to solve if the letters are distinct whole numbers from one to nine
the problem is AAA plus BBB plus CCC equals BAAC
I want to thank Luuk for sending me this email
Can you figure it out? Give this problem a try and when you're ready keep watching the video for the solution
So how can we solve this addition problem?
Problems of this type usually involve some guessing and checking, so let's try to limit the possibilities to check
The first thing we can do is imagine we have the largest possible values for A B and C
This would be 999 + 888 + 777
This results in a sum of 2664
This is the largest possible value for BAAC. What does that mean?
Since it's less than 3000 and
since B is not equal to 0, that means there are only two possible values for the digit B
We could either have B = 2 or B = 1
So now let's further limit the number of possibilities using what we've just figured out
We have two cases where B is either equal to 1 or B is equal to 2
Now let's consider the sum in the unit's column
Notice we have A + 1 + C = C
In other words A + 1 + C = C + 10
If we cancel out the C we have that A + 1 = 10
This means that A = 9
Similarly in our other case we must have A + 2 + C = C,
which means A + 2 = 10 and therefore A = 8 in this case
So we either have 999 + 111 or 888 + 222
So how can we figure out the value of C? Well remember that the largest possible sum was 2664
if we have A = 8 and B = 2
We end up with the sum that's larger than 2800
But this is larger than the largest possible sum we could have
Therefore we cannot have A = 8 and B = 2, so we can exclude this possibility
So we now know that A has to equal 9 and B has to equal 1, if there are any solutions
So is there any value of C that can make this possible?
Well let's add up what we know we have 999 + 111 which equals 1110
the final answer is 199C
so if we take 199C
minus 1110
we end up with 88C
So that the total reaches
1990 C by adding CCC, we must have C = 8
So we put that in and
we end up with something that works
This is our answer
We have 999 plus 111 plus 888 equals
1998
Did you figure it out ?
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