Mind Your Decisions. I'm Presh Talwalkar.
ABCDE x A = EEEEEE. [Six E's in a row.]
Each letter is a different digit.
The challenge is to solve for each letter.
This problem was given to nine-year-old students in Taiwan,
and it was considered so hard that it made the television news.
One teacher even took 20 minutes to solve this problem.
Can you figure it out?
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.
Here is one way to solve the problem.
First consider the case that A is equal to 1.
In that case, ABCDE x 1 = ABCDE [the same number].
This will NOT be equal to a six-digit number.
Therefore, A cannot be equal to 1.
We'll eliminate this possibility.
From here, let's consider the multiplication in the units column.
We have E multiplied by A is a number that has a units digit equal to E.
What numbers could result in this possibility?
We can work through the cases,
or you can consult a multiplication table.
From here, we can actually see which cases have E multiplied by A...
resulting in a number that ends in the digit E.
There are only eight possibilities.
We can further refine these
because each letter represents a different digit.
Therefore A cannot be equal to E.
And we'll remove two of the possibilities.
From here, we have only six possibilities,
which can be classified into two different cases.
We either have A is equal to 6,
or E is equal to 5.
Let's work out each of these cases.
First suppose A=6.
Where can we go from here?
We're going to convert this multiplication problem into a division problem.
Notice that if we have the resulting number divided by A,
we'll get ABCDE.
So let's work out each case.
Here, suppose E is equal to 2 and A is equal to 6.
We can then work out the following long division problem,
and we'll see which five-digit number results.
We get the following number [37,037], and the thing is,
it's not equal to ABCDE,
because we need each digit to be different.
We can then work through the other possibilities
in a similar fashion.
We can see that none of these possibilities will work.
Therefore, none of these cases will result in a solution to this problem.
So we eliminate all of these cases.
We then consider if E is equal to five.
We can again work out these long division problems.
Eventually we will get one case which COULD work.
And that will lead to our answer.
Here is the case that works.
And therefore, we have ABCDE multiplied by A
is equal to EEEEEE [the letter E six times].
And the number ABCDE
is A = 7, B = 9, C = 3, D = 6, and E = 5.
And THAT'S the answer to this problem!
Thanks for making Mind Your Decisions one of the best channels on YouTube.
See you next episode as we solve the world's problems one video at a time!