SOLUTION: Write one digit on each side of 10 to make a four digit multiple of 72. How many different solutions does this problem have?

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Question 805372: Write one digit on each side of 10 to make a four digit multiple of 72. How many different solutions does this problem have?
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
_10_

divisible by 72 --> divisible by 8 AND 9

The sum of the digits has to be a multiple of 9. If the digit is N, then 2N + 1 must be divisible by 9. We get N = 4.

N = 4 --> 4104/72 = 57

Even if you don't see this at first, there are only 9 digits you can use, and using brute force to find the solutions shouldn't take too much time.