# Back to Back

Pro Problems > Math > Number and Quantity > Number Theory > Digits## Back to Back

X is a three-digit number. Y is the number obtained when the digits of X are reversed. Z is the six-digit number obtained by writing X and Y back to back, with X written first. W is the six-digit number obtained by writing Y and X back to back, with Y written first. What is the largest number which the sum of Z and W must be divisible by?

## Solution

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The product of my digits is 600.

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- The product of two of my digits is 8.
- The sum of my digits is 13.
- My first digit is four times my second digit.

What number am I?

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_ _ _ x _ _ x _ =

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If you subtract my first, second, and third digit from my last digit, you get a perfect square.

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