take any 3-digit integer, reverse its digits, and subtract.

For example 742-247 = 495

This difference is divisible by 9.

Prove that, this must happen for all 3-digit numbers

Thank you in advance (Rofl)

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- Nov 12th 2008, 09:41 PMsabrina87prove that ...
take any 3-digit integer, reverse its digits, and subtract.

For example 742-247 = 495

This difference is divisible by 9.

Prove that, this must happen for all 3-digit numbers

Thank you in advance (Rofl) - Nov 12th 2008, 09:55 PMsabrina87SOLUTION
Any 3 digit number can be represented as

100x + 10y + z and its reverse would be

100z + 10y - x

Their difference would be

100(x-z) + (z-x) which can be written as 99(x-z).

99(x-z) is always divisable by 9

TRUE?