SOLUTION: How many three digit integers are increased by exactly 99 when the digits are reversed?

Algebra.Com
Question 1098024: How many three digit integers are increased by exactly 99 when the digits are reversed?
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
The necessary and sufficient condition for it is that 

    The "ones" digit is 1 more than the "hundreds" digit.

    And if this condition is in place, then it does not matter what the "tens" digit is.

Based on it, all the 3-digit numbers 
     1x2,  2x3,  3x4,  4x5,  5x6,  6x7,  7x8,  8x9

work,  for any   x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

In all,  you have  10*8 = 80 numbers satisfying the condition.




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