Question 1098024: How many three digit integers are increased by exactly 99 when the digits are reversed?
Answer by ikleyn(52824)   (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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