XYZ is a 3-digit number, where X, Y, Z are distinct non-zero digits. The difference between the two 3-digit numbers XYZ and YXZ is 90. How many possible values exist for the sum (X+Y) ?

Explanation

The value of XYZ = 100X+10Y+Z and YXZ = 100Y+10X+Z. The difference is 90|X-Y| = 90 \implies |X-Y| = 1. The adjacent non-zero digit pairs (X,Y) are (1,2), (2,3), ..., (8,9) and their reverses. The unique sums X+Y are 3, 5, 7, 9, 11, 13, 15, 17, which amounts to 8 possible values.

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