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2026
A is a 2-digit number with different digits. B is also a 2-digit number and is obtained by reversing the digits of A. If A − B is a multiple of 27, where A > B, how many such different A's are possible?
Explanation
For a 2-digit number A = 10a + b and its reverse B = 10b + a, A - B = 9(a - b). A - B is a multiple of 27 implies 9(a - b) is a multiple of 27, leading to a - b being a multiple of 3. The digits a and b (1 ≤ a ≤ 9, 0 ≤ b ≤ 9) can differ, giving pairs (a, b) such that a - b is 3, 6, or 9, leading to 9 valid combinations for A.
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