The difference 942-249 is a positive multiple of 7. If a, b, and c are nonzero digits, how many 3-digit numbers abc are possible such that the difference abc - cba is a positive multiple of 7?
142
71
99
20
18
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100a + 10b + c - (100c + 10b + a) = 99*(a - c) 要是7的倍数，那么 a - c 必须要是7的倍数 由于a, b, c 为非零 只能是 a = 9, c = 7 a = 8, c = 1 b为任意1到9 故 9 + 9 = 18
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100a + 10b + c - (100c + 10b + a) = 99*(a - c) 要是7的倍数，那么 a - c 必须要是7的倍数
由于a, b, c 为非零
只能是
a = 9, c = 7
a = 8, c = 1
b为任意1到9
故 9 + 9 = 18
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