If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?

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222

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Official Explanation

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Using THREE non-zero digits a, b, c only, we can construct 3! = 6 numbers: abc, acb, bac, bca, cab, cba.

Their sum will be:

x = (100a + 10b + c) + (100a + 10c + b) + (100b + 10a + c) + (100b + 10c + a) + (100c + 10a + b) + (100c + 10b + a)

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What this question tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.