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Without digging too deeply into this question, we can see immediately that it has no solution.

-- The largest possible sum of 3 digits is (9 + 9 + 9) = 27

-- 3 times (the largest possible sum of 3 digits) is (3 x 27) = 81

-- 3 times the largest possible sum of 3 digits is smaller than any 3-digit number.

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Q: What 3 digit number ia 3 times the sum of its digits?
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