Problem 5 · 2012 Math Kangaroo
Easy
Number Theory
digit-sum
The digit sum of a six-digit number is 5. How big is the product of the digits?
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Answer: A — 0
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Hint 1 of 2
A six-digit number has six digits, but they only add up to 5.
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Hint 2 of 2
Six positive digits would already add to at least 6 — so what must at least one digit be?
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Approach: forced zero digit
- The number has six digits whose sum is only 5.
- If every digit were at least 1 the sum would be at least 6, which is too big.
- So at least one digit must be 0, and a product with a factor of 0 is 0.
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