Problem 7 · 2012 Math Kangaroo
Medium
Number Theory
digit-sum
The digit sum of a seven digit number is 6. What is the product of the digits?
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Answer: A — 0
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Hint 1 of 2
A seven-digit number has seven digits; their sum is only 6.
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Hint 2 of 2
Seven positive digits would already sum to at least 7, so some digit must be 0.
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Approach: show a zero digit is forced, killing the product
- If all seven digits were at least 1, their sum would be at least 7, but the sum is only 6.
- So at least one digit must be 0.
- Any product that includes a 0 is 0.
- The product of the digits is 0 (A).
Mark:
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