Problem 8 · 2012 Math Kangaroo
Medium
Number Theory
digit-sum
The sum of the digits of a nine-digit number is 8. How big is the product of the digits of this number?
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Answer: A — 0
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Hint 1 of 2
Nine digits that add to only 8 — can they all be at least 1?
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Hint 2 of 2
If even one digit is 0, what happens to the product?
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Approach: a zero digit forces the product to vanish
- Nine positive digits would add to at least 9, but the sum is only 8.
- So at least one digit must be 0.
- A single 0 makes the product of all the digits 0.
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