Problem 12 · 2010 Math Kangaroo
Medium
Algebra & Patterns
sum-constraint
Which of the following two-digit numbers is the smallest that cannot be made by adding three different single-digit natural numbers?
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Answer: D — 25
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Hint 1 of 2
Three different single-digit numbers go from 1+2+3 up to 7+8+9.
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Hint 2 of 2
Find the largest sum you can reach, then the first two-digit number above it.
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Approach: find the reachable range, pick the first gap
- Three different digits 1–9 sum to at most 7+8+9 = 24, and every value up to 24 is reachable.
- Every listed value up to 23 can be made; the smallest two-digit number that cannot be made is 25 (it exceeds the maximum 24).
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