Problem 20 · 2021 Math Kangaroo
Stretch
Logic & Word Problems
caseworksum-constraint
Mia throws darts at balloons worth 3, 9, 13, 14 and 18 points. She scores 30 points in total. Which balloon does Mia definitely hit?
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Answer: A — 3
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Hint 1 of 2
Find every set of balloon values that adds up to 30.
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Hint 2 of 2
The balloon that appears in all of those sets is the one she definitely hit.
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Approach: list the subsets summing to 30 and find the common balloon
- Balloons are 3, 9, 13, 14, 18. The sums making 30 are 3+9+18 and 3+13+14.
- Both winning sets include the balloon worth 3.
- So whichever way she scored 30, she hit the 3.
- She definitely hit balloon 3 (A).
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