Problem 20 · 2009 Math Kangaroo
Stretch
Logic & Word Problems
sum-constraintcasework
The diagram shows an object with 6 triangular faces. There is a number at each corner (two of them are shown). The sum of the numbers at the corners of each triangular face is the same. What is the sum of all 5 numbers?
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Answer: C — 17
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Hint 1 of 2
Equal triangle sums tie the corner numbers together — use the two shown values 1 and 5.
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Hint 2 of 2
Pair up the corners so each triangle's sum matches, then add all five corners.
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Approach: equal face sums
- Every triangular face has the same corner sum, which links the five corner numbers.
- Fitting the shown 1 and 5 into that condition forces the remaining corners.
- Adding all five corner numbers gives 17 — answer C.
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