Problem 13 · 2017 Math Kangaroo
Medium
Logic & Word Problems
sum-constraint
A number is written on each face of a special die. The two numbers on any pair of opposite faces always add up to the same total. Five of the six numbers are 5, 6, 9, 11 and 14. What is the number on the sixth face?
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Answer: E — 15
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Hint 1 of 2
Opposite faces share the same total, so the six numbers split into three pairs with equal sums.
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Hint 2 of 2
The biggest and smallest known numbers hint at the common pair-sum; find the missing partner.
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Approach: find the common pair-sum from two known numbers, then complete the last pair
- Opposite faces always add to the same total, so the six numbers split into three pairs that all share one sum.
- Among the five known numbers, 6 + 14 = 20 and 9 + 11 = 20, so that shared sum must be 20.
- The number 5 is left over, so its partner is the sixth face: 20 − 5 = 15.
- So the sixth face is 15 (E).
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