Problem 28 · 2023 Math Kangaroo
Stretch
Logic & Word Problems
caseworksum-constraint
The numbers from 1 to 11 are written in the empty hexagons. The sums of the three numbers in three hexagons with a common bold point are always equal. Three of the eleven numbers are already written in (see diagram). Which number is written in the hexagon with the question mark?
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Answer: E — 9
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Hint 1 of 2
Each bold point ties three hexagons to a common sum.
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Hint 2 of 2
Chain those equal-sum conditions across the honeycomb, using the three given numbers.
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Approach: propagate the equal-triple-sum conditions
- Every bold point forces its three surrounding hexagons to share one common sum value.
- Linking these conditions with the placed numbers 6, 4 and 11 and the requirement that 1–11 each appear once determines the value at the marked hexagon.
- It works out to 9.
Mark:
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