Problem 4 · 2011 Math Kangaroo
Medium
Logic & Word Problems
sum-constraint
In the picture a number should be written next to each point. The sum of the numbers on the corners of each side of the hexagon should be equal. Two numbers have already been written. Which number should be in the place marked ‘x’?
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Answer: A — 1
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Hint 1 of 3
Every side of the big hexagon must have the same corner-sum, so use the two known numbers to find what that common sum is.
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Hint 2 of 3
Two sides share a corner; comparing two sides that share a corner forces the opposite corners to be equal.
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Hint 3 of 3
Chain equal-sum sides from the 4 and the 1 around to the point marked x.
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Approach: use that adjacent equal-sum sides force matching opposite corners
- Each side of the outer hexagon holds the same total, so two sides meeting at one shared corner must have equal sums of their other corners.
- Following that equality around the ring, a corner is forced to match the corner two steps away, propagating the known values.
- Tracing from the 4 and the 1 to the marked point this way pins the value at x to 1.
- So the number at x is 1, choice (A).
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