Problem 1 · 2011 Math Kangaroo
Easy
Logic & Word Problems
sum-constraint
In the picture on the right a number is written next to each marked point. Along every side of the large hexagon, the numbers at the points must add up to the same total. Two numbers are already filled in. Which number belongs at the point marked x?
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Answer: A — 1
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Hint 1 of 2
Every side of the hexagon must reach the same total, and two corner numbers are already fixed.
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Hint 2 of 2
Lock the common side-total from a side whose numbers you know, then carry it around to the side that contains x.
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Approach: use the equal side-sums to chase the value around to x
- Every side of the large hexagon must carry the same point-total, and the sides through the corners 4 and 1 let you pin that common total.
- Following the constraint from corner to corner around the hexagon forces each remaining value in turn.
- The point marked x is forced to be 1.
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