Problem 1 · 2024 Math Kangaroo
Easy
Spatial & Visual Reasoning
path-tracing
The diagram on the right is made up of five-sided tiles of equal size. Which tile can be inserted in the missing spot so that two closed lines are formed?
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Answer: C
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Hint 1 of 2
The grid in the corner already has lines running into the empty slot; the inserted tile must continue them.
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Hint 2 of 2
You need the two arcs in the hole to join up into exactly two separate closed loops, so match where each line meets the tile's edges.
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Approach: match the line endpoints so the curves close into two loops
- Look at where the existing curves hit the boundary of the missing pentagon-shaped slot.
- The added tile must have its two arcs touch those same edge points so the strokes connect.
- Only the tile whose arcs link the open ends into two complete closed lines works.
- That tile is C.
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