Problem 7 · 2025 Math Kangaroo
Medium
Spatial & Visual Reasoning
path-tracingwork-backward
A student throws five stones in turn, hitting a window at points A, B, C, D and E. Whenever a stone hits the window, it creates cracks starting from that point. These cracks end either at the edge of the window or at an existing crack. In which order did he throw the stones?
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Answer: A — DACBE
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Hint 1 of 3
A crack can only stop on a crack that already exists, so "X's crack ends on Y's crack" means Y was thrown before X.
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Hint 2 of 3
Find the stone whose cracks all run to the window edge—that one must be first.
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Hint 3 of 3
Then repeatedly pick the next stone whose cracks only touch the edge or already-placed points.
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Approach: order the throws by which cracks land on earlier cracks
- \(D\)'s cracks reach only the window edge, so \(D\) was thrown first.
- Next, \(A\)'s crack ends on \(D\)'s, then \(C\)'s ends on \(A\)'s, then \(B\)'s ends on \(C\)'s, and finally \(E\)'s ends on \(B\)'s.
- So the order is \(D, A, C, B, E\), choice (A).
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