Problem 24 · 2023 Math Kangaroo
Stretch
Spatial & Visual Reasoning
path-tracingcasework
Monika wants to find a path through the maze from “Start” to “Ziel”. She may only move horizontally or vertically. She must enter every white circle exactly once and may not enter any black circle. In which direction must Monika move when she reaches the circle marked with x?
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Answer: A — ↓
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Hint 1 of 3
A circle in a corner or with black circles around it usually has only one open neighbour, so its move is forced.
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Hint 2 of 3
Start filling in those forced moves first, because each one locks in the next.
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Hint 3 of 3
By the time the forced path reaches x, only one direction keeps every remaining white circle reachable exactly once.
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Approach: use the must-visit-each-white-circle-once rule to force the path at x
- Monika moves only horizontally and vertically, must enter every white circle exactly once, and cannot enter a black circle.
- Near corners and beside black circles, several moves are forced because there is only one legal way through.
- Tracing these forced moves up to the circle marked x leaves exactly one direction that still lets the path reach every remaining white circle: downward.
- So at x she must move down, answer A.
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