Problem 30 · 2020 Math Kangaroo
Stretch
Logic & Word Problems
careful-countingcasework
The map shows some islands connected by bridges. A navigator wants to visit each island exactly once. He started at Cang Island and wants to finish at Uru Island, and he has just reached the black island in the centre. In which direction must he go now to be able to complete his route?
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Answer: C — South.
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Hint 1 of 2
He has to visit every island exactly once, so the move he makes now must not strand any island he still needs to reach.
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Hint 2 of 2
If he picks a direction that walks him into a dead-end corner before the rest are visited, he can never get back; only one direction keeps a path open all the way to Uru.
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Approach: choose the only move that leaves a single-visit path to Uru
- He must pass through each island once and finish at Uru, so from the centre he cannot step toward any group of islands he would later be unable to leave.
- Going North, East or West leads him into a part of the map he would have to enter or leave twice, leaving some island unvisited.
- Heading South is the one move that still lets him reach every remaining island exactly once and end at Uru.
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