Problem 20 · 2019 Math Kangaroo
Stretch
Spatial & Visual Reasoning
path-tracing
Anna places matches along the dotted lines to make a path. She has placed the first match as shown in the diagram. The path is built so that in the end it leads back to the left end of the first match. The numbers in the small squares tell how many sides of that square have a match on them. What is the smallest number of matches she can use?
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Answer: C — 16
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Hint 1 of 2
The numbers say exactly how many sides of each small square carry a match.
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Hint 2 of 2
Build one closed loop that meets all those counts using as few matches as possible.
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Approach: build the cheapest closed loop fitting the side-counts
- Each labelled square must have exactly the stated number of its four sides covered by matches.
- The matches form one closed path returning to the start, which constrains how edges join up.
- The smallest such loop satisfying every count uses 16 matches.
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