Problem 6 · 2015 Math Kangaroo
Medium
Spatial & Visual Reasoning
path-tracing
How many of the following shapes can be drawn using one continuous line (i.e. without lifting the pencil) and without going over a line twice?
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Answer: D — 3
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Hint 1 of 2
A figure can be drawn in one stroke exactly when it has zero or two points where an odd number of lines meet.
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Hint 2 of 2
Count, at each crossing point, how many line-ends come together.
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Approach: Euler-path test: count odd-degree vertices
- A shape is traceable in one stroke (without retracing) exactly when it is connected and has at most two vertices where an odd number of edges meet.
- The circle with a line passing all the way through, and the two- and three-ring targets, each have only the two free line tips as odd vertices, so all three are traceable.
- The shape whose line stops on each side of the circle (two separate stubs) has four odd points and fails, leaving 3 drawable shapes (D).
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