Problem 5 · 2019 Math Kangaroo
Easy
Spatial & Visual Reasoning
path-tracing
Show answer
Answer: D — Diagram D.
Show hints
Hint 1 of 2
A figure can be traced in one stroke only if it has 0 or 2 corners where an odd number of lines meet.
Still stuck? Show hint 2 →
Hint 2 of 2
Count the lines meeting at each corner of every figure.
Show solution
Approach: Euler trail: count odd-degree vertices
- A drawing can be made in one stroke exactly when at most two of its points have an odd number of lines meeting there.
- In figure D (a square with both diagonals) each of the four corners has three lines meeting — four odd points.
- Four odd points is too many, so D cannot be drawn without lifting the pencil or retracing.
- So the answer is D.
Mark:
· log in to save