GK 2019 Q1
1. Which of the diagrams below cannot be drawn without lifting your pencil off the page and without drawing along the same line twice?
Grey Kangaroo 2019, Question 1. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D
It is known that any diagram with at most two points where an odd number of lines meet can be drawn without lifting your pencil off the page and without drawing along the same line twice. Any diagram with more than two such points cannot be drawn in this way. Of the options given, only diagram D has more than two such points. Hence the diagram which cannot be drawn is D.
Solution © UK Mathematics Trust, from the GK 2019 solutions.