Problem 15 · 2011 Math Kangaroo
Medium
Spatial & Visual Reasoning
path-tracingspatial-reasoning
In each square of the maze there is a piece of cheese. Ronnie the mouse wants to enter and leave the maze as shown in the picture. He doesn’t want to visit a square more than once, but would like to eat as much cheese as possible. What is the maximum number of pieces of cheese that he can eat?
Show answer
Answer: C — 37
Show hints
Hint 1 of 2
Plan a single path from the entrance to the exit that never revisits a square.
Still stuck? Show hint 2 →
Hint 2 of 2
Try to weave through as many squares as the walls allow before leaving.
Show solution
Approach: trace the longest non-repeating path
- Starting at the entrance, follow the corridors so the path never crosses itself.
- The walls let the mouse snake through at most 37 of the squares before reaching the exit.
- So the greatest number of cheese pieces he can eat is 37.
Mark:
· log in to save