Problem 14 · 2022 Math Kangaroo
Stretch
Spatial & Visual Reasoning
path-tracing
Dino walks from the entrance to the exit. He is only allowed to go through each room once. The rooms have numbers (see diagram). Dino adds up all the numbers of the rooms he walks through. What is the biggest result he can get this way?
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Answer: D — 34
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Hint 1 of 3
For the biggest total, Dino should try to walk through as many rooms as he can.
Still stuck? Show hint 2 →
Hint 2 of 3
Add up all eight room numbers first - then see whether the doorways really let him visit every single room.
Still stuck? Show hint 3 →
Hint 3 of 3
He cannot quite reach all eight; find the path that misses only the room worth the least points.
Show solution
Approach: add up all the rooms, then leave out the one room you are forced to skip
- All eight room numbers add up: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36, so the most he could ever score is 36.
- Trying paths through the doorways from the entrance (room 1) to the exit (room 8) without repeating a room, Dino cannot fit in every room - the best route leaves out exactly one room, and the smallest he can skip is room 2.
- So his biggest total is 36 − 2 = 34, which is answer D.
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