Problem 19 · 2018 Math Kangaroo
Stretch
Spatial & Visual Reasoning
path-tracing
The rooms in Kanga’s house are numbered. Eva enters through the main entrance. She must walk through the rooms so that each room she enters has a higher number than the previous one. Through which door does Eva leave the house?
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Answer: D — D
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Hint 1 of 3
Start at the entrance and only ever step into a room whose number is bigger than the room you are leaving — never into a smaller or equal one.
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Hint 2 of 3
From each room, look at the rooms next to it and walk to one with a higher number; this forces your route step by step.
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Hint 3 of 3
Keep climbing to higher numbers until you reach the bottom wall, and see which door A–E you come out of.
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Approach: walk from the entrance always stepping into the next room only if its number is larger, which pins down a single route to the exit
- From the main entrance Eva can step into a neighbouring room only when its number is larger than the one she is in, so at every step she has just the higher-numbered neighbour to choose.
- Following that climbing-numbers rule, she is funnelled along one route down through the house, since any move to an equal or smaller number is blocked.
- That single increasing path brings her to the bottom row and out through door D, answer D.
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