House Numbers
In a town of 16 houses built on a 4 x 4 grid, their distinct house numbers are arranged in ascending order both from left to right and from top to bottom.
Suppose I live in the bottom left house and Alice lives in another house. Since I can only look at the house numbers adjacent to me, I have devised the following strategy to find her:
- If the current house number is larger, look up.
- If the current house number is smaller, look right.
The diagram below shows an example arrangement of the 16 houses, where Alice lives in house number 8.
Does this strategy always guarantee that I will find Alice's house?
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