239 sats \ 2 replies \ @Scroogey 9 Oct \ parent \ on: [Daily puzzle] Maximum distance between 5 points in a square? science
This assumes that the optimal placement is the four corners and the center.
The 'pigeonhole principle' can be used to prove your answer is correct no matter the placement:
Divide the square into four equal smaller squares (in the obvious way).
At least one of these squares must contain two points.
The maximum distance of two points in a square of length 1/2 is 1/sqrt(2).
pigeonhole principle
Was hoping for someone to bring up this pigeonhole principle.
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I like it. I'm quite out of practice at doing proofs. Maybe these daily puzzles will get me back to peak form.
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