Indeed. I took "inside" as implying an open set.

Undisciplined

I'll second this, with the added note that if the square is a closed set you don't have to say arbitrarily close to the corner :)


SimpleStacker

> pigeonhole principle

Was hoping for someone to bring up this [pigeonhole principle](https://en.wikipedia.org/wiki/Pigeonhole_principle).

south_korea_ln

I like it. I'm quite out of practice at doing proofs. Maybe these daily puzzles will get me back to peak form.

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).

Scroogey

science

[Daily puzzle] Maximum distance between 5 points in a square?

I'll take half of the square root of 2. One point arbitrarily close to each corner and one in the center.