Skip to the content

Putnam 1954 A2

Session A

Consider any five points $P_{1}, P_{2}, P_{3}, P_{4}, P_{5}$ in the interior of a square $S$ of side-length 1. Denote by $d_{i j}$ the distance between the points $P_{i}$ and $P_{i}$ . Prove that at least one of the distances $d_{i j}$ is less than $\sqrt{2} / 2$ . Can $\sqrt{2} / 2$ be replaced by a smaller number in this statement?

Dataset text PutnamGAP. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

Similar problems

These problems have the most words in common with this statement.

Locator putnam/1954/a2 · Tag YRZ4DYV05F · Edit this page on GitHub · Keys: j next, k previous