Many thanks to Tom Wilkinson for contributing this week's puzzle.

This week we have a two part problem.

Part A: I place 5 points in an equilateral triangle of side length 2 units. Show that there is a pair of points that are no more than 1 units apart.

Part B: Now I place 9 points in a sphere of radius 1. Show that there is a pair of points that are no more than √2 units apart.