Sunday Times Teaser 3054 – Discs A Go-Go
by Howard Williams
Published Sunday April 04 2021 (link)
My kitchen floor is tiled with identically-sized equilateral triangle tiles while the floor of the bathroom is tiled with identically-sized regular hexagon tiles, the tiles being less than 1m across. In both cases the gaps between tiles are negligible. After much experimenting I found that a circular disc dropped at random onto either the kitchen or bathroom floor had exactly the same (non-zero) chance of landing on just one tile.
The length of each side of the triangular tiles and the length of each side of the hexagon tiles are both even triangular numbers of mm (ie, of the form 1+2+3+…).
What are the lengths of the sides of the triangular and hexagonal tiles?