Sunday Times Teaser 3129 – Bounce Count
by Mark Valentine
Published Sunday September 11 2022 (link)
At the local arcade, Claire and David played an air hockey game, consisting of a square table with small pockets at each corner, on which a very small puck can travel 1m left-right and 1m up-down between the perimeter walls. Projecting the puck from a corner, players earn a token for each bounce off a wall, until the puck drops into a pocket.
In their game, one puck travelled 1m farther overall than its left-right distance (for the other, the extra travel was 2m). Claire’s three-digit number of tokens was a cube, larger than David’s number which was trianglular (1+2+3+…). Picking up a spare token, they could then arrange all their tokens into a cube and a square combined.
How many tokens did they end up with?