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Sunday Times Teaser 3129 – Bounce Count

by Brian Gladman on September 10, 2022

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?

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