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Number theory Difficulty 5.0 AIME, harder Prove it United Kingdom

In the UK, 1p, 2p and 5p coins have thicknesses of $1.6$ mm, $2.05$ mm and $1.75$ mm respectively.

Using only 1p and 5p coins, Joe builds the shortest (non-empty) stack he can whose height in millimetres is equal to its value in pence. Penny does the same but using only 2p and 5p coins.

Whose stack is more valuable?

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.