Problem: The Sculptor's Problem

An ancient sculptor was commissioned to supply two statues, each on a cubical pedestal. It is with these pedestals that we are concerned. They were of unequal sizes, as will be seen in the illustration, and when the time arrived for payment a dispute arose as to whether the agreement was based on linear or cubical measurement.


But as soon as they came to measure the two pedestals the matter was at once settled, because, curiously enough, the number of linear feet was exactly the same as the number of cubical feet. The puzzle is to find the dimensions for two pedestals having this peculiarity, in the smallest possible figures. You see, if the two pedestals, for example, measure respectively $3$ ft. and $1$ ft. on every side, then the linear measurement would be $4$ ft. and the cubical contents $28$ ft., which are not the same, so these measurements will not do.

Solutions: 1

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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