We analyse an inverse problem for water waves posed by Richard Feynman in the BBC documentary Fun to Imagine. The problem can be modelled as an inverse Cauchy problem for gravity-capillary waves on a bounded domain. We do a detailed analysis of the Cauchy problem and give a uniqueness proof for the inverse problem. This results, somewhat surprisingly, in a positive answer to Feynman's question. In addition, we derive stability estimates for the inverse problem both for continuous and discrete measurements, propose a simple inversion method and conduct numerical experiments to verify our results.