A curious logic problem by Cambridge mathematician Max Newman, published in Hubert Phillips’ New Statesman puzzle column in 1933:
When Caliban’s will was opened it was found to contain the following clause:
‘I leave ten of my books to each of Low, Y.Y., and ‘Critic,’ who are to choose in a certain order:
- No person who has seen me in a green tie is to choose before Low.
- If Y.Y. was not in Oxford in 1920 the first chooser never lent me an umbrella.
- If Y.Y. or ‘Critic’ has second choice, ‘Critic’ comes before the one who first fell in love.’
Unfortunately, Low, Y.Y., and ‘Critic’ could not remember any of the relevant facts; but the family solicitor pointed out that, assuming the problem to be properly constructed (i.e., assuming it to contain no statement superfluous to its solution) the relevant data and order could be inferred. What was the prescribed order of choosing?