One of my all-time favorite puzzles is Caliban’s will. I like to think of it as the ultimate logic puzzle. I have posted a version of it before in rec.puzzles and have run it in a fanzine. At first sight it seems outrageously incomplete. However with a bit of inference… One of the reasons that I like it is that I have never seen any other puzzle quite like it; another is that it is quite subtle in the levels of reasoning required. Here then, for your delectation, is Caliban’s Will.

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.”

What was the prescribed order of choosing; and who lent Caliban an umbrella?

If you tackle this, remember that every statement is necessary. Also remember that the requirement (that the puzzle represented by the three statements is properly constructed) is not part of the original puzzle — it is a meta-statement about the base puzzle. [People regularly get confused about this point.] One further point you have to consider — was the family solicitor correct in claiming (a) that the relevant data could be inferred and (b) that the order be inferred.