This is a devilishly clever (and difficult) logic puzzle by Hubert Phillips. Here's the where I found the puzzle, along with its solution.
I reproduce the puzzle here, as it is so good.
Thanks to Richard Harter, not only for creating the web site, but also for putting me right, when I failed at the problem on my first attempt.
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; and who lent Caliban an umbrella?
Above is the original wording of the puzzle, but there is a flaw. It is not possible to determine who lent the umbrella.