Test your brain on Caliban's will

[Kit-Ginevra]

I found this in a book of puzzles I got for Christmas and at first it just made my brain go and wonder what on Earth I'd stumbled upon. Apparently the guy who set it taught Alan Turing some puzzles and inspired him to join the Bletchley Park mob so that's the level of brain fiendishness we are dealing with.




Caliban's will was opened and found to contain the following clause.

'I leave ten of my books each to Low,YY and 'The Critic'
1.No person who has seen me in a green tie is to choose before Low
2.If YY was not in Oxford in 1920,then the first chooser never lent me an umbrella
3.If YY or 'The Critic' has second choice,then 'The Critic' comes before the one who first fell in love.'

Nobody could remember any of these facts,but the family solicitor pointed out that assuming the puzzle contained no superfluous statements it could easily be solved.

In which order were the recipients to choose the books?'

[mjr]

'I leave ten of my books each to Low,YY and 'The Critic'
1.No person who has seen me in a green tie is to choose before Low
2.If YY was not in Oxford in 1920,then the first chooser never lent me an umbrella
3.If YY or 'The Critic' has second choice,then 'The Critic' comes before the one who first fell in love.'

Let's see...(spoilers)

1. This means that either YY or The Critic have seen Caliban in a green tie. Meaning that either YY or The Critic cannot choose before Low. Which we can assume that Low is first chooser. Which means that at this point YY or the Critic would choose 2nd.

2. This also means that YY was not in Oxford (since Low is first), and therefore Low did not lend Caliban the umbrella.

3. Since YY or The Critic are not the first to choose, The Critic would have second choice, and YY would have third.