Logic

[ralphmelton]

I've been slowly working my way through Raymond Smullyan's book What Is the Name of This Book? over the past few weeks, since I picked it up in Half-Price Books.

Historically, which this sort of puzzle book, I have a strong tendency to wimp out. When the puzzles get too tough to solve easily, I turn to the answers. But this time, I've been trying hard to be more persistent and solve the problems myself.

One problem (appended below) really stumped me:

The problem deals with small silver and gold caskets. All caskets of interest are made by one of two families: Bellini or his sons, or Cellini or his sons. Caskets made by Bellini or his sons only have true inscriptions on them; caskets made by Cellini or his sons only have false inscriptions on them. The problem, then, is to find a pair of inscriptions that for two caskets that has the following properties:
- From reading both inscriptions, a logician is able to conclude that one was made by Bellini and one was made by Cellini, but not to determine which was made by which.
- It is not possible to draw that conclusion from reading only one of the inscriptions.

I had been gnawing on it for at least a week, possibly more. But finally, as I was going to sleep on Saturday night, I figured out an answer. I felt very proud.

Comments

one more question

[cellio]

From reading both inscriptions, a logician is able to conclude that one was made by Bellini and one was made by Cellini, but not to determine which was made by which.

Bellini and Cellini specifically, and not their sons?

Re: one more question

[ralphmelton.livejournal.com]

Yes, Bellini and Cellini specifically.