March 11th, 2002



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.