T2B29

C. INTRODUCING BELLINI AND CELLINI
The suitor of the last tale passed both tests and happily claimed Portia II as his bride. They lived happily ever after and had a lovely daughter Portia III-henceforth to be called "Portia." When she grew up to young womanhood, she was born smart and beautiful-just like her mommy and grandmommy. She also decided to choose her husband by the casket method. The suitor had to pass three tests in order to win her! The tests were quite ingenious. She went back to her grandmother's idea of having only one state­ ment inscribed on each casket rather than two. But she introduced the following new wrinkle: She explained to the suitor that each casket was fashioned by one of two famous Florentine craftsmen-Cellini or Bellini. Whenever Cellini fashioned a casket, he always put a false inscription on it, whereas Bellini put only true inscriptions on his caskets.

69a. The First Test. In this unusual test the suitor (if he guessed blindly) would have a two out of three rather than a one out of three chance. Instead of using a portrait, Portia used a dagger which was placed in one of the three caskets; the other two caskets were empty. If the suitor could avoid the casket with the dagger, then he could take the next test. The inscrip­ tions on the caskets were as follows:
Gold
THE DAGGER IS IN THIS CASKET

Silver
THIS CASKET IS EMPTY

Lead
AT MOST ONE OF THESE THREE CASKETS WAS FASHIONED BY BELLINI

The Answer:
Suppose the lead casket had been fashioned by Bellini. Then the statement would be true, hence the other caskets must have been fashioned by Cellini. This means that the other statements are both false-in particular the state­ ment on the silver casket is false, so the dagger is in the silver casket. Thus, if the lead casket is the work of Bellini, then the silver casket contains the dagger. Now, suppose the lead casket had been fashioned by Cellini. Then the statement is false, so at least two caskets were fashioned by Bellini. This means that both the gold and silver caskets are Bellini caskets (since the lead one is assumed Cellini). Then the statements on both the gold and silver are true. In particular, the one on the gold is true. So in this case, the dagger lies in the gold casket. In neither case can the dagger be in the lead casket, so the. suitor should choose the lead casket.