T2B31

Third Tale Third Puzzle

69c. The Third Test
If the suitor passed these two tests, he was led into another room containing a gold, silver, and lead casket. Again, each casket was fashioned by either Cellini or Bellini. Now in this test, the suitor's chances were one out of three (if he guessed blindly); Portia used a portrait of herself, and the portrait was in one of the caskets. To pass the test, the suitor had to (1) select the casket containing the portrait; (2) tell the maker of each casket. The three inscriptions read:

Gold
THE PORTRAIT IS NOT IN HERE

Silver
THE PORTRAIT IS NOT IN HERE

Lead
AT LEAST TWO OF THESE CASKETS WERE FASHIONED BY CELLINI

What is the solution?

The Answer:
We first show that the lead casket must be a Bellini. Sup­ pose it were a Cellini. Then the statement is false, which means that there must be at least two Bellinis, which must be silver and gold. This is impossible, since the portrait can't be in both the silver and gold caskets. Thus the lead casket is really a Bellini. Hence the statement on it is true, so there are at least two Cellinis. This means that the gold and silver are both Cellinis. Hence the statements on both of them are false, so the portrait is neither in the gold nor the silver caskets. Therefore the portrait is in the lead casket. Also, we have proved that the lead casket is a Bellini and the other two are Cellinis, which answers the second question.