67. 

Portia, from Shakespeare's comedy "The Merchant of Venice," had three caskets: one of gold, one of silver, and one of lead. One of these caskets contained a portrait of Portia. A suitor was asked to choose a casket, and if he was lucky (or wise) enough to choose the casket with the portrait, he would have the right to call Portia his bride. On the lid of each casket, there was an inscription intended to help the suitor choose the "right" casket.

Suppose Portia decided to choose a husband not by virtue but by intelligence. She ordered the following inscriptions to be made on the lids of the caskets:

| On the gold | On the silver | On the lead |
| :--- | :--- | :--- |
| The portrait | The portrait | The portrait |
| is in this | is not in this | is not in the |
| casket | casket | gold casket |

Portia explained to her suitor that at least one of the three statements engraved on the caskets was true.

Which casket should the suitor choose?

$67 \mathrm{a}$.

The suitor correctly chose the casket with Portia's portrait, they got married, and lived happily (at least for a while). But one day, Portia had the following thoughts: "Although my husband, by choosing the casket with my portrait, showed a certain degree of intelligence, the task was not really that difficult. I should have come up with a more challenging puzzle. Then I would have a truly intelligent husband." Portia divorced her husband and decided to find a more intelligent spouse.

This time, she ordered the following inscriptions to be engraved on the caskets:

| On the gold | On the silver | On the lead |
| :--- | :--- | :--- |
| The portrait is | The portrait | The portrait |
| not in the silver | is not in this | is in this |
| casket | casket | casket |

Portia explained to her suitor that at least one of the three statements engraved on the caskets was true and at least one was false.

In which casket is Portia's portrait?

## Epilogue

By fate, the successful suitor for Portia's hand turned out to be her ex-husband. Being a wise man, he managed to solve the second puzzle as well. They got married again. Straight from the wedding, the husband brought Portia to their home, placed her on his knee, gave her a good spanking, and Portia was forever rid of foolishness.

## B. THE SECOND STORY

After remarrying, Portia and her husband lived happily. They had a daughter, Portia II, whom we will simply call Portia for brevity. When young Portia grew up, she became an exceptionally intelligent and beautiful young woman, just like her mother. She also decided to choose a husband "by the method of caskets." To win Portia's hand, a suitor had to pass two trials.
67. The statements engraved on the golden and lead caskets are opposite, so one of them must be true. Since no more than one of the three statements is true, the statement on the lid of the silver casket is false. Therefore, the portrait is actually in the silver casket.

This problem also allows for another solution. If the portrait were in the golden casket, we would have two true statements, contrary to the conditions of the problem. If the portrait were in the lead casket, we would also have two true statements (this time on the lead and silver caskets). Therefore, the portrait must be in the silver casket.

Both methods of solving the problem are entirely correct and serve as a vivid illustration of how in many problems several correct paths lead to the same conclusion.

67a. If the portrait were in the lead casket, all three statements would be true, contrary to the conditions of the problem. If the portrait were in the silver casket, all three statements would be false (also contrary to the conditions of the problem). Therefore, the portrait must be in the golden casket (then the first two statements are true, and the third is false, which is consistent with the conditions of the problem).