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Portia returns

December 13, 2007

Our friend Portia is back with another problem for us. This time she puts her picture into one of three caskets and places the following inscriptions on them:

Gold casket: The portrait is in here.
Silver casket: The portrait is in here.
Lead casket: At least two of the caskets have a false inscription.

Which casket should the suitor choose? Read more

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A problem courtesy of Shakespeare

November 29, 2007

This note is about a powerful tool for solving problems, viz. calculation. Consider the following problem from Shakespeare’s The Merchant of Venice:

Portia has a gold casket and a silver casket and has placed a picture of herself in one of them. On the caskets she has written the following inscriptions:

Gold: The portrait is not here.
Silver: Exactly one of these inscriptions is true.

Portia explains to her suitor that each inscription may be true or false, but that she has placed her portrait in one of the caskets in a manner that is consistent with this truth or falsity of the inscriptions. If he can choose the casket with her portrait, she will marry him. The problem for the suitor is to use the inscriptions (although they may be either true or false) to determine which casket contains her portrait.

How can we solve this problem? Read more