Families, caskets and suitors
Back when the Bellini and Cellini families were still alive, an Italian noblewoman decided to test the intelligence of a prospective suitor, as she did not wish to marry a dullard. They had already fallen in love with each other, and she told him that she would hide a portrait of her in one of three caskets, all of which were made by either Bellini (who always inscribes true statements) or Cellini (who always inscribes false statements.) The noblewoman did not want the sons involved, as caskets made by the masters themselves were worth far more. So all three caskets were made by either Bellini himself or Cellini himself. If the suitor could find the casket with her portrait, he could marry the noblewoman. She clearly specified that the portrait would be in exactly one -- no more, no fewer -- of the caskets.
When he arrived, he was confronted with three large caskets made of the finest gold.
Casket A read: "The portrait is in here."
Casket B read, "The portrait is in here."
Casket C read, "At most one of these three caskets was fashioned by Bellini."
To win the noblewoman, which casket should he choose?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Let us assume that the statement on casket C is false. Then C was made by Cellini, and since the statement on it is false, the other two caskets must both be made by Bellini.
However, this is impossible, as then the portrait would be in both casket A and casket B, and the portrait can be in only one casket.
Therefore, since the assumption that the statement on C is false leads to a contradiction, the statement on C must be true. So casket C was made by Bellini. But since C's statement is true, both A and B must by made by Cellini. . So the statements on A and B are false, and the portrait is not in either A or B. Therefore it must be in casket C.