## Note:

## The "Sultan's Dowry" problem

A sultan has granted a commoner
a chance to marry one of his hundred daughters. The commoner will be
presented the daughters one at a time. When a daughter is presented,
the commoner will be told the daughter's dowry. The commoner has only
one chance to accept or reject each daughter; he cannot return to a
previously rejected daughter. The sultan's catch is that the commoner
may only marry if he chooses the daughter with the highest dowry.
What is the commoner's best strategy assuming that he knows nothing
about the distribution of dowries?

## The answer

The answer (without all of the
probabilistic math) is that the commoner should wait until he has seen
37 of the daughters, and then choose the first one with a dowry bigger
than any so far. With this strategy, the odds of choosing the
daughter with the highest dowry are about 37%.