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?