358 Frequently Asked Questions In Quantitative Finance
Muddy faces A group of children are playing and some of
them get mud on their foreheads. A child cannot tell if
he has mud on his own forehead, although he can see
the mud on the foreheads of any other muddy children.
An adult comes to collect the children and announces
that at least one of the children has a dirty forehead,
and then asks the group to put up their hand if they
know that they have mud on their forehead. How can
each child determine whether or not their forehead is
muddy without communicating with anyone else?
(Thanks to weaves.)
Pirate puzzle There are 10 pirates in a rowing boat. Their
ship has just sunk but they managed to save 1000 gold
doubloons. Being greedy bastards they each want all the
loot for themselves but they are also democratic and
want to make the allocation of gold as fair as possible.
But how?
They each pick a number, from one to 10, out of a hat.
Each person in turn starting with number one, decides
how to divvy up the loot among the pirates in the boat.
They then vote. If the majority of pirates approve of the
allocation then the loot is divided accordingly, other-
wise that particular pirate is thrown overboard into the
shark-infested sea. In the latter case, the next pirate in
line gets his chance at divvying up the loot. The same
rules apply, and either the division of the filthy lucre
gets the majority vote or the unfortunate soul ends up
in Davy Jones’s locker.
Question, how should the first pirate share out the
spoils so as to both guarantee his survival and get a
decent piece of the action?
