SAMPLE PROBLEM
A team of three people meet and have the rules of the game
below described to them. They then have a strategy session.
Afterwards, they are taken into a room, and each person has a random 0
or 1 placed on their forehead (i.e., all 8 placements are equally
likely). They can see the numbers on the other two foreheads, but not
their own. Then they are each *simultaneously* and *without any
communication* required to make one of the following three statements:
"there is a 0 on my forehead", "there is a 1 on my forehead", or "I
pass". The team collectively shares a one million dollar prize if and
only if at least of them doesn't pass, and *all* non-pass statements
that are made are true statements.
An obvious strategy that gives them a 50/50 chance of collecting the
million dollars is for them to agree in the strategy session that
Alice will guess randomly and that the others will pass. Is there any
strategy that they can choose that gives them a better than 50/50
chance of winning?
The actual topics of the talk are (a) discrete geometry, and
(b) probability.
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