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Pigeonhole principle.
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Five points are placed anywhere  on an equilateral triangle
of side 1, show that at least two points will be no farther
apart than 0.5.

Five points are placed in or on a square of side 1, then show
that at least one pair of points will be no farther apart
than half the square root of 2.

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Probability
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A spider eats three flies a day.  Until he fills his quota
he has an even chance of catching any fly that attempts to
pass.  A fly is about to make the attempt. What are
the chances of survival, given that five flies have already
made the attempt today?



Smith's chance of hitting his target on a given shot is twice
that of his fellow prison guard Jones. One dark night they
each had time to fire one shot at an escaping prisoner.
Given that the prisoner had a even chance of avoiding injury
what kind of marksman was Jones?


Prove that at a recent convention of MIT alumni that the
number of alumni who shook hands an odd number of times
is even.


3n disks are stacked in decreasing order of diameter on
a TOH peg. There are n red, n yellow and n blue disks
in RYB cyclic order beginning from the bottom.  Using the
standard TOH rules, give a recursive algorithm to form three
stacks, one red, one yellow and one blue.
