Here are two puzzles with surprising solutions, and a paradox that
has fooled many professional mathematicians:
Puzzle no.
1
Connect the dots with four straight lines, without lifting
the pen.
Solution.


Puzzle no.
2
Form four equilateral triangles with six match sticks (without breaking
them).
Solution.
Monty
Hall's Paradox
This paradox is named for the host of a famous gameshow in the U.S.
in the 1960s. It has confounded a lot of people, including a number
of professional mathematicians, because of its counterintuitive nature.
See this
description, or any of a number of sites dedicated to the paradox.
Tit for tat
This is a strategy to handle the Prisoner's
Dilemma, a wellknown problem in Game Theory. The problem can
be stated as follows:
Two prisoners A and B are being questioned separately. If one confesses,
he goes free, while the other gets a 10year sentence. If both confess,
they each get a 5year sentence. If both refuse to confess, they each
get a 6month sentence.
In real life, of course your choice would be heavily influenced by
your assessment of the character of your fellow prisoner. But game
theorists are more interested in the optimal strategy when both prisoners
are completely rational (selfserving), and the game is repeated many
times. Many strategies have been discussed and tried in computer simulations.
It has turned out that the best strategy in the long run is to cooperate
with your fellow prisoner. If he defects on you, you should immediately
follow suit, hence the nickname "tit for tat".
During a management conference in the 1990s, I was subjected to a
variation of this game, along with a number of my colleagues at the
Swedish Space Corporation. As I recall, we played 8 rounds of the
game. Obviously, the consultant who ran the seminar had an agenda:
he wanted to demonstrate the value of trust and cooperation.
It did not turn out that way. The cowinners were a colleague of
mine and myself. We had both read an article in Scientific American
on the Prisoner's Dilemma problem and the TitforTat strategy. We
both chose to defect in round 7, reasoning that several of our colleagues
might defect in round 8, as there could be no penalty for doing so.
The way points were calculated, no one could catch us in round 8,
even when they tried to punish us by defecting themselves.
From the point of view of the seminar leader, this was of course
a fiasco. He lamely reminded us that "next time" we would
suffer the consequences, but of course there was no next time. The
wrath of our colleagues only added to our pleasure!