There were three medieval kingdoms on the shores of a lake. There was an
island in the middle of the lake, which the kingdoms had been fighting over for
years. Finally, the three kings decided that they would send their knights out
to do battle, and the winner would take the island. The night before the battle,
the knights and their squires pitched camp and readied themselves for the fight.

The first kingdom had 12 knights, and each knight had five squires, all of
whom were busily polishing armor, brushing horses, and cooking food. The second
kingdom had 20 knights, and each knight had 10 squires. Everyone at that camp
was also busy preparing for battle. At the camp of the third kingdom, there was
only one knight, with his squire. This squire took a large pot and hung it from
a looped rope in a tall tree. He busied himself preparing the meal, while the
knight polished his own armor.
When the hour of the battle came, the three kingdoms sent their squires out to
fight (this was too trivial a matter for the knights to join in). The battle
raged, and when the dust cleared, the only person left was the lone squire from
the third kingdom, having defeated the squires from the other two kingdoms, thus
proving that the squire of the high pot and noose is equal to the sum of the
squares of the other two sides.

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