Pythagorean fun

spotted this one today:

Once upon a time there were three kingdoms, all bordered on a single lake. In the middle of the lake was a hotly contested island. After decades of fighting over it, the three kings decided to end the dispute, once and for all. Each kingdom would send its best knights to the island and have an all-out fight. The last man standing wins the island for his kingdom.

The first kingdom is large and wealthy. It sends 50 knights, each with three squires. They arrive the day before the big fight and prepare. The knights drill and carouse, eat and drink, and tell stories of their bravery all night while the squires cook, shine armor, serve food and prepare weapons.

The second kingdom is not as wealthy, but still quite well off. They send 25 knights, each with two squires. They also arrive the night before and prepare. The knights drill and carouse, eat and tell stories while the squires cook, shine armor, sharpen weapons and prepare for battle.

The third kingdom has fallen on hard times, and has only one elderly knight and his faithful squire to send. They, like the others, arrive the night before and prepare. The knight eats, drills, and prepares for battle. The lone squire can’t cook and sharpen weapons, and serve, and shine armor at the same time, so he hangs a pot over the fire with a noose while he readies his master’s gear. To buy more time, he cooks the meal slowly by hanging the pot high over the fire.

The next morning, the squires try to rouse the knights for battle. The knights of the first kingdom are too hung over, and give the squires their swords. The knights of the second kingdom wake with the same problem, and come up with the same solution. The poor third squire finds his old master pale and exhausted from his preparations from the night before, so he too goes to battle.

A massive slaughter ensues. It lasts all day, into the night. Back on the shores of the lake, the shouts of battle can be heard throughout the darkness, finally tapering off just before dawn. When the dust settles, the lone squire comes limping from the battlefield, injured, bleeding, dressed in tatters carrying a broken sword, but victorious. Which just goes to prove….

The squire of the high pot and noose is equal to the sum of the squires of the other two sides.