Ancient Mesopotamian Puzzles
Even as a young boy, Amoritu's intelligence was noticed by the adults. He was nicknamed Jemdet Kirka, or the "Precocious Child." Though Amoritu was born into a peasan't household, his wits destined him to do great things.
At age 25, he was appointed guard of the Ziggurat of Seleucid, a most noble position. He spent most of his time adorning the grand monument with puzzles to drive off evil spirits.
However, many found his puzzles controversial and sought to behead him. On the day of his 28th birthday, Amoritu vanished, never to be found again. Many historians argue that he is still alive today. Here are three of his most famous puzzles.
A king gave a young widow two dried cobras. The widow was told that each cobra would burn for an etermen (approximately equal to 50 minutes). However, the rate at which the cobras burned would be inconsistent and impossible to predict—in other words, it may take 5/6th of an etermen to burn 1/6th of the cobra, and then 1/6th of an etermen to burn the remaining 5/6th. If the widow could measure 3/4th of an etermen with these two cobras, the king would bring the widow's deceased spouse back to life.
How does the widow do this?
One hundred demons have been imprisoned by Esagila, the Keeper of Evil Spirits. They have been held in prison with no windows, where each demon resides in its own room and cannot communicate or see another demon.
One day, Esagila gives the demons an offer. Each day, he will pick one demon randomly and send him to the zanbil room. There is a chair in that room. The demon has the choice of leaving the chair as is, or it can push the chair over if it is standing (or stand it up if it has fallen). Esagila tells the demon that originally the chair is standing. The demons are unable to leave anything in this room.
Upon leaving the room, the demon will have the opportunity to tell Esagila that all of the 100 demons have entered the room. If the demon chooses to do this and is correct, Esagila will release all the demons. If the demon is wrong, all the demons will be immediately turned into stone and sand. Therefore, a demon should not confront Esagila unless it is absolutely certain that all of the other demons have also entered the zanbil room.
Esagila gives the demons a moment to gather and formulate a strategy among themselves. What should the demons' strategy be?
Esagila has captured 16,384 demons. He has lined them up such that a demon can only see the demons standing before him. Therefore, the last demon in line sees all the other demons (but itself), while the first demon sees no one.
Esagila then tells the demons. "I will place either a dab of white or a dab of purple dye on the back of each of your heads. Then, starting from the last one in line, I will ask you one by one what color dye is on your head. If you answer correctly, I will release you. If you are incorrect, I will turn your skin into mud and bones into pebbles."
Each demon can see the dyes on the heads of demons in line before it. Each demon can also hear the responses of the demons in line behind it. No demon will attempt to cheat, for fear of Esagila's wrath.
Again, Esagila allows the demons to gather for a moment and formulate a plan first. What plan should they use to maximize the number of demons released?
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