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The great problem of Columbus

The great problem of Columbus

Recently I came across a writing that talked about the madness for the bets that existed during the 15th century where among other games of chance or intelligence that the knights were so excited to the point of making them gamble uncontrollably, the game of lay eggs on a cloth.

This was possibly the true origin of the story of the egg of Columbus that despite having a cunning moral has always seemed too lazy for the time. I realized that the game required ingenuity and originality of thought.

It is a game for two participants who should alternately place eggs of uniform size on a square cloth. When an egg has been placed it cannot be touched or moved by another and the game continues until the fabric is so full that it is impossible to place another egg. The person who laid the last egg is the winner. Since the size of the cloth or eggs as well as the distances between egg and egg are unimportant, it would seem that the question of placing the last egg was simply a thing of luck. However, the first player can always win thanks to a clever strategy that, as expressed by the great navigator, "It is the easiest thing in the world once we have been told how to do it!"

What is the strategy to be followed by the first player to ensure victory?

Solution

For the second player, the strategy is to place the egg in the position diametrically opposite to that of our opponent so that whenever the first player is able to place an egg, the second player can place his in the indicated position until there are no more free gaps.

The only way to avoid the defeat of the first player is to place the first egg exactly in the center of the cloth but because of the ovoid nature of the egg this is not possible. From here emerged the legend of the egg of Colon since if we slightly chamfer the egg we can place it standing exactly in the center and our opponent will not be able to replicate our movement at the opposite end.