Beetles

The workings

Today’s Divertimento fills our blog with beetles, bugs that for me are more literary than real. I remember reading Edgar Allan Poe’s The Golden Beetle (1843) when I was eleven or twelve, and Mujica Lainez’s The Beetle (1982) when I was in my twenties. I think Poe’s story was my first encounter with a cryptographic problem solved in a way we can call scientific: using the probabilities with which the letters of the alphabet are repeated in the English language. Along with The Black Cat, it made me an insatiable reader of Poe’s stories. El escarabajo was the last novel by the Argentinian Manuel Mujica Lainez, and tells the three thousand year history of an Egyptian talisman created for Queen Nefertari; I came to it after having read Bomarzo and El unicornio; all three respond to one of the demands Borges made one day to Mujica himself: “One of the writer’s missions is to rescue the past”.

And I almost forgot Kafka!: wasn’t the monstrous insect Gregorio Samsa in The Metamorphosis a beetle after waking up one morning from an uneasy dream?

The fun

Nine beetles are placed in a circular loop whose length is 100 m, so that the distances in metres between the beetles are distinct prime numbers. At the initial moment, each beetle starts walking clockwise or counterclockwise, at random, at a speed of 1 metre per minute. When two of them collide, they change direction.

What are the distances between the beetles when 50 minutes have passed?

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Solutions

We encourage the readers to try to solve the divertimento for themselves. Whether you succeed or not, you can always consult the solution in this link.