Josephus Problem and the Down/Under Deal

Josephus Flavius was a first century Roman-Jewish historian who told the story of surviving a suicide pact with the help of a little mathematics.

The year was 67 CE, and Josephus was among a small, vastly outnumbered, group of Jewish soldiers who were about to be captured by the Roman army. Preferring death to capture the soldiers decided on a procedure where each soldier would be killed by another - except for the last who was expected to take his own life. Needless to say, Josephus was the last and chose not to die.


To Do the Trick - 2 versions

  • Using a book
  • Using Cards
            ..... The Kruskal Count was discovered by Martin Kruskal, a mathematician and physicist.

Martin Gardner popularized it with Magic Tricks. He demonstrated it with a long paragraph and used the length of the words for the step size.

Mathematically it is related to Coupling Models for Markov Chains (see Lagarias and Vandervei article below)

John Pollard uses it in Cryptography for finding the Discrete Logorithm and breaking encryption codes. Instead of a deck of cards he uses a Cyclic Group. Instead of counting the number of the card he uses a Hash Function for the step size. He called his Algorithm "The Lambda Method for Catching Kangaroos".

            Penn and Teller's Finding Love Card Trick
James Grime Version
            Explanation by James Grime