Saturday, July 25, 2009

The Josephus Puzzle. An oriental setting

An oriental setting of this decimation problem runs somewhat as follows. Once upon a time, there lived a rich farmer who had thirty children, fifteen by his first wife who was dead, and fifteen by his second wife. The latter woman was eager that her eldest son should inherit the property. Accordingly one day she said to him, "dear husband, you are getting old; we ought to settle who shall be your heir; let us arrange our thirty children in a circle, and counting from one of them, remove every tenth child until there remains but one, who shall succeed to your estate". The proposal seemed reasonable. As the process of selection went on, the farmer grew more and more astonished as he noticed that the first fourteen to disappear were children by his first wife, and he observed that the next to go would be the last remaining member of that family. So he suggested that they should see what would happen if they began to count backwards from this lad. She, forced to make an immediate decision, and reflecting that the odds were now fifteen to one in favour of her family, readily assented.