# The Riddle of the Vanishing Camel: From Puzzles to Number Theory

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A lecture to investigate the mathematics behind the following fable…

Three Arabian princes gathered around the aged Sheikh’s deathbed to witness their father’s final bequests. The family had fallen on hard times, but the Sheikh still owned a number of fine camels.

“To you, my eldest son Fuad, I bequeath half my camels,” intoned the Sheikh. “Use them wisely.”

“I will, O my father,” said the boy, close to tears.

“Next, to my second son Khalid, I bequeath one third of my camels.” In a hoarse voice, Khalid thanked the old man for his generosity.

“Finally, to my youngest son Ahmed- one ninth of my camels.” Ahmed had not expected anything, and found himself unable to speak, so strong was his emotion.

Within the night, the Sheikh was dead. Fuad, now the new Sheikh, was in charge of carrying out his father’s bequest. He sent a servant to count the camels.

“Seventeen?” The servant bowed low and confirmed the number. “How in the name of the Dust Devils of the Dismal Desert can I divide 17 camels? I cannot split a camel like a loaf of bread. A dead camel is of no use to anybody save the glue-makers.”

“Father would consult the Wise One,” suggested Khalid tentatively.

“Make it so.”

The Wise One (the local name for “mathematician”) considered the problem carefully, making inscrutable notes in the margin of a small textbook of number theory and muttering to himself. He then instructed the Sheikh’s servant to bring in his own, somewhat disreputable, camel.

Without a word, the Wise One led nine camels (half of 18) and handed their reins to Fuad. Next, he handed six camels (one third of 18) to Khalid. Then Ahmed received two camels (one ninth of 18). Only one camel was left: the Wise One’s own mangy beast. He clambered on to its back and rode away in silence, leaving the three princes to contemplate the miracle.

## Professor Ian Stewart FRS

### Professor of Geometry

Ian Stewart read Mathematics at Churchill College, Cambridge before completing his doctorate at the University of Warwick where he is now a Professor of Maths...

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