Riddle of the vanishing camel
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.
"How will this help?" asked Fuad sarcastically. "The problem is unchanged!"
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.
It's a classic puzzle, and your first task is to explain why it works. Your second, less classic task, concerns a second Sheikh who also had three sons, and also left half his camels to his first son and one third to his second son, but left one seventh of his camels to the third son. Again the Wise One's single camel unlocked the riddle. So: how many camels did the second Sheikh have?
ANSWER
The sum of 1/2, 1/3, and 1/9 is not 1, but 17/18. The extra camel makes up the total so that the division is possible; the missing 1/18 accounts precisely for the Wise One's camel.
The sum of 1/2, 1/3, and 1/7 is 41/42. By similar reasoning, the second Sheikh had 41 camels.
