Enigma 258: Monkey business
14 February 2015
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From New Scientist #1405, 12th April 1984 [link]
A group of monkeys had a sackful of nuts. One night one of the monkeys decided secretly to take his share of the nuts, so he divided them into equal piles, one for each monkey: there was one nut left over so he gave it to his organ-grinder. He hid his own pile away and returned the remaining piles to the sack.
A little later than night the second monkey did precisely the same thing, divided the nuts into equal piles, one pile for each of the monkeys, and gave the odd remaining nut to the organ-grinder. He hid away his own pile and returned the rest of the piles to the sack.
This continued through the night, each monkey repeating the same performance not knowing that the others had already removed their shares.
The number of nuts originally in the sack was the smallest number possible for all this to have happened to that particular group of monkeys.
At this point the organ-grinder turned to the monkeys and said: “Isn’t this a rather clichéd puzzle?”, to which one of the monkeys replied: “Ah, yes, but in this case we are now able to divide the remaining nuts equally between all the monkeys and you, my organ-grinding friend”.
How many monkeys were there?