Enigma 1237: Odd socks
29 April 2015
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From New Scientist #2393, 3rd May 2003 [link]
George recently suffered a nightmare involving a seemingly bottomless drawer containing large numbers of socks of each of the seven colours of the rainbow. Old Nick whispered in George’s ear that if he selected two socks at random from the drawer the odds were exactly even that they would be the same colour.
The ghost of George’s mother-in-law then appeared, declared a distaste for violet socks, and threw out all the socks of that colour. With six colours remaining, the devil repeated that two socks selected at random had a 50:50 chance of being the same colour.
Four more ghosts appeared and threw out in turn all the indigo, blue, green and yellow socks. The Devil repeated his assertion each time, with reducing numbers of colours, that a pair selected at random had a 50:50 chance of being the same colour.
“There are 25 socks left, but how many have been thrown out?” George asked the Devil.
“I don’t give straight answers,” replied the Devil, “but I can tell you that it is an exact multiple of the original number of socks of your favourite colour.”
What is that multiple, and what is George’s favourite colour?