Enigma 1108: Every vote counts
From New Scientist #2264, 11th November 2000 [link]
George was nominated for president of the Golf Club. There was only one other candidate, and the president was elected by a simple ballot of the 350 members, not all of whom in fact voted.
The ballot papers were taken from the ballot box one at a time and placed in two piles — one for each candidate — with tellers keeping a count on each pile.
George won (what did you expect?), and furthermore his vote was ahead of his opponent’s throughout the counting procedure.
“That must be a one-in-a-million chance,” said the demoralised loser.
“No,” said George. “Now that we know the number of votes we each received, we can deduce that the chance of my leading throughout the count was exactly one in a hundred.”
How many members did not vote?