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Brain-teaser - July 2001

William and Fred had both been nominated for president of the local club. Under the rules of the club, an election for the presidency had to be held and all 350 members were allowed to cast a single vote each. After all the members who wished to vote had voted, the ballot box was taken to the counting table. Each vote was taken out of the ballot box and placed in two piles marked William and Fred. As each vote was placed on one of the piles the tellers shouted out the current number of votes for each candidate.

William won and in addition his vote had been ahead of Fred's at every stage of the count. "There must be odds of a million to one against that happening ," said Fred. "That's not true," said William," Now that we know the number of votes we each received, we can calculate that the chance of my leading throughout the count was exactly one in a hundred. "

How many members did not vote? 

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