Enigma 1264: Unlucky draw
11 January 2015
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From New Scientist #2420, 8th November 2003
It was time to make the draw for a knockout stage in the cup. To make it easy for viewers to spot the most interesting match-ups, every team left in the competition was allocated a ball: white if they were in division 1 of the league and black if they were in division 2. As it happened, there were an equal number of black and white balls in the velvet bag at the start. The format of the draw was to pick out at random two balls at a time — these two teams would play each other — until there were no balls left.
As the draw progressed, the various team representatives couldn’t help but notice that the matches were consistently between one team from division 1 and one team from division 2. In fact, when the draw was complete this was true of every single match. The representatives of the division 2 teams were furious and claimed [that the odds of this happening by chance] were only a tiny bit better than 1 in 100.
How many teams were in the cup at the start of the draw?
I don’t have a complete source for this puzzle, so I’ve guessed at the wording in square brackets. It seems to make sense as a question and matches the answer given in the magazine.
If anyone has the complete text, or (even better) an image of the puzzle in New Scientist, please get in touch.