Enigma 1029: Chancelot
4 January 2019
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From New Scientist #2185, 8th May 1999
The company Chancelot has been asked to set up a lottery for a foreign country. It will work a bit like Britain’s own lottery with participants choosing some numbers: then the winning numbers will be decided by the company choosing some numbered balls at random.
The government has laid down some strict guidelines:
1. It wants participants to have to choose six numbers from 1, 2, …, N, where the top number N has not yet been decided. Then six of the numbered balls will be chosen and the winner’s choices must match all six.
2. It believes that the public is always suspicious when the winning selection includes two consecutive numbers. Therefore of all the combinations of six numbers from the N, it wants more than half of them not to include two consecutive numbers.
3. To give the public a fair chance of winning, it wants N to be the lowest possible satisfying the above conditions.
How many balls will there be in Chancelot’s lottery?