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A Canadian Lottery Wheel

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In Canada's Lotto 6/49, a $1 ticket has six numbers from 1 to 49. The lottery officials choose six numbered balls from 1 to 49 at random. If the ticket matches three or more numbers, it wins a prize. (The bonus ball is ignored in this Demonstration.)

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A group of tickets that guarantees a $10 return is known as a lottery wheel. At the moment, the smallest known wheel for Lotto 6/49 consists of 163 tickets. (In combinatorics, finding a minimal lottery wheel is known as a covering problem.)

This Demonstration stores a fixed set of such a wheel. You act as the lottery officials and choose any sorted list of six winning numbers. The winning tickets from the preset lottery wheel are displayed.

Note that it costs $163 to win at least $10 with this system.

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Contributed by: Ed Pegg Jr (January 2008)
Open content licensed under CC BY-NC-SA

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Dan Gordon, La Jolla Covering Repository.

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