Mayor Bud Mountain of the city of Wencroy has a problem.
He decides to create a new lottery game to fleece the citizens and fill the coffers.
In order to do so successfully, he decides the lottery will:
1) Only carry 50% of unwon prize money forward from one drawing to the next.
2) Appear to have good odds to a potential player.
3) In actuality be quite difficult to win.
Mayor Mountain decides that the new lottery will have thirty-six numbers, 1 thru 36.
Now he needs your help.
If the drawing required picking one out of one number correctly, the odds of a single ticket being a winner would be 1/36.
If the drawing required picking two out of two numbers correctly, the odds of a single ticket being a winner would be significantly lower.
To make the likelihood of a winning ticket being sold as small as possible, how many numbers should the new game draw and require a player to match to win?