a) Shown is a photograph of a logic game at the Ontario Science Centre. There are 12 balls...

a) Shown is a photograph of a logic game at the Ontario Science Centre. There are 12 balls on top of the game board, numbered from left to right, with ball 1 on the extreme left and ball 12 on the extreme right. On the platform in front of the players are 12 buttons. Button 1 corresponds to ball 1, button 2 corresponds to ball 2, and so on. When 6 buttons are pushed, the 6 respective balls are released. When 1 or 2 balls reach an and gate or an or gate, a single ball may or may not pass through the gate. The object of the game is to select a proper combination of 6 buttons that will allow 1 ball to reach the bottom. Using your knowledge of and and or, select a combination of 6 buttons that will result in a win. (There is more than one answer.) Explain how you determined your answer.

b) Construct a game similar to this one where 15 balls are at the top and 8 balls must be selected to allow 1 ball to reach the bottom.

c) Indicate all solutions to the game you constructed in part (c).