Unit 5: Polynomial Functions Assignment Booklet 5 8. Patterns and Games: Logic a

Question

Unit 5: Polynomial Functions Assignment Booklet 5 8. Patterns and Games: Logic and Strategy Game In a two player strategy game, players take turns shading one or two circles on a board. The goal of the game is to shade the last of the ten circles on the board. In the game below, Player A is shading in a solid colour, and Player B is shading with lines. It's now Player B's turn. How many circles should Player B shade to guarantee a win? Explain why this move will guarantee a win, using diagrams if necessary. (3 marks) End of Assignment ADLC Mathematics 30-2

Explanation / Answer

Player B will shade two circles to guarantee a win. Suppose player B shades two circles, then only 3 circles will left and A can shade either 2 circles or 1 circle.

Case 1: Player A shades 1 circle then only 2 circles will be left and its B turn now so he will shade the 2 left circles and will win.

Case 2; Player A shades 2 circles then only 1 circle will be left and its B turn now, so he will shade the last left out circle and will win.

So if Player B shades two circles he will definitely win.

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