*****Using a systematic list or eliminating the possibilities strategy Explain h

Question

*****Using a systematic list or eliminating the possibilities strategy

Explain how you got your solution....please don't just give me an answer

Suppose that a new version of ping-pong is invented and that the rules of the game are different. The game is still played between two people and the first player to get 21 points wins the game. However, each time the score reaches a ratio that can be reduced, it is immediately reduced, it is immediately reduced to lowest terms. For example, if the score reaches 4-2, it is reduced to 2-1. If it reaches 12-9,it is reduced to 4-3. If it reaches 14-12, it is reduced to 7-6 and so on. Even a score of 21-7 will be reduced to 3-1. What are the possible final scores for the game?

Explanation / Answer

Lets start with 1-1

then 2-1

if player 2 wins i.e. 2-2 it becomes 1-1 again

so if A continues to win 2-1

3-1

4-1

5-1

6-1

if Player B gets any point it will be reduced.

SO to finish this game final socre will be 21-1 or 1 - 21

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