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# Modelling the Rules of a Game

Alex and Mark are playing a game. The goal is to get to 100. The first player picks a whole number from 1 to 10, inclusive, and then the second player picks a whole number from 1 to 10 and adds it to the score so far. The first player repeats this move. They continue this way. The player who makes the score exactly 100 wins.

A. Play the game and figure out a strategy for always winning as the first player.
B. Change the rules so that the goal is 200 and numbers from 1 to 20 can be used.
C. Change the rules so that the goal is 200 and numbers from 5 to 20 can be used.
D. Change the rules so that the goal is 200 and numbers from 3 to 30 can be used.
E. Give a general rule for winning the game if g is the goal and whole numbers from p to q (p<q) can be used.

I have tried playing the game about 2 dozen times and still havent figured it out. The teachers told me that there is something you can do to every number to always win, but the only strategy I could figure out is that you want player 2 to always end up with a number 1 higher than the maximum amount they can put. I need help comming up with a strategy without playing the game and what is it for parts A-D.

#### Solution Summary

A game is modeled using variables.

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