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8daysAweek
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There is a game with two players: A and B.
Each turn the players shoot at each other simultaneously.
Player A has 100 life points and the damage he inflicts is 50% of his remaining life points. Player B deals 25% respectively. Life points are rational numbers.
A player wins the game when his life points are higher than 1, while his opponent's life points are smaller than 1.
Find the minimum, natural starting life points that player B should have in order to win the game.
I decided to start by representing the life points of each player as a series. I got this:
[tex]a_0 = 100[/tex]
[tex]b_0 = X[/tex]
[tex]a_n = a_{n-1}-{0.25}b_{n-1}[/tex]
[tex]b_n = b_{n-1}-{0.5}a_{n-1}[/tex]
But I got stuck here unable to solve the equations.
Any help or ideas will be appreciated.*This is not homework
Each turn the players shoot at each other simultaneously.
Player A has 100 life points and the damage he inflicts is 50% of his remaining life points. Player B deals 25% respectively. Life points are rational numbers.
A player wins the game when his life points are higher than 1, while his opponent's life points are smaller than 1.
Find the minimum, natural starting life points that player B should have in order to win the game.
I decided to start by representing the life points of each player as a series. I got this:
[tex]a_0 = 100[/tex]
[tex]b_0 = X[/tex]
[tex]a_n = a_{n-1}-{0.25}b_{n-1}[/tex]
[tex]b_n = b_{n-1}-{0.5}a_{n-1}[/tex]
But I got stuck here unable to solve the equations.
Any help or ideas will be appreciated.*This is not homework
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