- #1

8daysAweek

- 10

- 0

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.

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}
Last edited: