RTS Problem
In a real time strategy game, a group of 20 units together usually has more fighting power than separating them into two groups of 10 units, this is because more units not only means surviving longer, but also killing enemies faster, which prevent enemies from killing own units.
There are 41 red units and 40 blue units, all identical. During the clash, assume the rate of decrease of number of unit is proportional to the number of opposing unit. How many red unit were left after all blue unit were killed?
Bonus: In this case, let X=41, Y=40. Generalize a formula for X and Y.
The answer is 9.
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1 solution
hint1: x ′ ( t ) = − k y ( t ) y ′ ( t ) = − k x ( t ) hint2: x ( t ) = A e k t + B e − k t y ( t ) = − A e k t + B e − k t hint3: A = 2 X − Y B = 2 X + Y hint4: 4 1 2 − 4 0 2 = 9