Carp and perch
Carp and perch are natural enemies and ALWAYS fight when they see each other.
One perch can kill one or two carp, is held at bay by three carp, and is killed by carp in minutes, where n is any positive integer.
When carp meet perch, the carp automatically split into the most even groups possible. In the course of the battle, if the carp are winning, when they kill one or more perch the carp instantly reorganize into balanced groups to fight the remaining perch.
Example: If 6 perch battle 20 carp, the carp split into 4 groups of 3 (each holding off 1 perch) and 2 groups of 4 (who each kill 1 perch in 3 minutes.) As soon as the 2 perch are killed, the carp now reorganize into 4 groups of 5, each battling one of the remaining perch.
4 perch take on 14 carp. How long does it take for the carp to kill all the perch? Give answer in minutes, to 2 decimal places.
The answer is 3.75.
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1 solution
The carp split into 2 groups of 3 (holding off 2 perch) and 2 groups of 4 (each of whom kills 1 perch in 3 minutes).
After the 2 perch are killed, there are now 2 perch fighting 14 carp. Each perch faces 7 carp. 7 = 3 + 4, so each remaining perch dies in 3/4 of a minute.
Total time: 3 minutes (1st stage) + 3/4 minute (2nd stage) = 3.75 minutes