In the jungles of Noway Magic Island there are the following animals: 17 A
ntelopes, 55 W
olves and 5 L
The following laws of the jungle exist:
Lion eats both Wolves and Antelopes.
W eats A only.
When L eats a W he becomes an A.
When he eats a A he becomes an W.
When W eats a A he becomes an L.
What is the maximal possible amount of animals, such that no one can eat anyone?
The first thing to note is that any of the three laws change the parity of all three populations. The stable monolithic population pf animals sought in the problem has the other two populations at zero. This means the two animals that are to be removed must be the same parity. In this case all three animals have the same parity - odd. Then the final population can consist of any one of the three animals.
Wolves start with a large lead. 5 rounds of L+A=W yields 60 wolves and 12 antelopes. Then 6 rounds of (W+A)+A=W eliminates the remaining antelope population leaving just the 60 wolves.
Lets try lions. This time 17 rounds of A+W=L yields 22 lions and 38 antelopes. Then 6 rounds of (L+A)+A=L leaves just the 22 lions.
Finally antelopes. 5 rounds of L+W=A yields 22 antelopes and 50 wolves. Then 25 rounds of (A+W)+W = A leaves just the 22 antelopes.