I was told this problem comes from Poland's biggest math competition for high school students from the year 2014. I am not sure of the answer but I am sharing since someone here can probably shed light on it.
In a magical forest there are 3 species - rabbits, wolves and lions. Wolves can eat rabbits, lions can eat both rabbits and wolves.
- Whenever a wolf eats a rabbit, that wolf transforms into a lion.
- If a lion eats a rabbit, it transforms into a wolf.
- If a lion eats a wolf, it transforms into a rabbit.
In the beginning, there are 17 rabbits, 55 wolves and 6 lions in the forest.
What is the highest possible number of animals when no more animals can be eaten?
A related problem: the problem is similar to the chameleons of three colors puzzle, but I was not able to adapt the method to prove the answer in this problem.