Combinatorics · Invariants · Parity · Extremal process · State transitions
Problem 5, 2014
In the Mad Forest there lived \(6\) werewolves, \(17\) unicorns and \(55\) spiders. A werewolf can eat a spider or a unicorn, but not another werewolf; a spider can eat a unicorn, but neither a werewolf nor another spider; and a unicorn can eat none of the three. Eating transforms the eater: a werewolf that eats a spider becomes a unicorn, a werewolf that eats a unicorn becomes a spider, and a spider that eats a unicorn becomes a werewolf.
What is the largest number of creatures that can remain in the forest at a moment when no creature is able to eat any other?
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Serbian Regional Competition 2014, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source