You own a bunch of cats. These cats have special properties. Firstly, the cats come in yellow, purple and green. Secondly, if two differently coloured cats spend time together, they both change into the third colour cat. You have 14 blue cats, 16 red cats and 18 green cats. Is it possible to get the same number of cats for each colour?.
2026-04-12 01:07:31.1775956051
{14, 16, 18} to {16, 16, 16} by -1 from any 2 columns and adding 2 to the 3rd column.
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The answer is usually no. The usual approach is to find a quantity that is invariant under the transformations, then to show that the quantity is different in the start state and the end state.
Hint: what happens to the vector of cat numbers $\bmod 3$ at each meeting?