Let a, b, c be the count of each species in no particular order. Three operations exist: 1. a++; b--; c-- 2. a--; b++; c-- 3. a--; b--; c++
Note that a' = (b+c) either decreases by two or is unchanged. This implies two properties: a' cannot change from odd to even. a' cannot increase.
The surviving species at the end (a' = 0) has to be Ξ³, since the others have odd initial a'. And no more than 29 can be of this type, limited by the initial a' of the Ξ± species.
@khird My thought was the following: First, the atoms perform operation (3) ten times and then operation (1) is performed 14 times. Not very likely but possible. The pot ends up with z=91-10+14=95 alpha atoms.
Sounds like you aren't implementing this line from the problem description : "When he returns, he notices that all Xmasium-atoms in the pot now are of the same type."
Solution
@pschwede
Let a, b, c be the count of each species in no particular order. Three operations exist:
1. a++; b--; c--
2. a--; b++; c--
3. a--; b--; c++
Note that a' = (b+c) either decreases by two or is unchanged. This implies two properties:
a' cannot change from odd to even.
a' cannot increase.
The surviving species at the end (a' = 0) has to be Ξ³, since the others have odd initial a'. And no more than 29 can be of this type, limited by the initial a' of the Ξ± species.