Nine trolls are placed in the cells of a three-by-three square.
The trolls in neighboring cells shake hands with each other.
Later they re-arrange themselves in the square and the neighbors greet each other once more.
Then they repeat it again for the 3rd time.

Prove (or provide a counterexample) that there is at least one pair of trolls who didn’t greet each other.

Based on a problem in Russian "Kvantik",2012

(In reply to re: Solution.....needs editing by Ady TZIDON)

Fixed.

Thanks Ady, I appreciate how you catch my typos because I am very prone to them.

Posted by Jer on 2015-07-23 20:46:43