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 Solution by Jer)

Please edit:  Over the course of 3 rounds, there are 4 centers, 12 edges, and 12 corners available.

4 s.b. 3 , 

& revise accordingly.

Posted by Ady TZIDON on 2015-07-23 10:51:38