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Nine trolls (Posted on 2015-07-23) Difficulty: 2 of 5
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

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): computer solution | Comment 8 of 9 |
(In reply to re: computer solution by Charlie)

BTW, an example of the farthest it was able to get without duplicating a handshake is:


123
456
789

135
849
627

192
738
5--

  Posted by Charlie on 2015-07-23 12:22:03
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