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P1 Bosnia and Herzegovina JBMO TST

Source: Bosnia and Herzegovina JBMO TST 2018

July 14, 2018
combinatoricscounting

Problem Statement

Students are in classroom with nn rows. In each row there are mm tables. It's given that m,n3m,n \geq 3. At each table there is exactly one student. We call neighbours of the student students sitting one place right, left to him, in front of him and behind him. Each student shook hands with his neighbours. In the end there were 252252 handshakes. How many students were in the classroom?