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National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2018 Bosnia and Herzegovina Junior BMO TST
1
1
Part of
2018 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
P1 Bosnia and Herzegovina JBMO TST
Source: Bosnia and Herzegovina JBMO TST 2018
7/14/2018
Students are in classroom with
n
n
n
rows. In each row there are
m
m
m
tables. It's given that
m
,
n
≥
3
m,n \geq 3
m
,
n
≥
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
252
252
252
handshakes. How many students were in the classroom?
combinatorics
counting