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Kvant 2022
M2706
M2706
Part of
Kvant 2022
Problems
(1)
Number of teams with non-negative balance of wins
Source: VII Caucasus Mathematical Olympiad
3/13/2022
16 NHL teams in the first playoff round divided in pairs and to play series until 4 wins (thus the series could finish with score 4-0, 4-1, 4-2, or 4-3). After that 8 winners of the series play the second playoff round divided into 4 pairs to play series until 4 wins, and so on. After all the final round is over, it happens that
k
k
k
teams have non-negative balance of wins (for example, the team that won in the first round with a score of 4-2 and lost in the second with a score of 4-3 fits the condition: it has
4
+
3
=
7
4+3=7
4
+
3
=
7
wins and
2
+
4
=
6
2+4=6
2
+
4
=
6
losses). Find the least possible
k
k
k
.
combinatorics