В круговом шахматном турнире ( каждый игрок играет одну партию с каждым другим участником турнира) сыграно 78 партий. найдите количество участников турнира.

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Let's denote the number of participants in the tournament as n.

Each participant plays against every other participant once, which means that the total number of games played is given by the formula nC2 = 78, where nC2 represents the number of combinations of n taken 2 at a time.

Solving the equation nC2 = 78, we get:

n! / (2!(n-2)!) = 78
(n)(n-1) / 2 = 78
n^2 - n = 156
n^2 - n - 156 = 0
(n - 13)(n + 12) = 0

So, n = 13 or n = -12.

Since the number of participants cannot be negative, we can conclude that there were 13 participants in the tournament.