A group of $n$ people play a board game with the following rules: 1) In each round of the game exactly $3$ people play 2) The game ends after exactly $n$ rounds 3) Every pair of players has played together at least at one round Find the largest possible value of $n$
Problem
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Tags: combinatorics, max
science_man_88
16.03.2020 18:28
parmenides51 wrote: A group of $n$ people play a board game with the following rules: 1) In each round of the game excactly $3$ people play 2) The game ends after excactly $n$ rounds 3) Every pair of players have played together at least once Find the largest possible value of $n$
$n\leq 5$
science_man_88
17.03.2020 14:05
parmenides51 wrote:
7
I must have got my inequality wrong but $6n\geq n(n+1)$ if $n$ is 5.
parmenides51
17.03.2020 15:19
a solution is here