MHB Discover the Game Champion: 115 Kids Tournament

[evinda]

Hello! (Wasntme)

I am looking at this exercise:

A board game can be played with $3,4,5 \text{ or } 6$ players.
There is a winner at each round of the game.
A group of $115$ children decides to organize a tournament of this game,for the emergence of the champion of the game,so that at each round participates the same number of children $n \in \{ 3,4,5,6\}$ and the total number of rounds that will be played is the minimum.Which must be $n$ and how many rounds will be played?I thought that $n$ must be $5$,because that is the only number of the possible $n$s that divides $115$,is it right?

And because of the fact that $115=5 \cdot 23$, $23$ rounds will be played.. Or am I wrong??

Could I solve the second subquestion,using graphs?

 

[I like Serena]

Hey! (Wasntme)

And because of the fact that $115=5 \cdot 23$, $23$ rounds will be played.. Or am I wrong??

That leaves you with 23 contestants.
How will they play to get 1 winner? (Thinking)

Could I solve the second subquestion,using graphs?

Sounds like a plan!

We must have 1 winner at the end.
If we play with $n=5$, we must have had $5$ players in the last round.
In the round before that, we might have had $25$ players... but we might also have $21$ players... (Thinking)