MHB Discover the Game Champion: 115 Kids Tournament

  • Thread starter Thread starter evinda
  • Start date Start date
  • Tags Tags
    Game Kids
AI Thread Summary
A group of 115 children is organizing a tournament for a board game that accommodates 3 to 6 players per round, aiming to minimize the total number of rounds. The optimal number of players per round is determined to be 5, as it evenly divides 115, resulting in 23 rounds. Each round will yield one winner, leading to a final round with 5 players. The discussion also touches on the possibility of using graphs to analyze the tournament structure. The goal is to ensure a single champion emerges from the competition.
evinda
Gold Member
MHB
Messages
3,741
Reaction score
0
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? :confused:
 
Physics news on Phys.org
Hey! (Wasntme)

evinda said:
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? :confused:

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)
 
Hello, I'm joining this forum to ask two questions which have nagged me for some time. They both are presumed obvious, yet don't make sense to me. Nobody will explain their positions, which is...uh...aka science. I also have a thread for the other question. But this one involves probability, known as the Monty Hall Problem. Please see any number of YouTube videos on this for an explanation, I'll leave it to them to explain it. I question the predicate of all those who answer this...
I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
Back
Top