Logical question (no variations, permutations or combinations)

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Homework Help Overview

The problem involves determining the number of contestants in a chess tournament based on the total number of games played, which is stated to be 210. The original poster specifies that the solution should not involve variations, permutations, or combinations, but rather a quadratic equation approach.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the number of contestants and the total games played, with one participant suggesting a summation approach. There is also mention of the formula for calculating games played in a round-robin format, leading to the equation n(n-1)/2 = 210.

Discussion Status

The discussion includes various attempts to articulate the reasoning behind the number of games and contestants. Some participants express uncertainty about their explanations, while others acknowledge the connections being made. There is no explicit consensus, but the conversation is progressing with shared insights.

Contextual Notes

Participants are operating under the constraint that the solution must not involve variations, permutations, or combinations, which influences the methods being discussed. The original poster expresses a lack of understanding regarding the problem setup.

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Homework Statement



How many contestants have on one chess tournament, if every person have played only one game with all of the other contestants separately, and there are 210 games played.

This problem should not be solved by variations, permutations or combinations. This problem should be solved by using the quadric equation. (we should put some condition, and out of there make some quadric equation).

Homework Equations




The Attempt at a Solution



I have no idea.

x- the number of players

I really don't know.
 
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The answer just popped up into my head. Don't know how to explain it :confused:

[tex]\sum^x_{N=1} N-1 = 210[/tex] x is the number of participants
 
Last edited:
armis said:
The answer just popped up into my head. Don't know how to explain it :confused:

[tex]\sum^x_{N=1} N-1 = 210[/tex] x is the number of participants
Then how do you know it is the answer?

If there are n contestants then, for each one, there are n- 1 "other contestants" and so each plays n-1 games. n people, each playing n-1 games, means there are n(n-1) games- except that each game involves two players: there are actually n(n-1)/2 games played. Since there were a total of 210 games, n(n-1)/2= 210.

(Which is, by the way, exactly what armis is saying!)
 
Oh, exactly. Thanks HallsofIvy
 
I understand. Thank you.
 

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