Logical question (no variations, permutations or combinations)

In summary, the problem is asking for the number of contestants in a chess tournament where each person plays one game with all other contestants and there are 210 games played. This can be solved using the quadratic equation by setting up the equation n(n-1)/2 = 210, where n represents the number of contestants. The final solution is n = 21, meaning there were 21 contestants in the tournament.
  • #1
Physicsissuef
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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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  • #2
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:
  • #3
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!)
 
  • #4
Oh, exactly. Thanks HallsofIvy
 
  • #5
I understand. Thank you.
 

1. What is a logical question?

A logical question is a type of inquiry that requires reasoning and critical thinking to arrive at an answer. It is based on facts and evidence rather than opinions or emotions.

2. How do you formulate a logical question?

To formulate a logical question, you need to start with a clear and specific topic or problem. Then, break it down into smaller parts and use the 5 W's (who, what, where, when, why) and 1 H (how) to guide your inquiry. Additionally, make sure your question is open-ended and can be answered with evidence.

3. What is the purpose of asking logical questions?

The purpose of asking logical questions is to gain a deeper understanding of a topic or problem, to challenge assumptions and biases, and to arrive at a logical and evidence-based conclusion. It also helps to improve critical thinking skills and decision-making abilities.

4. Can logical questions be used in any field of study?

Yes, logical questions can be used in any field of study as they are based on reasoning and evidence. They are commonly used in science, mathematics, philosophy, and even in everyday life when problem-solving or making decisions.

5. What are some examples of logical questions?

Examples of logical questions include "What evidence supports this claim?", "How does this phenomenon occur?", "What is the relationship between these two variables?", and "What are the potential consequences of this decision?" These questions require critical thinking and can be answered through research and evidence.

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