Help! First day and I'm lost already

[em0925]

Today was my first day in geometry and the teacher gave this problem as one of our homework questions.

A number of chess players played in a tournament, which consisted of several rounds.
If 144 games were played, compute how many players participated in the tournament?
How many rounds there were if in each round each player plays with all others?

*my dad tried to help me with this and said there were 16 players in the tournament and 9 rounds. I am not sure if this is right and have no idea how he got the answer because he couldn't explain it to me. Please help!!
Thank you!

 

[stapel]

What were the rules for the tournament? Did everybody play in the first round, and then only the winners (that is, half of the original number) played in the second round? Or was there some other set of rules?

Thank you! :wink:

 

[soroban]

Hello, em0925!

Are you sure of the wording of the problem?
. . Part (a) is meaningless.
Also, I found three possible answers.

(This is from a Geometry class?)

A number of chess players played in a tournament, which consisted of several rounds.

(a) If 144 games were played, compute how many players participated in the tournament?
. . . At his point, the question cannot be answered.

(b) How many rounds there were if in each round each player plays with all others ?

Your father misread the italicized phrase: "each player plays with all others."



\(\displaystyle \text{Suppose there were 3 players: }\:\{A,B,C\}\)

\(\displaystyle \text{Since }each\text{ players plays against }all\text{ the othesr,}\)
. . \(\displaystyle \text{the players can be paired like this: }\;(A,B),\;(A,C),\;(B,C)\)

\(\displaystyle \text{Hence, in one round, }three\text{ games were played.}\)

\(\displaystyle \text{Therefore, there were }\frac{144}{3} \:=\:48\text{ rounds.}\)



\(\displaystyle \text{Suppose there were 4 players: }\:\{A,B,C,D\}\)

\(\displaystyle \text{Since }each\text{ player plays against }all\text{ the others,}\)
. . \(\displaystyle \text{the players can be paired like this: }\;(A,B),\;(A,C),\;(A,D),\;(B,C),\;(B,D),\;(C,D)\)

\(\displaystyle \text{Hence, in one round, }six\text{ games were played.}\)

\(\displaystyle \text{Therefore, there were: }\:\frac{144}{6} \:=\:24\text{ rounds.}\)



\(\displaystyle \text{Suppose there }nine\text{ players.}\)

\(\displaystyle \text{Since }each\text{ players plays against }all\text{ the others,}\)
. . \(\displaystyle \text{there are: }\:_9C_2 \:=\:{9\choose2} \:=\:36\text{ pairings.}\)

\(\displaystyle \text{Hence, in one round, }thirty\!-\!six\text{ games were played.}\)

\(\displaystyle \text{Therefore, there were: }\:\frac{144}{36} \:=\:4\text{ rounds.}\)