Jump to content
BrainDen.com - Brain Teasers
  • 0

My friend and I play in a chess tournament


BMAD
 Share

Question

I was on my junior-high chess team! One time, another seventh grader and I entered an eighth-grade tournament. Every player played every other player once (round-robin); a win counted as one point and a draw was 1/2 point. My friend and I got a total of 8 points, while all the 8th-graders got the same number of points (as each other). How many eighth-graders were in the tourney, and why?

*Note there are two possible answers

Link to comment
Share on other sites

10 answers to this question

Recommended Posts

  • 0

1). 7 8th graders in the tournament, 9 people total. Where two 7th graders got 8 points (could be 4 each), and 7 8th graders got 4 points each.


2). 14 8th graders, 16 people total. Each 8th grader got 8 points, the two 7th graders got 8 points between the two of them.

Corollary: none ot the players was Bobby Fischer.
Link to comment
Share on other sites

  • 0

12 players. Divide 8-graders into 2 groups of 5 players. You beat each player from group 1, and tie with each player from group 2 and with your friend. This gives you 5 + 2.5 + 0.5 = 8 points. Your friend beats each player from group 2 and ties with other players, also scoring 8 points. Each game between two 8-graders is a tie, so each 8-grader gets 4.5 against other 8-graders and 0.5 total against you and your friend, finishing competition with 5 points.

Edited by witzar
Link to comment
Share on other sites

  • 0

32 players. Divide 8-graders into 2 groups of 15 players. You tie with each player from group 1, lose with each player from group 2, and tie with your friend. This gives you 7.5 + 0 + 0.5 = 8 points. Your friend ties with each player from group 2, loses with each player from group 1 and ties with you, also scoring 8 points. Each game between two 8-graders is a tie, so each 8-grader gets 14.5 points against other 8-graders and 1.5 total against you and your friend, finishing competition with 16 points.

Link to comment
Share on other sites

  • 0

First I read it as the 7th graders got a total of 8 points between them.


The number of games played is (N-1)*(N/2) which is also the number of points awarded. So the 8th graders received a totl of (N-1)*N/2)-8 ponts. These points are then split evenly between N-2 players. Thus,( (N-1)*N/2-8)/(N-2) must be a multiple of 1.0 or 0.5. The only solutions that neet this is for N=9 or N=16
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...