/sci/ - Science & Math » Thread #11807849

20KiB, 400x325, +_817fb23af4589c4d7af51babb9cc2258.jpg

View Same Google iqdb SauceNAO

Short Riddle

syndra Wed 17 Jun 11:28:50 2020 No.11807849 View Reply Original Report

Quoted By: >>11807895 >>11807943 >>11807949

In one chess tournament the total number of matches played was 210. Figure out the number of contestants if every contestant played a match against every other contestant.

Anonymous

Anonymous Wed 17 Jun 2020 11:29:31 No.11807851 Report

Quoted By:

Yes

Anonymous

Anonymous Wed 17 Jun 2020 11:31:30 No.11807854 Report

Quoted By:

If every contestant matched every other one, then we would have n(n-1) games. n(n-1) = 210 is a simple quadratic to solve. take the real root and get:

15
But this is a mistake, don't count the same games twice, in that case, divide by two basically using gauss's trick to count and you get 21

Anonymous

Anonymous Wed 17 Jun 2020 11:31:30 No.11807855 Report

Quoted By: >>11807856 >>11807858

2 people.

They played over and over 105 times

Anonymous

Anonymous Wed 17 Jun 2020 11:32:33 No.11807856 Report

Quoted By: >>11807857

>>11807855
Err I meant 2 people and 210 matches

Anonymous

Anonymous Wed 17 Jun 2020 11:33:24 No.11807857 Report

Quoted By:

>>11807856
That's the correct answer.

Anonymous

Anonymous Wed 17 Jun 2020 11:34:02 No.11807858 Report

Quoted By:

>>11807855
If there's only two people it can't be considered a tournament

Anonymous

Anonymous Wed 17 Jun 2020 11:52:36 No.11807895 Report

Quoted By:

>>11807849
n * (n - 1) = 210
n^2 - n = 210
(n-1/2)^2-1/4= 210
(n-1/2)^2 = 210.25
(n-1/2) = +-14.5
n = 1/2 +- 14.5
there are either 15 or - 14 people

Anonymous

Anonymous Wed 17 Jun 2020 12:15:47 No.11807943 Report

Quoted By:

>>11807849
There are 21 contestants (imagine a graph with 21 verticies where each vertex represents a contestent and have an edge between every vertex to represent a game between 2 contestents, if there are 21 verticies (21 contestents) then there are 210 edges (210 games played) to connect all the verticies)

Anonymous

Anonymous Wed 17 Jun 2020 12:20:12 No.11807949 Report

Quoted By:

>>11807849
210 = 1/2 * n(n-1)
420 = n(n-1)
So the answer is close to 20. Let's try 20.
20 * 19 = 380 nope, not that, maybe 21?
21 * 20 = 420

Ah ha, 21 works, let's put it back in the original.

1/2 * 21 * 20 = 21 * 10 = 210

So the answer is 21.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches