Chess game
Hello all,
Can someone help me in solving the problem?
There were 2 women participating in a chess tournament. Every participant played 1 game with all the other participants. The number of games that the men played between themselves proved to exceed by 33 the number of games that the men played with the women. How many paarticipants were there in the tournament and how many games were played.
Thanks in advance.
Note: I solved the problem. But, the answer i was provided with is not matching the outcome which i had got. That is why i am checking with you.
Let the number participant
Let the number participant be n
Number of possible games = C ( n, 2)
Only Men = n - 2
Number of possible games among men = C ( n-2, 2)
Number of possible games among women = 1
As per the given condition
C (n-2 , 2) -[C ( n, 2) - C (n-2 , 2) - 1] = 33
=>2 C (n-2 , 2) - C(n, 2) = 32
=>2 x (n-2)!/2! (n-4)! - n!/ 2! (n-2)! = 32
=>2(n-3)(n-2) - n (n-1) = 64
=>n2 -9n + 12 = 64
=>n2 -9n -52 = 0
so n can be 4 or 13
But 4 cant be the answer as it z not satisfying the first eqn so the answer is 13
(Hopefully I have not done any calculation mistake and writing everything on a go to publish the answer with in 5 mins of the Qs)
let the number of men be
let the number of men be n
number of women is 2
total games among men = nC2
total games between men and women = 2n
now nC2 - 2n = 33
the positive soution is n = 11
thus total number of particaipants = 11+2 = 13
anithaji,
ur solution is
anithaji,
ur solution is wrong...check it ............my frnd 
@RAJORSHI
Rajorshi..i dnt thnk even ur ans is correct !!!!
u wrote:
nC2 - 2n = 33, even m gettin the same eqn, bt nC2 - 2n = n(n+1)/2 - 2n
therefore n(n+1)/2 - 2n-33 = 0 or
n^2-3n-66 = 0 (n=11 as u wrote is nt satisfying this eqn)
i got stuck after it.....sumi plz find integral value of "n" !!!!!!
dear ! nC2 = n(n-1)/2 NOT
dear ! nC2 = n(n-1)/2 NOT n(n+1)/2
Hey the answers are---
Total
Hey the answers are---
Total no. of players=13 (11 man and 2 woman)
Total games =78
SOLUTION
I am also getting same answer...... there are total 13 contestant
11 man
2 women
and total number of game will be 13c2 = 78
Hi........
Dj's
Hi......friends........u r gettin right answers..............(11 m +2 w ).............. 55(b/w only men)
------------------------ +22(b/w men n women)
Total 13 people +01(only women)
-------------------------------------------
Total 78 games
nC2-2n=33
n2-5n-66=0
n=11
The
nC2-2n=33
n2-5n-66=0
n=11
Therefore
no of men=11
no of women=2
No of games= 55 men-men
no of games= 22 men-women
no of games=1 woman-woman
Therefore total=55+22+1=78 games :)
Regards,
Mayungk Kapur