Re: Math problem
 

I didn't read all the replies, so pardon this if already stated, but aren't you talking about the statistical formula for combinations? Mathematically, it means: how many ways can I group n things in groupings of r where the order of grouping is not important. (There is a separate formula for permutations where order is important)

The general formula for C(n,r) = n!/[r!(n-r)!]

Where the number of combinations C(n,r) is a function of the total number of people n taken r at a time.

You don't need any particular number of players to start with. If n = 10 and r = 3 then the required number of games is 10!/[3!x7!] = 120

Exactly how to arrange the people in each game is most easily worked out by hand although I suppose it could be done with a program.

Slick.

Re: Math problem
 

Only solutions are 3, 7, 15, 31,...

Other numbers of players leave a three some with two players and no one to match them with. Someone demonstrated this earlier with 9 players.

Re: Math problem
 

Sorry slick, this is way over my head.

"The general formula for C(n,r) = n!/[r!(n-r)!]"

What do n and r represent in the formula, and what are the exclamation points for?

And is C(n,r) the total numebr of players needed in the tourney, or the number of games played by each person in the tourney, or something else alltogether? http://forum.shrapnelgames.com/image...s/confused.gif

Re: Math problem
 

<font size="2" face="Verdana, Helvetica, sans-serif">Right, but other then working them out by hand, or having you plug it into yoru black box and give me the result, can you explain how you know this? What I am trying to learn is not the answer, but how the answer is derived.

Geoschmo

Re: Math problem
 

Here is the code. Crudely done by brute force in a rather esoteric flavor of basic:

PRIMES = '2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61 ,67,71,73,79,83,89,97,101,103,109,113,127,131,137'
SWAP ',' WITH @AM IN PRIMES
ILIMIT = DCOUNT(PRIMES,@AM)
PRINT ILIMIT
FOR I = 4 TO ILIMIT
NBR = I
COMBOS = ''
COMBOX = ''
IDX = 1
FOR J = 1 TO I
FOR K = J+1 TO I
FOR L = K+1 TO I
GOSUB FIND.DUPLICATE
IF NOT(FOUND.DUPLICATE) THEN
COMBOS<-1> = PRIMES<J>*PRIMES<K>*PRIMES<L>
COMBOX<-1> = J:',':K:',':L
END
NEXT L
NEXT K
NEXT J
GOSUB CHECK.SOLUTION
NEXT I
PRINT 'DONE'
STOP
*
SOLVED:*
PRINT '---------------------'
PRINT 'SOLVED'
PRINT NBR
FOR M = DCOUNT(COMBOX,@AM) TO 1 STEP -1
PRINT COMBOX<M>
NEXT M
INPUT CH,1_
RETURN
*
CHECK.SOLUTION: *
FOR J = 1 TO I
FOR K = J + 1 TO I
NBR.MATCHES = 0
FOR M = DCOUNT(COMBOS,@AM) TO 1 STEP -1
A.COMBO = COMBOS<M>
IF MOD(A.COMBO,PRIMES<J>)=0 AND MOD(A.COMBO,PRIMES<K>)=0 THEN
NBR.MATCHES = NBR.MATCHES + 1
IF NBR.MATCHES > 1 THEN RETURN
END
NEXT M
IF NBR.MATCHES = 0 THEN RETURN
NEXT K
NEXT J
GOSUB SOLVED
RETURN
*
FIND.DUPLICATE: *
FOUND.DUPLICATE = 0
FOR M = DCOUNT(COMBOS,@AM) TO 1 STEP -1
A.COMBO = COMBOS<M>
J.MOD = MOD(A.COMBO,PRIMES<J>)
K.MOD = MOD(A.COMBO,PRIMES<K>)
L.MOD = MOD(A.COMBO,PRIMES<L>)
IF J.MOD = 0 THEN
IF K.MOD=0 OR L.MOD=0 THEN
FOUND.DUPLICATE = 1
END
END ELSE IF K.MOD=0 AND L.MOD=0 THEN
FOUND.DUPLICATE = 1
END
NEXT M
RETURN

Re: Math problem
 

Ok, so bascially you are having the couputer run through all the possible options fast and see if a number works. Ok, that does the job but isn't really what I was looking for. Mayeb there is no simple mathematical formula for what I am looking for.

Basically I can take x players and group them into games of three players each and see fairly quickly that 7 players will work, but 5 will not. What I was hoping to find was a formula that I could plug the numbers in and be able to tell if a combination of x and y would work without having to go through all teh grouping by hand.

Geoschmo

Re: Math problem
 

By the way LGM, what is the reason for using the prime numbers in the program? I'm not a programmer so I can't really make heads or tails of your code there, not that it wasn't apprecieated. http://forum.shrapnelgames.com/images/icons/icon10.gif

Re: Math problem
 

Try X raised to the Yth power and subtract one. Just a theory. I am not sure if that works for 4 or 5 man games yet. X is Number of players per game minus 1. Incidentally, that does not work for 2 players games as any number works for 'round robin' leagues.

Re: Math problem
 

Prime numbers are a nice way to test if something is a member of a set. Products of prime numbers is a common way of encoding sets because you can divide by a given prime. If the remainder is zero, it is an element of the set.

Re: Math problem
 

You could use 21 players (3 sets of 7) with a championship game from the winners of each set.

Or you could use 49 players (7 sets of 7) and have a championship round of the top 7 playing each of the top 7.

[ August 06, 2003, 21:13: Message edited by: LGM ]