I’m the secretary of a bowling league. Between the alley and I we screwed up the schedule. We bowl two separate halves of 14 games each with 8 teams. What I need is a way to make the first half so that no two teams bowl each other more than twice and not in the same lane-pair. I think if I get an answer for 7 games I can do the 14. Also I want to not have the same team bowl in the same lane-pair two weeks in a row unless it’s absolutely necessary.
Easy enough except we already bowled two weeks from two different schedules.
This is what was already bowled:
7/3 2/5 6/8 1/4
6/8 5/7 2/4 1/3
I can get everyone bowling each other twice but they do it in the same lanes half the time. I would appreciate any suggestions or solutions.
I take it you originally wanted each team to bowl with each of the others 4 times.
I notice that team 6 and team 8 bowled each other twice in a row without realizing it. Leave those teams alone, none of the other teams would want to compete against such forgetful opponents, so rotate the other 6 so each plays 4 times(20 rounds) and let the clueless bowl each other each round and see how it takes before they say sometime.
Yes, each team does bowl each other team 4 times. Since the halves are scored independantly I can just use the correct schedule for the second half.
The clueless team did notice (and was quite unhappy about it), but since the second week was the correct schedule I thought we should just go ahead with it and I would be able to make some minor adjustments and fix things. HA…I was so wrong. I didn’t have much time to think when it happened.
I might just have to go with what I have, the correct games but not the correct lanes. I don’t really care but some other people might notice and have a fit about it.
I just signed on to tell anyone who cared that I finally did it. Whew!! I have spent many hours at this, too many to admit to.
aahala Thanks for trying it for me. I hope you didn’t spend much time on it. I’m going to see with your numbers if by shifting each week one time more than the previous over to the right,and putting the leftovers in the beginning I can have something that makes the whole season perfect.
Did you use a program to figure that out or is there a pattern I’m not seeing?
The hardest part of this was getting the teams to bowl on every lane but not in the same lane twice in a row.
If you’re interested here is what I got:
7/3 2/5 6/8 1/4
6/8 5/7 2/4 1/3
8/4 3/5 6/1 7/2
6/5 7/4 1/2 3/8
2/8 1/3 7/6 4/5
1/7 5/8 6/3 2/4
3/2 4/6 5/7 8/1
5/1 8/7 4/3 2/6
1/2 3/4 5/6 7/8
3/6 7/2 1/5 8/4
4/7 6/1 8/2 3/5
3/8 5/2 4/6 7/1
4/1 6/7 8/5 2/3
5/4 8/1 6/2 3/7 The second half I just used the standard rotation so I won’t type it. I ended up with a few teams bowling in the same lane 2 times, once in the first 1/2 and once in the second.
My method. I spent a fair amount of time trying to assignment each of all combinations and learned this was a most complication problem using the “eyeball method.”
Then I had an aha moment .
The first week - 7/3 2/5 6/8 1/4 - could be interpreted as a beginning round robin between two divisions of four teams each. The blue division were teams 7, 2, 6, 1 and the red the second digits in each pair. I could do that, have each team play the four others in the other division. Then the next three weeks, each team plays the three in its own division.
Since you had a second week already which was not compatable to the first, I did the same thing, this time with a different division organization - first digit of each pair were again in the blue division. I had to trade a few weeks in the first block of 14 so the same pairs didn’t play consecutively.
The last 14 weeks is simply the first 7 week block doubled without adjustments or the second week already played.
