Cafe Brainiacs: Need help creating a FF schedule

[Plindsey88]

This is actually a really cool brain teaser... I enjoyed working on it...

I do think Newbie is over-simplifying a bit, but he did touch on a very important point...

The problem you are running into with the schedule, as originally stated, is that it is impossible... I could show you a proof, but for the sake of keeping this simple let me just tell you that you can't set-up the schedule so that every team plays a single-header (7) times and double-header (6) times AND that the single-headers and double-headers line-up such that every team plays a single-header in the same week as every other team and every team plays a double-header in the same week as every other team... That simply doesn't work...

So, you have to relax the restrictions such that every team will play (7) single-headers and (6) double-headers, but they do not have to align themselves with every other team in order to make the thing mathematically solvable...

Now, if you are willing to accept those conditions, then there are multiple unique solutions to this puzzle... I'll give you a chance to work on it on your own if you want to... And, if any of the other Cafe guys want to try their hand at the puzzle, I highly suggest it... It's a good brain work-out...

But, I do have (1) possible solution that I can e-mail you if and when you want it... Just give me your e-mail address, and I'll send it to you...

Great Question...

[Plindsey88]

Remember that there are 7 teams per division and there is no possible way for each team to play all the teams exactly once within 6 weeks. There are ways to overlap them, but not where they only play each other once.

Yes, I failed to account for the odd number of teams in each division. In that case, the problem is a little more complex than I originally thought, but there are still very viable solutions.

For example, in week 2, you have the following divisional schedules:

Team 1 vs. Team 4
Team 2 vs. Team 5
Team 3 vs. Team 6
Team 4 vs. Team 7

Team 8 vs. Team 11
Team 9 vs. Team 12
Team 10 vs. Team 13
Team 11 vs. Team 14

Then in week 4, it looks like this:

Team 1 vs. Team 5
Team 2 vs. Team 6
Team 3 vs. Team 7

Team 8 vs. Team 12
Team 9 vs. Team 13
Team 10 vs. Team 14

Team 4 vs. Team 11 (inter-divisional)

In that case, you would simply move one inter-divisional game from the following week (when a double-header was scheduled) to the current week. This would be done for each team once during the year. Not every team would be in a double-header on the exact same week, but by the end of the year, everyone would have the correct number of games both in and out of the division.

I'm not sure if your system here works... I went a totally different route to come up with my solution... I do think it's a little more complex than you are giving it credit for, though... It's really not at all as simple as it seems at first glance... Like you, I took a look at the question, ran through a couple weeks in my head, and thought the solution was immediately apparent, but like Biju said, the complexity doesn't become clear until you get towards the end... I found this puzzle to be sort of like a Rubik's Cube... It was really easy to get one side all matched-up, but not simultaneously to all the other sides... Eventually I figured it out, but it definitely took some thinking...

I would be interested to see if you can flesh out this example into a viable solution... PM me if you can make it work... I'd like to see how your solution stacks up to mine...

[dream_017]

The problem you are running into with the schedule, as originally stated, is that it is impossible... I could show you a proof, but for the sake of keeping this simple let me just tell you that you can't set-up the schedule so that every team plays a single-header (7) times and double-header (6) times AND that the single-headers and double-headers line-up such that every team plays a single-header in the same week as every other team and every team plays a double-header in the same week as every other team... That simply doesn't work...

I disagree



PM me for the solution

[Plindsey88]

The problem you are running into with the schedule, as originally stated, is that it is impossible... I could show you a proof, but for the sake of keeping this simple let me just tell you that you can't set-up the schedule so that every team plays a single-header (7) times and double-header (6) times AND that the single-headers and double-headers line-up such that every team plays a single-header in the same week as every other team and every team plays a double-header in the same week as every other team... That simply doesn't work...

I disagree

Nice job, Dream... I haven't had a chance to verify that that works out, but I am sure you have... Good Show...

I suppose my logic behind the impossibility leaves a little to be desired...

Very cool... I couldn't make it work without staggering the double-headers... I'd be interested to know your approach...

Wait... Now I see... I was running under the mistaken assumption that the double-header weeks, as stated in the original problem, had to include (1) in-conference and (1) out-of-conference game... THAT was what I concluded was impossible... And I still think it is...

But you're right... You fulfilled all the original qualifications... I'm impressed...

I wish you wouldn't have posted a solution, though... I was curious to know how many guys could come up with one on their own...

[FF Newbie]

I'm not sure if your system here works... I went a totally different route to come up with my solution... I do think it's a little more complex than you are giving it credit for, though... It's really not at all as simple as it seems at first glance... Like you, I took a look at the question, ran through a couple weeks in my head, and thought the solution was immediately apparent, but like Biju said, the complexity doesn't become clear until you get towards the end... I found this puzzle to be sort of like a Rubik's Cube... It was really easy to get one side all matched-up, but not simultaneously to all the other sides... Eventually I figured it out, but it definitely took some thinking...

I would be interested to see if you can flesh out this example into a viable solution... PM me if you can make it work... I'd like to see how your solution stacks up to mine...

Yeah, I wasn't giving Biju enough credit at first. The problem really wasn't as simple as I immediately assumed, without reallly thinking through every aspect of this. I believe something approximating what I suggested above will, in fact, work, but I haven't worked the entire thing out, so I can't guarantee it. I'd love to spend some more time on it and propose a full solution. Maybe I can find some time for that next week.

[FF Newbie]

Nice job, Dream... I haven't had a chance to verify that that works out, but I am sure you have... Good Show...

I suppose my logic behind the impossibility leaves a little to be desired...

Very cool... I couldn't make it work without staggering the double-headers... I'd be interested to know your approach...

Wait... Now I see... I was running under the mistaken assumption that the double-header weeks, as stated in the original problem, had to include (1) in-conference and (1) out-of-conference game... THAT was what I concluded was impossible... And I still think it is...

I haven't worked out the impossibility of it, but I did notice that dream is mixing the inter-divisional and intra-divisional games in a manner similar to what I proposed.

[dream_017]

Nice job, Dream... I haven't had a chance to verify that that works out, but I am sure you have... Good Show...

I suppose my logic behind the impossibility leaves a little to be desired...

Very cool... I couldn't make it work without staggering the double-headers... I'd be interested to know your approach...

Thanks.

I double checked a couple of times, so if anyone sees any problems with it please let me know.

Based on the original post, I didn't see any reason for it not to work. My approach is pretty much just taking it as a puzzle. I have made quite a few fantasy schedules and I have always made my own for my leagues I just come up with all the possible combinations of games, then just start placing them in weeks, by team (all of A1 games, then all A2 and so on.) Near the end is where it turns into a puzzle, I have yet to have one come out correct on the first try, you end up with some games that are impossible to place in the open week. Then you remove a game or 2 from a previous week until you come up with the correct combination...similar to a rubik cube

[dream_017]

Wait... Now I see... I was running under the mistaken assumption that the double-header weeks, as stated in the original problem, had to include (1) in-conference and (1) out-of-conference game... THAT was what I concluded was impossible... And I still think it is...

But you're right... You fulfilled all the original qualifications... I'm impressed...

I wish you wouldn't have posted a solution, though... I was curious to know how many guys could come up with one on their own...

I took down the solution for those that want to try it on their own

Yeah, I didn't read it like that(include (1) in-conference and (1) out-of-conference game) and haven't looked into if that is possible or not. I would guess that you are correct

[biju]

This is an unbelievable testament to how awesome the Cafe is. There are truly some smart people on this board...

[biju]

Wait... Now I see... I was running under the mistaken assumption that the double-header weeks, as stated in the original problem, had to include (1) in-conference and (1) out-of-conference game... THAT was what I concluded was impossible... And I still think it is...

But you're right... You fulfilled all the original qualifications... I'm impressed...

I wish you wouldn't have posted a solution, though... I was curious to know how many guys could come up with one on their own...

I took down the solution for those that want to try it on their own

Yeah, I didn't read it like that(include (1) in-conference and (1) out-of-conference game) and haven't looked into if that is possible or not. I would guess that you are correct

Sorry folks, I don't mean to kick a dead horse here but...

Huge props to dream_017!!!

His solution not only works, but beautifully has most of the intra-divisional games towards the end of the season allowing teams on the bubble the best chance to have playoff hopes.

I really couldn't have asked for anything better.

Thanks again!