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# A Fun Puzzle!! (Fredrik where are you!!)

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Here is an overly complicated "puzzle" that I have been trying to figure out over the past few weeks. This is my fourth attempt so far.

Alright so here's the low down. I run a league twice per year for those that are into really competitive Doom CTF called the International Doom League. This upcoming Winter 2008 season is expected to have a large turnout of the best players and, as always, I've taken to some popular suggestions.

Many have asked that I make the Winter season shorter than the Summer season and the number that seems to be most well regarded is 9 weeks. So I set out to make a schedule for 12 teams that spans 9 weeks.

Now, there are 12 teams that make up the league. These 12 teams are then split into two groups of six, each called a Conference. Within each conference they are then split in half again to two groups of three teams called Divisions. So there are four divisions with three teams: IDC North, IDC South, WDC West, WDC East.

Out of the 11 weeks of play each team MUST have one week off between the weeks of Week 3 and Week 8. That is two teams off per week from Week 3 to Week 8. That means that weeks 1, 2, and 9 will have 6 games and weeks 3-8 will have only 5. This means that every team will only play 8 games over 9 weeks.

Each Team must meet each divisional opponent twice. That means that there are _4_ divisional games for every team in the league. Additionally, they must play every team in their conference at least once. That is another 3 games. So we are up to 7 games and a bye which is 8 weeks.

On top of this, each team must play ONLY ONE team from the other conference once. So one team from the IDC North would play ONLY ONE team from the WDC East or West. This additional game adds up to the 9 weeks. There is no requirement on which team must play as long as its a team represented by a number against a team represented by a letter (more on my system at the end).

Additionally, there are a few side rules to help keep the schedule interesting. No two opponents may ever play back to back games with eachother. Team A could not play Team B in weeks 4 and 5 for instance.

On top of this, no team can have 3 divisional games in a row. The max amount of consecutive divisional games is two for any team.

I'm assuming a math wizard on here can come up with some type of formula to lay this all out or tell me if its impossible. I think it's impossible but I feel that I may have laid a few wrong bricks somewhere that I can't spot.

Below is my latest attempt at the schedule in which I come within 3 games of completing it. I split it up as Teams 1-3 in IDC North, Teams 4-6 in IDC South, Teams A-C in WDC East, and Teams D-F in the WDC West. This is only important if you plan on naming yours using my same system.

```Schedule
----------------

Week 1
Team A vs Team D CONF
Team B vs Team F CONF

Team 1 vs Team 5 CONF
Team 2 vs Team 4 CONF
Team 3 vs Team 6 CONF

Week 2
Team 5 vs Team 6 DIV
Team D vs Team F DIV
Team B vs Team C DIV
Team 1 vs Team 2 DIV
Team A vs Team E CONF
Team 3 vs Team 4 CONF

Week 3
BYE: Team C & Team 3
Team A vs Team B DIV
Team 4 vs Team 5 DIV
Team E vs Team F DIV
Team 2 vs Team 6 CONF
Team 1 vs Team D

Week 4
BYE: Team E & Team 5
Team A vs Team C DIV
Team 1 vs Team 3 DIV
Team 4 vs Team F

Week 5
BYE: Team A & Team 1
Team 4 vs Team 6 DIV
Team D vs Team E DIV
Team 2 vs Team 3 DIV
Team C vs Team F CONF
Team 5 vs Team B

Week 6
BYE: Team D & Team 2
Team B vs Team C DIV
Team E vs Team F DIV
Team 1 vs Team 4 CONF
Team 3 vs Team 5 CONF
Team A vs Team 6

Week 7
BYE: Team F & Team 6
Team A vs Team C DIV
Team 1 vs Team 3 DIV
Team 4 vs Team 5 DIV
Team 2 vs Team E
Team B vs Team D CONF

Week 8
BYE: Team B & Team 4
Team 1 vs Team 2 DIV
Team 5 vs Team 6 DIV
Team D vs Team E DIV
Team A vs Team F CONF
Team 3 vs Team C

Week 9
Team A vs Team B DIV
Team 4 vs Team 6 DIV
Team D vs Team F DIV
Team 2 vs Team 5 CONF
Team C vs Team E CONF

Games Left
-----------------

Team B vs Team E CONF
Team C vs Team D CONF
Team 1 vs Team 6 CONF

------------------------------------
------------------------------------

Team 1 vs Team D - Week 3
Team 2 vs Team E - Week 7
Team 3 vs Team C - Week 8
Team 4 vs Team F - Week 4
Team 5 vs Team B - Week 5
Team 6 vs Team A - Week 6
```

```Week 1
TEAM_A vs. TEAM_D
TEAM_B vs. TEAM_E
TEAM_C vs. TEAM_F
TEAM_1 vs. TEAM_4
TEAM_2 vs. TEAM_5
TEAM_3 vs. TEAM_6

Week 2
TEAM_A vs. TEAM_E
TEAM_B vs. TEAM_F
TEAM_C vs. TEAM_D
TEAM_1 vs. TEAM_5
TEAM_2 vs. TEAM_6
TEAM_3 vs. TEAM_4

Week 3
TEAM_B vs. TEAM_C
TEAM_D vs. TEAM_E
TEAM_F vs. TEAM_6
TEAM_2 vs. TEAM_3
TEAM_4 vs. TEAM_5

Week 4
TEAM_A vs. TEAM_C
TEAM_D vs. TEAM_F
TEAM_E vs. TEAM_5
TEAM_1 vs. TEAM_3
TEAM_4 vs. TEAM_6

Week 5
TEAM_A vs. TEAM_B
TEAM_E vs. TEAM_F
TEAM_D vs. TEAM_4
TEAM_1 vs. TEAM_2
TEAM_5 vs. TEAM_6

Week 6
TEAM_A vs. TEAM_1
TEAM_B vs. TEAM_C
TEAM_D vs. TEAM_E
TEAM_4 vs. TEAM_6
TEAM_2 vs. TEAM_3

Week 7
TEAM_A vs. TEAM_B
TEAM_D vs. TEAM_F
TEAM_C vs. TEAM_3
TEAM_1 vs. TEAM_2
TEAM_4 vs. TEAM_5

Week 8
TEAM_1 vs. TEAM_3
TEAM_B vs. TEAM_2
TEAM_5 vs. TEAM_6
TEAM_A vs. TEAM_C
TEAM_E vs. TEAM_F

Week 9
TEAM_A vs. TEAM_F
TEAM_B vs. TEAM_D
TEAM_C vs. TEAM_E
TEAM_1 vs. TEAM_6
TEAM_2 vs. TEAM_4
TEAM_3 vs. TEAM_5
```

that was fun

Once again Cernel Johnson solves the weird random scheduling puzzle, why there are two of these so near each other in the forum I don't know...

I haven't checked the entire thing over but you've run into some similar issues that we did. For instance, team B plays 3 divisional games in a row from weeks 5-7.

So it's close, but no cigar

I had a feeling I might have forgotten something. I'll try again later.

```Week 1
TEAM A vs. TEAM D
TEAM B vs. TEAM E
TEAM C vs. TEAM F
TEAM 1 vs. TEAM 4
TEAM 2 vs. TEAM 5
TEAM 3 vs. TEAM 6

Week 2
TEAM A vs. TEAM E
TEAM B vs. TEAM F
TEAM C vs. TEAM D
TEAM 1 vs. TEAM 5
TEAM 2 vs. TEAM 6
TEAM 3 vs. TEAM 4

Week 3
TEAM B vs. TEAM C
TEAM D vs. TEAM E
TEAM F vs. TEAM 6
TEAM 2 vs. TEAM 3
TEAM 4 vs. TEAM 5

Week 4
TEAM A vs. TEAM B
TEAM D vs. TEAM F
TEAM E vs. TEAM 5
TEAM 1 vs. TEAM 2
TEAM 4 vs. TEAM 6

Week 5
TEAM A vs. TEAM C
TEAM E vs. TEAM F
TEAM D vs. TEAM 4
TEAM 1 vs. TEAM 3
TEAM 5 vs. TEAM 6

Week 6
TEAM A vs. TEAM 1
TEAM B vs. TEAM C
TEAM D vs. TEAM E
TEAM 4 vs. TEAM 5
TEAM 2 vs. TEAM 3

Week 7
TEAM A vs. TEAM B
TEAM D vs. TEAM F
TEAM C vs. TEAM 3
TEAM 1 vs. TEAM 2
TEAM 4 vs. TEAM 6

Week 8
TEAM 1 vs. TEAM 3
TEAM B vs. TEAM 2
TEAM 5 vs. TEAM 6
TEAM A vs. TEAM C
TEAM E vs. TEAM F

Week 9
TEAM A vs. TEAM F
TEAM B vs. TEAM D
TEAM C vs. TEAM E
TEAM 1 vs. TEAM 6
TEAM 2 vs. TEAM 4
TEAM 3 vs. TEAM 5
```

Fredrik Johansson waited. The lights above him blinked and sparked out of the air. There were maths in the base. He didn't see them, but had expected them now for years. His warnings to Cernel Joson were not listenend to and now it was too late. Far too late for now, anyway.
Fred was a mathematician for 3.14 years. When he was young he watched the spaceships and he said to dad "I want to be on the ships daddy."
Dad said "No! You will BE KILL BY MATHS"
There was a time when he believed him. Then as he got oldered he stopped. But now in the space station base of MIT he knew there were maths.
"This is Joson" the radio crackered. "You must solve the maths!"
So Fred gotted his pocket protector and put on the glasses.
"HE GOING TO DIFFERENTIATE US WITH RESPECT TO X" said the numbers
"I will shoot at him" said the partial differential equation and he integrated into a recursive infinite series. John Newton-Raphson methoded at him and tried to solve for y=0. But then the ceiling fell and they were trapped and not able to solve.
"No! I must solve the maths" he shouted
The radio said "No, Fred. You are the maths"
And then Fred was a mathematician.

This is the point where I should insert a witty remark.

I would too, but my usual lines are already done in fraggle's post.

Thanks for solving the maths Joson, much appreciated!

Cernel Joson said:
I would too, but my usual lines are already done in fraggle's post.

Yeah, if I were you I'd sue Simon Howard for plagiarism!