Math/Logic expert help needed please!
Discussion
Guys,
I need an expert on logics or mathematical sequencing etc.
I need to draw up a tournament bracket/roster for a games tournament I am organising. It is proving to be particularly tricky and I have spent a few unsuccessful hours on it.
1) There are 16 teams (in two groups; A-H and I-P)
2) There are 8 game stations
3) There are 8 sequential time slots
For every time slot, two teams will challenge each other in a different each game station. The order of the game stations is not important. The only conditions are that:
1) Every team play at every station once.
2) Teams from A-H must play against a team from I-P. So, team A cannot challenge team C, but team A will challenge all teams in I-P once.
I have been trying to find a pattern for this to draw up a roster, but am failing. There must be some mathematical way of computing this, and I hope you smart guys can lend a hand.
Thanks!
I need an expert on logics or mathematical sequencing etc.
I need to draw up a tournament bracket/roster for a games tournament I am organising. It is proving to be particularly tricky and I have spent a few unsuccessful hours on it.
1) There are 16 teams (in two groups; A-H and I-P)
2) There are 8 game stations
3) There are 8 sequential time slots
For every time slot, two teams will challenge each other in a different each game station. The order of the game stations is not important. The only conditions are that:
1) Every team play at every station once.
2) Teams from A-H must play against a team from I-P. So, team A cannot challenge team C, but team A will challenge all teams in I-P once.
I have been trying to find a pattern for this to draw up a roster, but am failing. There must be some mathematical way of computing this, and I hope you smart guys can lend a hand.
Thanks!
JAYB has the right idea, sort-of. Try this instead:-
Time 1: AI/BJ/CK/DL/...
Time 2: AJ/BK/CL/DM/...
Time 3: AK/BL/CM/DN/...
etc...
Basically you've got 3 axes. Keep one fixed (in this case "Team A-H" - note they don't move in the above chart), and flex the other two linearly to each other, so as "Time" processes forwards, "Team I-P" processes forwards too.
Time 1: AI/BJ/CK/DL/...
Time 2: AJ/BK/CL/DM/...
Time 3: AK/BL/CM/DN/...
etc...
Basically you've got 3 axes. Keep one fixed (in this case "Team A-H" - note they don't move in the above chart), and flex the other two linearly to each other, so as "Time" processes forwards, "Team I-P" processes forwards too.
Edited by havoc on Tuesday 24th November 13:16
Close guys, and appreciate the help, but no cigar. There ends up being a situation where two teams play each other twice.
To make it easier to map out and to see, I've created an Excel spreadsheet - fill in the top row of each box with A-H, and the bottom of I-P. No two boxes can have the same combinations, but yet every team must occupy each row of time and column of station once.
http://www.xrcmedia.com/file.xls
It's harder than it looks, and would really appreciate assistance. Am pulling my hair out!
To make it easier to map out and to see, I've created an Excel spreadsheet - fill in the top row of each box with A-H, and the bottom of I-P. No two boxes can have the same combinations, but yet every team must occupy each row of time and column of station once.
http://www.xrcmedia.com/file.xls
It's harder than it looks, and would really appreciate assistance. Am pulling my hair out!
-DeaDLocK- said:
Close guys, and appreciate the help, but no cigar. There ends up being a situation where two teams play each other twice.
To make it easier to map out and to see, I've created an Excel spreadsheet - fill in the top row of each box with A-H, and the bottom of I-P. No two boxes can have the same combinations, but yet every team must occupy each row of time and column of station once.
http://www.xrcmedia.com/file.xls
It's harder than it looks, and would really appreciate assistance. Am pulling my hair out!
No repetition, I assure you. To make it easier to map out and to see, I've created an Excel spreadsheet - fill in the top row of each box with A-H, and the bottom of I-P. No two boxes can have the same combinations, but yet every team must occupy each row of time and column of station once.
http://www.xrcmedia.com/file.xls
It's harder than it looks, and would really appreciate assistance. Am pulling my hair out!
1 A vs I B vs K C vs M D vs O E vs I F vs K G vs M H vs O
2 B vs J C vs L D vs N E vs P F vs J G vs L H vs N A vs P
3 C vs K D vs M E vs O F vs I G vs K H vs M A vs O B vs I
4 D vs L E vs N F vs P G vs J H vs L A vs N B vs P C vs J
5 E vs M F vs O G vs I H vs K A vs M B vs O C vs I D vs K
6 F vs N G vs P H vs J A vs L B vs N C vs P D vs J E vs L
7 G vs O H vs I A vs K B vs M C vs O D vs I E vs K F vs M
8 H vs P A vs J B vs L C vs N D vs P E vs J F vs L G vs N
Station number to the left, each column pairing represents a time period. Every team from the first group plays every team from the second, and at a different station.
Edited by Justayellowbadge on Tuesday 24th November 14:04
Justayellowbadge said:
-DeaDLocK- said:
Close guys, and appreciate the help, but no cigar. There ends up being a situation where two teams play each other twice.
To make it easier to map out and to see, I've created an Excel spreadsheet - fill in the top row of each box with A-H, and the bottom of I-P. No two boxes can have the same combinations, but yet every team must occupy each row of time and column of station once.
http://www.xrcmedia.com/file.xls
It's harder than it looks, and would really appreciate assistance. Am pulling my hair out!
No repetition, I assure you. To make it easier to map out and to see, I've created an Excel spreadsheet - fill in the top row of each box with A-H, and the bottom of I-P. No two boxes can have the same combinations, but yet every team must occupy each row of time and column of station once.
http://www.xrcmedia.com/file.xls
It's harder than it looks, and would really appreciate assistance. Am pulling my hair out!
1 A vs I B vs K C vs M D vs O E vs I F vs K G vs M H vs O
2 B vs J C vs L D vs N E vs P F vs J G vs L H vs N A vs P
3 C vs K D vs M E vs O F vs I G vs K H vs M A vs O B vs I
4 D vs L E vs N F vs P G vs J H vs L A vs N B vs P C vs J
5 E vs M F vs O G vs I H vs K A vs M B vs O C vs I D vs K
6 F vs N G vs P H vs J A vs L B vs N C vs P D vs J E vs L
7 G vs O H vs I A vs K B vs M C vs O D vs I E vs K F vs M
8 H vs P A vs J B vs L C vs N D vs P E vs J F vs L G vs N
Station number to the left, each column pairing represents a time period. Every team from the first group plays every team from the second, and at a different station.
Edited by Justayellowbadge on Tuesday 24th November 14:04
Edited by Size Nine Elm on Tuesday 24th November 14:15
Size Nine Elm said:
Justayellowbadge said:
-DeaDLocK- said:
Close guys, and appreciate the help, but no cigar. There ends up being a situation where two teams play each other twice.
To make it easier to map out and to see, I've created an Excel spreadsheet - fill in the top row of each box with A-H, and the bottom of I-P. No two boxes can have the same combinations, but yet every team must occupy each row of time and column of station once.
http://www.xrcmedia.com/file.xls
It's harder than it looks, and would really appreciate assistance. Am pulling my hair out!
No repetition, I assure you. To make it easier to map out and to see, I've created an Excel spreadsheet - fill in the top row of each box with A-H, and the bottom of I-P. No two boxes can have the same combinations, but yet every team must occupy each row of time and column of station once.
http://www.xrcmedia.com/file.xls
It's harder than it looks, and would really appreciate assistance. Am pulling my hair out!
1 A vs I B vs K C vs M D vs O E vs I F vs K G vs M H vs O
2 B vs J C vs L D vs N E vs P F vs J G vs L H vs N A vs P
3 C vs K D vs M E vs O F vs I G vs K H vs M A vs O B vs I
4 D vs L E vs N F vs P G vs J H vs L A vs N B vs P C vs J
5 E vs M F vs O G vs I H vs K A vs M B vs O C vs I D vs K
6 F vs N G vs P H vs J A vs L B vs N C vs P D vs J E vs L
7 G vs O H vs I A vs K B vs M C vs O D vs I E vs K F vs M
8 H vs P A vs J B vs L C vs N D vs P E vs J F vs L G vs N
Station number to the left, each column pairing represents a time period. Every team from the first group plays every team from the second, and at a different station.
Edited by Justayellowbadge on Tuesday 24th November 14:04
Teams dont duplicate, but the second group repeat the same 4 stations.
Bugger.
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