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My country has more then 50 cities, each has a football team, and a stadium. Our sports minister ordered me to make a schedule so that if a team makes a match this week on its own stadium, next week the match must be on rivals stadium, the other week again on its own stad. I mean the schedule should be in such a order: ....0101010101.... I'm trying for weeks but I couldn't manage it. Please help me, how many cities are needed for that quite ordered schedule ?. I'll request our president to establish new cities. (Excuse me for bad english.)

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My country has more then 50 cities, each has a football team, and a stadium. Our sports minister ordered me to make a schedule so that if a team makes a match this week on its own stadium, next week the match must be on rivals stadium, the other week again on its own stad. I mean the schedule should be in such a order: ....0101010101.... I'm trying for weeks but I couldn't manage it. Please help me, how many cities are needed for that quite ordered schedule ?. I'll request our president to establish new cities. (Excuse me for bad english.)

Not sure I understand what you're asking.

Half the teams [group A] play at home on odd numbered weeks, away the other weeks.

The other half [group B] play at home on even numbered weeks, at home the other weeks.

Group A teams can never play each other.

Group B teams can never play each other.

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Not sure I understand what you're asking.
Half the teams [group A] play at home on odd numbered weeks, away the other weeks.

The other half [group B] play at home on even numbered weeks, at home the other weeks.

Group A teams can never play each other.

Group B teams can never play each other.

I'm guessing that by "football" he means soccer.

Why is that important? American football games are traditionally played once a week, with most or all games played on the same day. Other sports, soccer included, don't have this restriction. In that case, Group A teams could play each other because one team's odd-numbered game could be the other team's even-numbered game.

EDIT: That being said, I'm also not sure what the question is.

Edited by Chuck Rampart
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He means if any team plays away one week, the next week they have to play at home. So basically, yes, you'd have to arrange that half play away on odd-numbered days, then half would play away on even. So yeah, Bonanova is correct - the even--numbered teams would never play each other, and the odd numbered teams would never play each other.

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He means if any team plays away one week, the next week they have to play at home. So basically, yes, you'd have to arrange that half play away on odd-numbered days, then half would play away on even. So yeah, Bonanova is correct - the even--numbered teams would never play each other, and the odd numbered teams would never play each other.

What I'm saying is that the teams' schedules don't have to line up - it's not that the teams play at home on even numbered days, but that they play at home in even numbered games. For instance, consider a three team league with teams A, B and C. In this league, teams can play on consecutive days (so it's like baseball, I don't know how often major professional soccer leagues play).

Day 1: Team A @ Team B

Day 2: Team C @ team A

Day 3: Team B @ Team C

All three teams play each other, and they all go away-home or home-away. This (of course) gets more complicated for a 50 team league, but it is possible if the teams don't have to always all play simultaneously.

This could even work for an NFL-type schedule if you used the bye weeks appropriately. Although for an N-team league, you would probably need log2(N)/2 (or something like that) bye weeks per team to make it possible for everyone to play everyone else.

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We in Europe call that game football (not soccer). Americans invented that name I guess to differentiate it from American football (I don't even know why they call it like that, they carry the ball around).

So you have (European) football and American football!

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What I'm saying is that the teams' schedules don't have to line up - it's not that the teams play at home on even numbered days, but that they play at home in even numbered games. For instance, consider a three team league with teams A, B and C. In this league, teams can play on consecutive days (so it's like baseball, I don't know how often major professional soccer leagues play).

Day 1: Team A @ Team B

Day 2: Team C @ team A

Day 3: Team B @ Team C

All three teams play each other, and they all go away-home or home-away. This (of course) gets more complicated for a 50 team league, but it is possible if the teams don't have to always all play simultaneously.

This could even work for an NFL-type schedule if you used the bye weeks appropriately. Although for an N-team league, you would probably need log2(N)/2 (or something like that) bye weeks per team to make it possible for everyone to play everyone else.

Well he said "if a team makes a match this week on its own stadium, next week the match must be on rivals stadium, the other week again on its own [stadium]" which to me, suggests that each team plays 1 game a week, and plays it alternately at home, away, at home, etc etc

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I guess I've messed it up when asking the question. Excuse me for that. Indeed I intended soccer, we call it football in europe. Bonanova solved it quickly by naming the teams as odds and evens. But I don't think as Rampart who says that it will be possible if they don't play simultaneously. In his example with 3 teams, "A" doesn't play the second week, because it is off that week, that is okey but in a big number league, again only one team will be off each week, and it will not help us. If each week 1/3 of teams are off, only this way it will work.

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I guess I've messed it up when asking the question. Excuse me for that. Indeed I intended soccer, we call it football in europe. Bonanova solved it quickly by naming the teams as odds and evens. But I don't think as Rampart who says that it will be possible if they don't play simultaneously. In his example with 3 teams, "A" doesn't play the second week, because it is off that week, that is okey but in a big number league, again only one team will be off each week, and it will not help us. If each week 1/3 of teams are off, only this way it will work.

I think that, as the league gets bigger, the fraction of teams with a bye each week will decrease (but I haven't gone all the way through a larger example to test that). While it might not be a great solution, it is better than impossible.

EDIT: Moved background info to separate post.

Edited by Chuck Rampart
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Interesting side note (from Wikipedia): "The term soccer originated in England, first appearing in the 1880s as a slang abbreviation of the word 'association,' often credited to former England captain Charles Wreford-Brown."

All the different "football" games we have today - association/soccer, rugby, American, Australian - are descended from an even wider variety of different games of the 1800's that usually had their own local rules. Rugby football and Association football are the two that became standardized and enduringly popular in Europe. While calling American football "football" doesn't make much sense from a semantic standpoint (since the foot doesn't touch the ball all that often), it does make sense from a historical standpoint.

Also from Wikipedia -

"While it is widely believed that the word football, or "foot ball", originated in reference to the action of a foot kicking a ball, this may be a false etymology. An alternative explanation has it that the word originally referred to a variety of games in medieval Europe, which were played on foot. These sports were usually played by peasants, as opposed to the horse-riding sports more often enjoyed by aristocrats. This explanation is supported by the fact that the word football has always implied a wide variety of games played on foot, not just those that revolved around kicking a ball. In some cases, the word has been applied to games which involved carrying a ball and specifically banned kicking."

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