perplexus.info :: General : The soccer tournament

The soccer tournament (Posted on 2005-07-26)

Eight (8) soccer teams (named A, B, C, D, E, F, G and H) are ready to a tournament among them, where each team will play against each of the other 7 teams once, and only once. They have 7 stadiums available, and agree that each team must play in all the 7 stadiums, once in each. In each round the 8 teams will play, so it will have 4 matches every day, and the tournament will last in 7 days.

Schedule the matches in each of the seven days, and in what stadiums they will be played.

Submitted by pcbouhid

Rating: 2.3333 (3 votes)

Solution: (Hide)

One basic schedule is :
(stadiums) (1) (2) (3) (4) (5) (6) (7) +-----+-----+-----+-----+-----+-----+-----+ 1st round | AxH | | | ExG | | CxD | BxF | +-----+-----+-----+-----+-----+-----+-----+ 2nd round | CxG | BxH | | | AxF | | DxE | +-----+-----+-----+-----+-----+-----+-----+ 3rd round | ExF | AxD | CxH | | | BxG | | +-----+-----+-----+-----+-----+-----+-----+ 4th round | | FxG | BxE | DxH | | | AxC | +-----+-----+-----+-----+-----+-----+-----+ 5th round | BxD | | AxG | CxF | ExH | | | +-----+-----+-----+-----+-----+-----+-----+ 6th round | | CxE | | AxB | DxG | FxH | | +-----+-----+-----+-----+-----+-----+-----+ 7th round | | | DxF | | BxC | AxE | GxH | +-----+-----+-----+-----+-----+-----+-----+
One curiosity in this solution : there is a symmetry (or an antisymmetry) in respect to the main diagonal (from the upper left cell to the right bottom cell) : if one "cell" is filled, the corresponding symmetrical "cell" is empty, and vice-versa.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution	FrankM	2022-12-22 20:42:08
To pcbouhid :-)	Penny	2005-07-29 21:54:11
re: Prettier Solution	Jack	2005-07-29 01:35:22
From a recent problem posted by Charley - literally	pcbouhid	2005-07-27 18:47:38
Prettier Solution	bernie	2005-07-27 18:35:26
The Conversing Club 3	Penny	2005-07-27 15:39:14
re: Solution !!!	bernie	2005-07-27 00:55:17
Solution !!!	Penny	2005-07-27 00:19:29
re: Correct solution	pcbouhid	2005-07-26 19:17:52
Correct solution	Namita	2005-07-26 18:41:16
wrong	Namita	2005-07-26 18:39:45
Did I get the problem right??	Namita	2005-07-26 18:37:05

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