[bonanova]

Twenty friends, call them A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T,

decide to play bridge in foursomes for 5 days. To add to the fun, none of the

players will have the same partner, nor play against any other player, more

than once during the week.

Can you provide the schedule of foursomes [NEWS] that will accomplish their wishes?

Mon | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ |

Tue | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ |

Wed | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ |

Thu | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ |

Fri | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ |

[Guest]

Mon | A B C D | E F G H | I J K L | M N O P | Q R S T |

Tue | A F K P | E J O T | I N S D | M R C H | Q B G K |

Wed | A J S H | E N C L | I R G P | M B K T | Q F O D |

Thu | A N G T | E R K D | I B O H | M F S L | Q J C P |

Fri | A R O L | E B S P | I F C T | M J G D | Q N K H |

I didn't check it through, but I think it works

[Guest]

Mon | A B C D | E F G H | I J K L | M N O P | Q R S T |

Tue | E I M Q | A J N R | B F O S | C G K T | D H L P |

Wed | F J N R | A I M Q | B E P T | C H L S | D G K O |

Thu | G K O S | A L P T | B H M Q | C E I R | D F J N |

Fri | H L P T | A K O S | B G N R | C F J Q | D E I M |

[Guest]

Would it be possible to add that no player were allowed to play in the same group either?

/Uhre

[Guest]

Would it be possible to add that no player were allowed to play in the same group either?

/Uhre

I guess so

Mon | A B C D | E F G H | I J K L | M N O P | Q R S T |

Tue | E I M Q | A J N R | B F O S | C G K T | D H L P |

Wed | F J N R | B I M Q | A E P T | D H L S | C G K O |

Thu | G K O S | C L P T | D H M Q | A E I R | B F J N |

Fri | H L P T | D K O S | C G N R | B F J Q | A E I M |

Edit: Arh... I screwed that up. Yet, I still think it should be possible - or what?

/Uhre

Edited April 2, 2009 by uhre

[Guest]

I guess so

Mon | A B C D | E F G H | I J K L | M N O P | Q R S T |

Tue | E I M Q | A J N R | B F O S | C G K T | D H L P |

Wed | F J N R | B I M Q | A E P T | D H L S | C G K O |

Thu | G K O S | C L P T | D H M Q | A E I R | B F J N |

Fri | H L P T | D K O S | C G N R | B F J Q | A E I M |

Edit: Arh... I screwed that up. Yet, I still think it should be possible - or what?

/Uhre

Sorry, but at first glance I saw the same flaw in your both series:

Fist team at wed. and last team at thru. F and N plays together twice.

[Guest]

First my basic solution:

Mon A B C D | E F G H | I J K L | M N O P | Q R S T

Tue A R O L | E B S P | I F C T | M J G D | Q N K H

Wed A N G T | E R K D | I B O H | M F S L | Q J C P

Thu A J S H | E N C L | I R G P | M B K T | Q F O D

Fri A F K P | E J O T | I N S D | M R C H | Q B G L

You just need to cycle the players at different speeds;

The first column doesnt' move. The second column moves one table to the right for the next day. So B starts at table one, move to table two on Tuesday, table three on Wednesday and so on. F, J, N and R do the same.

Then the third column moves two tables to the right and the last column moves three tables to the right.

Yes, it's possible to add the extra constraint that a player can't play at the same table twice.

Mon A B C D | E F G H | I J K L | M N O P | Q R S T

Tue E R O L | I B S P | M F C T | Q J G D | A N K H

Wed I N G T | M R K D | Q B O H | A F S L | E J C P

Thu M J S H | Q N C L | A R G P | E B K T | I F O D

Fri Q F K P | A J O T | E N S D | I R C H | M B G L

Same solution as before, only the first column moves four tables to the right (=one to the left) every day.

[Prof. Templeton]

Mon, ABCD, EFGH, IJKL, MNOP, QRST

Tue, AEIM, BFJQ, CGNR, DKOS, HLPT

Wed, AFOT, BELR, CIPS, DGJM, HKNQ

Thu, AJPR, BHMS, CEKT, DFIN, GLOQ

Fri, ALNS, BGIT, CHJO, DEPQ, FKMR