In two weeks I have the responsibility of arranging a special singles bridge tournament for 21 people. Bridge is played by 4 people at a time, 2 pairs, so there will 5 tables playing in parallell (the same boards; three duplicates), and one person sits out each board.Anyone (including computer programs) up for the challenge?
For various reasons (minimize change and movement is one reason) it has been decided to conduct the tournament as follows:
- in the first round player A, B, C and D sit down at a table and play boards 1, 2 and 3. A partners B against C and D when playing board 1;
A partners C (against B&D) when playing board 2, and finally A partners D (against B&C) when playing board 3. Similarly, EFGH do the same on the next table (playing the same boards 1, 2 and 3), and so does IJKL and MNOP.
- QRSTU is slightly trickier, because only 4 can play at a time.
Basically Q and R sit still and partner S, T and U who rotate. So Q&S against R&T, U sit out board 1. Q&U against R&S, T sit out board 2. Finally Q&T against R&U, S sit out board 3. Note that Q and R do _not_ partner each other in this round.
- 9 rounds of 3 boards each, so 27 boards.
I want to design the seating in round 2, 3, .., 9 so that:
- all possible player pairs partner each other at least once, and no more than twice
- all players sit out at least one board, and no more than two boards
Using inspired guesswork and some Sudoku-like skills, I am unable to get rid of the last couple of triples (players who, in my scheme, will partner each other 3 times).
Monday, September 3, 2007
Real Combinatorial Problem
I found this real combinatorial problem on a puzzle group. And wanted to share it to all. Have a look