Re^3: Unique Combos with Math::Combinatorics (fair)

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Re^4: Unique Combos with Math::Combinatorics (perfect) by tye (Sage) on Mar 03, 2008 at 23:03 UTC
Interestingly, it says that the maximum can be achieved, however, the given solution: 7 rounds play in 6 groups of 4 golfers [ 1 2 11 21 \| 9 10 19 5 \| 17 18 3 13 \| 4 7 6 24 \| 8 12 14 15 \| 16 20 2 +2 23 ] [ 1 3 12 22 \| 9 11 20 6 \| 17 19 4 14 \| 5 8 7 18 \| 2 13 15 16 \| 10 21 2 +3 24 ] [ 1 4 13 23 \| 9 12 21 7 \| 17 20 5 15 \| 6 2 8 19 \| 3 10 14 16 \| 11 18 2 +2 24 ] [ 1 5 14 24 \| 9 13 22 8 \| 17 21 6 16 \| 7 3 2 20 \| 4 10 11 15 \| 12 18 1 +9 23 ] [ 1 6 15 18 \| 9 14 23 2 \| 17 22 7 10 \| 8 4 3 21 \| 5 11 12 16 \| 13 19 2 +0 24 ] [ 1 5 16 19 \| 9 15 24 3 \| 17 23 8 11 \| 2 5 4 22 \| 6 10 12 13 \| 14 18 2 +0 21 ] [ 1 8 10 20 \| 9 16 18 4 \| 17 24 2 12 \| 3 6 5 23 \| 7 11 13 14 \| 15 19 2 +1 22 ] [download] Obviously doesn't work since 1 is paired with 5 in both the 4th and 6th round. But that appars to be a typo and should be a 7 in round 6. Spot checking didn't turn up any other problem but I didn't fully verify the solution, which using our A..X notation would be: `ABKU IJSE QRCM DGFX HLNO PTVW ACLV IKTF QSDN EHGR BMOP JUWX ADMW ILUG QTEO FBHS CJNP KRVX AENX IMVH QUFP GCBT DJKO LRSW AFOR INWB QVGJ HDCU EKLP MSTX AGPS IOXC QWHK BEDV FJLM NRTU AHJT IPRD QXBL CFEW GKMN OSUV` [download] - tye	[reply] [d/l] [select]

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Re^4: Unique Combos with Math::Combinatorics (perfect)
by tye (Sage) on Mar 03, 2008 at 23:03 UTC

Interestingly, it says that the maximum can be achieved, however, the given solution:

7 rounds play in 6 groups of 4 golfers
[ 1 2 11 21 | 9 10 19 5 | 17 18 3 13 | 4 7 6 24 | 8 12 14 15 | 16 20 2
+2 23 ]
[ 1 3 12 22 | 9 11 20 6 | 17 19 4 14 | 5 8 7 18 | 2 13 15 16 | 10 21 2
+3 24 ]
[ 1 4 13 23 | 9 12 21 7 | 17 20 5 15 | 6 2 8 19 | 3 10 14 16 | 11 18 2
+2 24 ]
[ 1 5 14 24 | 9 13 22 8 | 17 21 6 16 | 7 3 2 20 | 4 10 11 15 | 12 18 1
+9 23 ]
[ 1 6 15 18 | 9 14 23 2 | 17 22 7 10 | 8 4 3 21 | 5 11 12 16 | 13 19 2
+0 24 ]
[ 1 5 16 19 | 9 15 24 3 | 17 23 8 11 | 2 5 4 22 | 6 10 12 13 | 14 18 2
+0 21 ]
[ 1 8 10 20 | 9 16 18 4 | 17 24 2 12 | 3 6 5 23 | 7 11 13 14 | 15 19 2
+1 22 ]
[download]

Obviously doesn't work since 1 is paired with 5 in both the 4th and 6th round. But that appars to be a typo and should be a 7 in round 6. Spot checking didn't turn up any other problem but I didn't fully verify the solution, which using our A..X notation would be:

ABKU IJSE QRCM DGFX HLNO PTVW
ACLV IKTF QSDN EHGR BMOP JUWX
ADMW ILUG QTEO FBHS CJNP KRVX
AENX IMVH QUFP GCBT DJKO LRSW
AFOR INWB QVGJ HDCU EKLP MSTX
AGPS IOXC QWHK BEDV FJLM NRTU
AHJT IPRD QXBL CFEW GKMN OSUV
[download]

- tye

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