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Tournament blocks (view source)

Revision as of 18:21, 31 January 2015

3,013 bytes removed ,  31 January 2015
Fresh data, it's Warwick invading on Trundle's turf. {Saving to not lose anything}
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(Fresh data, it's Warwick invading on Trundle's turf. {Saving to not lose anything})
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The obvious flaw with this solution is that players are segregated into blocks. The method is fair as long as players draw from one pool with all entries mixed AND that the draw occurs fairly, in the presence of all players, or failing that, that the location and time of draw be published beforehand with a fair chance for all to attend. Both NMB tournaments (2011 in Utrecht) and the 2014 WRC used this method, however they both had flaws in their implementation.
The obvious flaw with this solution is that players are segregated into blocks. The method is fair as long as players draw from one pool with all entries mixed AND that the draw occurs fairly, in the presence of all players, or failing that, that the location and time of draw be published beforehand with a fair chance for all to attend. Both NMB tournaments (2011 in Utrecht) and the 2014 WRC used this method, however they both had flaws in their implementation.


The general formula is that table t consists of players [t, t + n/4, t + 2n/4, t + 3n/4] in hanchan 1, and for future hanchan h, tables consist of [t, ((t + 1*h) % n/4) + n/4, ((t + 2*h) % n/4) + 2n/4, ((t + 3*h) % n/4) + 3n/4]. Its usefulness can be demonstrated as soon as there are 44 or more participants, and preferably not a multiple of 6. Heavily composite numbers of players will lead to collisions when {...}
The general formula is that table t consists of players [t, t + n/4, t + 2n/4, t + 3n/4] in hanchan 0 {mathematically speaking so the formula works}, and for future hanchan h, tables consist of [t, ((t + 1*h) % n/4) + n/4, ((t + 2*h) % n/4) + 2n/4, ((t + 3*h) % n/4) + 3n/4]. Its usefulness can be demonstrated as soon as there are 44 or more participants, and preferably not a multiple of 3. Heavily composite numbers of players will lead to collisions when tables = h * factor. The 2014 WRC had 120 players over 30 tables: as 120 (as well as 30) is divisible by 3, it would lead to a collision when h = 10, making the 11th hanchan place naively two players who met before across all 30 tables.


Notes:
Notes:
[http://www.mathpuzzle.com/MAA/54-Golf%20Tournaments/mathgames_08_14_07.html Mathpuzzle.com] has a few non-Dutch solutions for the "Social Golfer Problem".<br />
[http://www.mathpuzzle.com/MAA/54-Golf%20Tournaments/mathgames_08_14_07.html Mathpuzzle.com] has a few non-Dutch solutions for the "Social Golfer Problem". -- As does the web archive, from [http://web.archive.org/web/20050407074608/http://www.icparc.ic.ac.uk/~wh/golf/solutions.html Warwick Harvey]<br />
 
===== Blocks of 4 =====
{| class="wikitable"
{| class="wikitable"
|-
|-
! Players !! Method !! Dutch !! Social Golfer !! Comment
! Players !! Block !! Of !! Raw data
|-
| 16 || 1 || 5 || ABCD EFGH IJKL MNOP
|-
| 16 || 2 || 5 || AEIM BFJN CGKO DHLP
|-
| 16 || 3 || 5 || AFKP BELO CHIN DGJM
|-
| 16 || 4 || 5 || AGLN BHKM CEJP DFIO
|-
| 16 || 5 || 5 || AHJO BGIP CFLM DEKN.
|-
| 20 || 1 || 5 || ABCD EFGH IJKL MNOP QRST
|-
| 20 || 2 || 5 || AEIM BFJQ CGNR DKOS HLPT
|-
| 20 || 3 || 5 || AFOT BELR CIPS DGJM HKNQ
|-
| 20 || 4 || 5 || AJPR BHMS CEKT DFIN GLOQ
|-
| 20 || 5 || 5 || ALNS BGIT CHJO DEPQ FKMR.
|-
| 24 || 1 || 7 || ABKU IJSE QRCM DGFX HLNO PTVW
|-
| 24 || 2 || 7 || ACLV IKTF QSDN EHGR BMOP JUWX
|-
| 24 || 3 || 7 || ADMW ILUG QTEO FBHS CJNP KRVX
|-
| 24 || 4 || 7 || AENX IMVH QUFP GCBT DJKO LRSW
|-
| 24 || 5 || 7 || AFOR INWB QVGJ HDCU EKLP MSTX
|-
| 24 || 6 || 7 || AEPS IOXC QWHK BEDV FJLM NRTU
|-
| 24 || 7 || 7 || AHJT IPRD QXBL CFEW GKMN OSUV.
|-
| 28 || 1 || 9 || ABCD EFGH IJKL MNab cdef ghij klmn
|-
| 28 || 1 || 9 || AEgk BFMc Ndhl GIem HJai CKbn DLfj
|-
| 28 || 1 || 9 || AFjn BEae bfim HKcl GLMh CINk DJdg
|-
| 28 || 1 || 9 || AIci BJNn EKMj FLdm begl CGaf DHhk
|-
| 28 || 1 || 9 || AGbd BHgm ELNi achn FKfk CJej DIMl
|-
| 28 || 1 || 9 || AKeh BLbk FIag EJfl Ncjm CHMd DGin
|-
| 28 || 1 || 9 || AHNf BGjl FJbh Meik EIdn CLcg DKam
|-  
|-  
| 16 (4*4) || SG || || 5 || ABCD EFGH IJKL MNOP, <br />AEIM BFJN CGKO DHLP, <br />AFKP BELO CHIN DGJM, <br />AGLN BHKM CEJP DFIO, <br />AHJO BGIP CFLM DEKN.
| 28 || 1 || 9 || ALal BKdi GJck Mfgn HIbj CEhm DFNe
|-  
|-  
| 20 (5*4) || Both || 5 || 5 || ABCD EFGH IJKL MNOP QRST, <br />AEIM BFJQ CGNR DKOS HLPT, <br />AFOT BELR CIPS DGJM HKNQ, <br />AJPR BHMS CEKT DFIN GLOQ, <br />ALNS BGIT CHJO DEPQ FKMR.
| 28 || 1 || 9 || AJMm BIfh CFil DEbc GKNg HLen adjk.  
|-  
|-  
| 24 (6*4) || SG || || 7 || ABKU IJSE QRCM DGFX HLNO PTVW, <br />ACLV IKTF QSDN EHGR BMOP JUWX, <br />ADMW ILUG QTEO FBHS CJNP KRVX, <br />AENX IMVH QUFP GCBT DJKO LRSW, <br />AFOR INWB QVGJ HDCU EKLP MSTX, <br />AEPS IOXC QWHK BEDV FJLM NRTU, <br />AHJT IPRD QXBL CFEW GKMN OSUV.
| 32 || 1 || 10 || ABCD EFGH IJKL MNPO abcd efgh ijkl mnop
|-  
|-  
| 28 (7*4) || SG || || 9 || ABCD EFGH IJKL MNab cdef ghij klmn, <br />AEgk BFMc Ndhl GIem HJai CKbn DLfj, <br />AFjn BEae bfim HKcl GLMh CINk DJdg, <br />AIci BJNn EKMj FLdm begl CGaf DHhk, <br />AGbd BHgm ELNi achn FKfk CJej DIMl, <br />AKeh BLbk FIag EJfl Ncjm CHMd DGin, <br />AHNf BGjl FJbh Meik EIdn CLcg DKam, <br />ALal BKdi GJck Mfgn HIbj CEhm DFNe, <br />AJMm BIfh CFil DEbc GKNg HLen adjk.
| 32 || 2 || 10 || AEIm BgcH DFKp kPdf Maei ChbG jNoL lJnO
|-  
|-  
| 32 (8*4) || SG || || 10 || ABCD EFGH IJKL MNPO abcd efgh ijkl mnop, <br />AEIm BgcH DFKp kPdf Maei ChbG jNoL lJnO, <br />Alof Bhkm DNGi FaLO MbHK CPeJ Ejcp gIdn, <br />AciL BjdK DkbJ FgoP fGOp CIla EhMn NeHm, <br />AgNK BElP DIoH hdiO beLp Cjfm FMcJ kaGn, <br />AhJp BFin DcmO INbf leGK CMod EgkL jPaH, <br />AFde BoGJ DEaf hlNc PiKm CHLn gjbO IkMp, <br />APbn BNap DglM koce fHiJ CEKO FhIj dGLm, <br />AjMG BIeO DhPL gaJm cfKn CFkN Eobi ldHp, <br />AkHO BMfL Djen Flbm IPcG Cgip ENdJ hoaK.  
| 32 || 3 || 10 || Alof Bhkm DNGi FaLO MbHK CPeJ Ejcp gIdn
|-
| 32 || 4 || 10 || AciL BjdK DkbJ FgoP fGOp CIla EhMn NeHm
|-
| 32 || 5 || 10 || AgNK BElP DIoH hdiO beLp Cjfm FMcJ kaGn
|-
| 32 || 6 || 10 || AhJp BFin DcmO INbf leGK CMod EgkL jPaH
|-
| 32 || 7 || 10 || AFde BoGJ DEaf hlNc PiKm CHLn gjbO IkMp
|-
| 32 || 8 || 10 || APbn BNap DglM koce fHiJ CEKO FhIj dGLm
|-
| 32 || 9 || 10 || AjMG BIeO DhPL gaJm cfKn CFkN Eobi ldHp
|-
| 32 || 10 || 10 || AkHO BMfL Djen Flbm IPcG Cgip ENdJ hoaK.  
|-
| 36 || 1 || 8 || [&#160;[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], [17, 18, 19, 20], [21, 22, 23, 24], [25, 26, 27, 28], [29, 30, 31, 32], [33, 34, 35, 36]&#160;]
|-
| 36 || 2 || 8 || [&#160;[1, 5, 9, 13], [2, 6, 10, 17], [3, 7, 11, 21], [4, 8, 12, 25], [14, 18, 22, 29], [15, 19, 23, 33], [16, 26, 30, 34], [20, 27, 31, 35], [24, 28, 32, 36]&#160;]
|-
| 36 || 3 || 8 || [&#160;[1, 6, 11, 25], [2, 7, 9, 16], [3, 5, 10, 20], [4, 14, 21, 33], [8, 15, 18, 32], [12, 13, 17, 22], [19, 27, 30, 36], [23, 28, 31, 34], [24, 26, 29, 35]&#160;]
|-
| 36 || 4 || 8 || [&#160;[1, 10, 18, 21], [2, 8, 13, 29], [3, 14, 31, 36], [4, 9, 20, 23], [5, 15, 17, 28], [6, 12, 16, 19], [7, 26, 32, 33], [11, 24, 27, 34], [22, 25, 30, 35]&#160;]
|-
| 36 || 5 || 8 || [&#160;[1, 14, 24, 30], [2, 12, 18, 34], [3, 9, 17, 32], [4, 6, 28, 35], [5, 21, 29, 36], [7, 10, 19, 25], [8, 16, 23, 27], [11, 13, 20, 33], [15, 22, 26, 31]&#160;]
|-
| 36 || 6 || 8 || [&#160;[1, 12, 23, 26], [2, 11, 22, 36], [3, 6, 13, 24], [4, 10, 16, 32], [5, 18, 27, 33], [7, 20, 28, 30], [8, 14, 19, 35], [9, 15, 29, 34], [17, 21, 25, 31]&#160;]
|-
| 36 || 7 || 8 || [&#160;[1, 19, 28, 29], [2, 5, 23, 30], [3, 12, 15, 27], [4, 11, 18, 31], [6, 9, 26, 36], [7, 14, 17, 34], [8, 10, 22, 33], [13, 21, 32, 35], [16, 20, 24, 25]&#160;]
|-
| 36 || 8 || 8 || [&#160;[1, 7, 15, 35], [2, 14, 25, 32], [3, 16, 18, 28], [4, 17, 27, 29], [5, 11, 19, 26], [6, 20, 22, 34], [8, 9, 21, 30], [10, 13, 23, 36], [12, 24, 31, 33]&#160;]
|- style="background:#ccf"
|- style="background:#ccf"
| 40 (10*4) || Unkn. || 5/6ND || ||  
| 40 (10*4) || Unkn. || 5/6ND ||
|-  
|-  
| 44 (11*4) || Dutch || 11 || ||
| 44 (11*4) || Dutch || 11 ||
|-  
|-  
| 52 (13*4) || Dutch || 13 || ||
| 52 (13*4) || Dutch || 13 ||
|-  
|-  
| 68 (17*4) || Dutch || 17 || ||  
| 68 (17*4) || Dutch || 17 ||
|-  
|-  
| 76 (19*4) || Dutch || 19 || ||  
| 76 (19*4) || Dutch || 19 ||  
|}
|}


Line 52: Line 132:
{| class="wikitable"
{| class="wikitable"
|-
|-
! Players !! P1 !! P2 !! P3 !! P4 !! P5 !! Comment
! Players !! Round !! Of !! Match-ups
|-  style="background:#ccf"
| 25 || 1st || of 6 || [&#160;[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]&#160;]
|-  style="background:#ccf"
| 25 || 2nd || of 6 || [&#160;[1, 6, 11, 16, 21], [2, 7, 12, 17, 22], [3, 8, 13, 18, 23], [4, 9, 14, 19, 24], [5, 10, 15, 20, 25]&#160;]
|-  style="background:#ccf"
| 25 || 3rd || of 6 || [&#160;[1, 7, 13, 19, 25], [2, 8, 14, 20, 21], [3, 9, 15, 16, 22], [4, 10, 11, 17, 23], [5, 6, 12, 18, 24]&#160;]
|-  style="background:#ccf"
| 25 || 4th || of 6 || [&#160;[1, 8, 15, 17, 24], [2, 9, 11, 18, 25], [3, 10, 12, 19, 21], [4, 6, 13, 20, 22], [5, 7, 14, 16, 23]&#160;]
|-  style="background:#ccf"
| 25 || 5th || of 6 || [&#160;[1, 9, 12, 20, 23], [2, 10, 13, 16, 24], [3, 6, 14, 17, 25], [4, 7, 15, 18, 21], [5, 8, 11, 19, 22]&#160;]
|-  style="background:#ccf"
| 25 || 6th || of 6 || [&#160;[1, 10, 14, 18, 22], [2, 6, 15, 19, 23], [3, 7, 11, 20, 24], [4, 8, 12, 16, 25], [5, 9, 13, 17, 21]&#160;]
|-  
|-  
| 30 || 0 || 0 || 0 || 0 || 0 || 2 sessions.
| 30 || 1st || of 6 || [&#160;[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30]&#160;]
|-  
|-  
| 30 || 0 || 1 || 2 || 3 || 4 ||
| 30 || 2nd || of 6 || [&#160;[1, 6, 11, 16, 21], [2, 7, 13, 19, 30], [3, 8, 14, 24, 29], [4, 9, 20, 25, 28], [5, 15, 18, 23, 27], [10, 12, 17, 22, 26]&#160;]
|-  
|-  
| 35 || 0 || 0 || 0 || 0 || 0 || 7 sessions (28P-35P)
| 30 || 3rd || of 6 || [&#160;[1, 8, 13, 20, 22], [2, 6, 12, 23, 28], [3, 9, 11, 18, 30], [4, 15, 16, 24, 26], [5, 7, 17, 25, 29], [10, 14, 19, 21, 27]&#160;]
|-  
|-  
| 35 || 0 || 1 || 2 || 3 || 4 ||
| 30 || 4th || of 6 || [&#160;[1, 7, 18, 24, 28], [2, 10, 11, 20, 29], [3, 6, 15, 19, 22], [4, 14, 17, 23, 30], [5, 9, 13, 21, 26], [8, 12, 16, 25, 27]&#160;]
|-  
|-  
| 35 || 0 || 2 || 4 || 6 || 1 ||
| 30 || 5th || of 6 || [&#160;[1, 10, 15, 25, 30], [2, 9, 17, 24, 27], [3, 7, 12, 20, 21], [4, 6, 13, 18, 29], [5, 14, 16, 22, 28], [8, 11, 19, 23, 26]&#160;]
|-  
|-  
| 35 || 0 || 3 || 6 || 2 || 5 ||  
| 30 || 6th || of 6 || [&#160;[1, 9, 12, 19, 29], [5, 6, 20, 24, 30], [4, 7, 11, 22, 27], [8, 15, 17, 21, 28], [3, 10, 13, 16, 23], [2, 14, 18, 25, 26]&#160;]
|-  style="background:#ccf"
| 35 || all || of 7 || <colspan="4"> | Dutch cycles. {28P-35P}
|-  
|-  
| 35 || 0 || 4 || 1 || 5 || 2 ||
| 40 || 1st || of 6 || [&#160;[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30], [31, 32, 33, 34, 35], [36, 37, 38, 39, 40]&#160;]
|-  
|-  
| 35 || 0 || 5 || 3 || 1 || 6 ||
| 40 || 2nd || of 6 || [&#160;[1, 6, 11, 16, 21], [2, 7, 12, 26, 31], [3, 8, 13, 17, 36], [4, 9, 14, 27, 32], [5, 10, 15, 22, 37], [18, 23, 28, 33, 38], [19, 24, 29, 34, 39], [20, 25, 30, 35, 40]&#160;]
|-  
|-  
| 35 || 0 || 6 || 5 || 4 || 3 ||
| 40 || 3rd || of 6 || [&#160;[1, 7, 14, 17, 22], [2, 6, 13, 28, 34], [3, 10, 11, 27, 40], [4, 8, 12, 20, 33], [5, 9, 16, 25, 39], [15, 21, 29, 31, 38], [18, 24, 26, 35, 36], [19, 23, 30, 32, 37]&#160;]
|-  
|-  
| 45 || 0 || 0 || 0 || 0 || 0 || 3 sessions
| 40 || 4th || of 6 || [&#160;[1, 8, 15, 19, 35], [2, 16, 22, 27, 33], [3, 9, 12, 24, 38], [4, 6, 30, 31, 36], [5, 14, 23, 34, 40], [7, 11, 20, 28, 39], [10, 17, 21, 26, 32], [13, 18, 25, 29, 37]&#160;]
|-  
|-  
| 45 || 0 || 1 || 2 || 3 || 4 ||
| 40 || 5th || of 6 || [&#160;[1, 9, 13, 31, 40], [2, 15, 20, 24, 32], [3, 14, 21, 33, 39], [4, 16, 26, 34, 37], [5, 7, 27, 35, 38], [6, 12, 17, 23, 29], [8, 11, 18, 22, 30], [10, 19, 25, 28, 36]&#160;]
|-  
|-  
| 45 || 0 || 2 || 4 || 6 || 8 ||  
| 40 || 6th || of 6 || [&#160;[1, 10, 12, 18, 39], [2, 9, 11, 23, 35], [3, 6, 15, 25, 26], [4, 13, 19, 22, 38], [5, 17, 24, 30, 33], [7, 16, 29, 32, 40], [8, 14, 28, 31, 37], [20, 21, 27, 34, 36]&#160;]
|-  style="background:#ccf"
| 45 || 1st || of 6 || [&#160;[20, 24, 32, 39, 43], [6, 29, 31, 33, 42], [7, 11, 17, 34, 45], [12, 14, 15, 18, 25], [2, 5, 8, 9, 19], [1, 4, 16, 27, 28], [3, 13, 23, 30, 35], [10, 22, 26, 38, 40], [21, 36, 37, 41, 44]&#160;]
|-  style="background:#ccf"
| 45 || 2nd || of 6 || [&#160;[5, 17, 28, 40, 41], [11, 13, 22, 24, 27], [8, 25, 32, 33, 37], [9, 10, 20, 30, 45], [2, 12, 16, 29, 44], [3, 15, 36, 42, 43], [4, 6, 18, 23, 26], [1, 14, 19, 21, 34], [7, 31, 35, 38, 39]&#160;]
|-  style="background:#ccf"
| 45 || 3rd || of 6 || [&#160;[4, 21, 25, 31, 40], [13, 16, 41, 43, 45], [2, 20, 22, 33, 34], [9, 14, 23, 27, 38], [17, 18, 19, 29, 32], [7, 8, 12, 30, 36], [1, 15, 26, 37, 39], [3, 5, 6, 24, 44], [10, 11, 28, 35, 42]&#160;]
|-  style="background:#ccf"
| 45 || 4th || of 6 || [&#160;[19, 27, 40, 42, 45], [4, 12, 17, 22, 39], [8, 13, 20, 26, 44], [18, 24, 30, 37, 38], [7, 23, 28, 29, 43], [6, 11, 15, 21, 32], [3, 9, 16, 25, 34], [1, 5, 33, 35, 36], [2, 10, 14, 31, 41]&#160;]
|-  style="background:#ccf"
| 45 || 5th || of 6 || [&#160;[4, 7, 9, 15, 41], [11, 25, 26, 29, 36], [8, 16, 18, 39, 40], [27, 30, 31, 34, 44], [14, 22, 35, 37, 43], [5, 12, 13, 21, 42], [6, 19, 20, 28, 38], [1, 2, 3, 32, 45], [10, 17, 23, 24, 33]&#160;]
|-  style="background:#ccf"
| 45 || 6th || of 6 || [&#160;[4, 8, 24, 29, 45], [6, 13, 14, 36, 40], [15, 16, 19, 22, 23], [5, 7, 10, 18, 27], [3, 17, 20, 31, 37], [1, 11, 38, 43, 44], [9, 21, 26, 28, 33], [12, 32, 34, 35, 41], [2, 25, 30, 39, 42]&#160;]
|-  
|-  
| 50 || 0 || 0 || 0 || 0 || 0 || 5/6 sessions (40P-50P)
| 50 || all || of 5 || Dutch cycles work for 5 sessions only.
|-  
|-  
| 50 || 0 || 1 || 2 || 3 || 4 ||
| 50 || 1st || of 7 || [&#160;[5, 16, 18, 25, 29], [1, 7, 27, 42, 46], [4, 6, 15, 21, 41], [3, 11, 26, 30, 32], [9, 19, 24, 37, 38], [8, 13, 33, 43, 45], [35, 40, 47, 48, 49], [17, 23, 31, 34, 50], [2, 12, 14, 20, 36], [10, 22, 28, 39, 44]&#160;]
|-  
|-  
| 50 || 0 || 2 || 4 || 6 || 8 ||
| 50 || 1st || of 7 || [&#160;[8, 20, 40, 42, 44], [15, 16, 17, 22, 47], [1, 10, 23, 29, 38], [3, 6, 28, 36, 48], [2, 24, 27, 33, 39], [7, 11, 13, 21, 31], [4, 32, 35, 45, 46], [9, 14, 18, 34, 41], [25, 30, 37, 43, 50], [5, 12, 19, 26, 49]&#160;]
|-  
|-  
| 50 || 0 || 3 || 6 || 9 || 2 ||
| 50 || 1st || of 7 || [&#160;[19, 21, 29, 32, 47], [8, 24, 25, 28, 34], [3, 18, 31, 44, 46], [4, 14, 39, 43, 49], [2, 10, 15, 42, 45], [9, 11, 16, 20, 50], [5, 7, 23, 37, 40], [1, 13, 26, 41, 48], [22, 33, 35, 36, 38], [6, 12, 17, 27, 30]&#160;]
|-  
|-  
| 50 || 0 || 4 || 8 || 2 || 6 ||
| 50 || 1st || of 7 || [&#160;[10, 14, 16, 21, 26], [23, 25, 36, 39, 42], [9, 13, 32, 44, 49], [3, 5, 8, 22, 27], [4, 11, 17, 38, 40], [12, 24, 43, 46, 48], [2, 7, 19, 41, 50], [1, 18, 28, 30, 33], [6, 34, 37, 45, 47], [15, 20, 29, 31, 35]&#160;]
|-  
|-  
| 50 || 0 || 9 || 5 || 4 || X0 || (non-Dutch, one repeat for 10 pairs.)
| 50 || 1st || of 7 || [&#160;[13, 20, 22, 30, 34], [26, 27, 38, 45, 50], [1, 11, 36, 43, 44], [16, 32, 33, 37, 41], [4, 9, 12, 31, 47], [14, 28, 29, 40, 46], [5, 6, 24, 35, 42], [7, 15, 18, 39, 48], [2, 8, 21, 23, 49], [3, 10, 17, 19, 25]&#160;]
|-  
|-  
| 55 || 0 || 0 || 0 || 0 || 0 || 11 sessions (44P-55P)
| 50 || 1st || of 7 || [&#160;[6, 26, 31, 39, 40], [11, 14, 22, 37, 42], [2, 5, 9, 17, 48], [4, 24, 29, 44, 50], [15, 19, 34, 36, 46], [3, 7, 20, 33, 49], [10, 18, 27, 32, 43], [13, 16, 23, 28, 35], [1, 12, 21, 25, 45], [8, 30, 38, 41, 47]&#160;]
|-  
|-  
| 55 || 0 || 1 || 2 || 3 || 4 ||
| 50 || 1st || of 7 || [&#160;[11, 18, 23, 24, 47], [22, 31, 41, 45, 49], [3, 9, 21, 40, 43], [2, 6, 13, 38, 46], [14, 25, 27, 35, 44], [12, 15, 28, 32, 50], [4, 5, 10, 33, 34], [7, 8, 26, 29, 36], [1, 17, 20, 37, 39], [16, 19, 30, 42, 48]&#160;]
|-  style="background:#ccf"
| 55 || all || of 11 || Dutch cycles. {44P-55P}
|-  
|-  
| 55 || 0 || 2 || 4 || 6 || 8 ||  
| 60 || all || of 6 || G(25+35) or G(30+30).
|-  style="background:#ccf"
| 65 || all || of 13 || Dutch cycles. {52P-65P}
|-  
|-  
| 55 || 0 || 3 || 6 || 9 || 1 ||  
| 70 || all || of 7 || G(35+35).
|-  style="background:#ccf"
| 75 || all || of 6 || G(35+40), G(30+45) {both 60P-75P}; G(25+25+25) {72P-75P}.
|-  
|-  
| 55 || 0 || 4 || 8 || 1 || 5 ||  
| {5*prime} || all || of {prime} || Dutch cycles. {{4*prime}P-{5*prime}P}; prime>=5. (25 is the special case, where it gets the sixth extra session by virtue of being 25 = 5^2.)
|-
| 55 || 0 || 5 || 10 || 4 || 9 ||
|-  
| 55 || 0 || 6 || 1 || 7 || 2 ||
|-
| 55 || 0 || 7 || 3 || 10 || 6 ||
|-
| 55 || 0 || 8 || 5 || 2 || 10 ||
|-
| 55 || 0 || 9 || 7 || 5 || 3 ||
|-
| 55 || 0 || 10 || 9 || 8 || 7 ||
|}
|}


Line 141: Line 241:




==== 15-player season ====
==== X-player season ====
 
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! Session and Table !! Player 1 !! Player 2 !! Player 3 !! Player 4 !! Player 5 !! Deadline
! Min. Players !! Max Players !! Mechanism !! Comment
|- style="background:#ccf"
|-  
| Session 1 - Table 1 (+1) || P1 || P2 || P3 || P4 || P5 || Saturday 2015-04-04 23:59 UTC
| 10 || 10 || 5P randomize || Repeats will forcibly occur.
|- style="background:#ccf"
|-  
| Session 1 - Table 2 || P6 || P7 || P8 || P9 || P10 || Saturday 2015-04-04 23:59 UTC
| 11 || 12 || Not possible || With thirds promotion, 10 in top group, 18 in next, top group gets 13+.
|- style="background:#ccf"
|-  
| Session 1 - Table 3 || P11 || P12 || P13 || P14 || P15 || Saturday 2015-04-04 23:59 UTC
| 13 || 15 || Mix and randomize || Repeats will forcibly occur.
|-
|-  
| Session 2 - Table 1 (+3) || P1 || P4 || P7 || P10 || P13 || Saturday 2015-04-18 23:59 UTC
| 16 || 16 || 4P perfect + Siberian or Random (6th) || 5 sessions covered, 6th pairing could be done randomly at the start or drawn later (at a pre-announced time) relative to current ranking.
|-
|-  
| Session 2 - Table 2 || P2 || P5 || P8 || P11 || P14 || Saturday 2015-04-18 23:59 UTC
| 17 || 23 || Mix and randomize || Repeats will most likely occur.
|-
|-  
| Session 2 - Table 3 || P3 || P6 || P9 || P12 || P15 || Saturday 2015-04-18 23:59 UTC
| 24 || 25 || 5P perfect || For 24 players, ignore 25th player in grid, those sessions are 4P
|- style="background:#ccf"
|-  
| Session 3 - Table 1 (+8) || P1 || P9 || P2 || P10 || P3 || Saturday 2015-05-02 23:59 UTC
| 26 || 27 || Mix and randomize || {TBD.}
|- style="background:#ccf"
|-  
| Session 3 - Table 2 || P11 || P4 || P12 || P5 || P13 || Saturday 2015-05-02 23:59 UTC
| 28 || 28 || Use 4P ||
|- style="background:#ccf"
|-  
| Session 3 - Table 3 || P6 || P14 || P7 || P15 || P8 || Saturday 2015-05-02 23:59 UTC
| 29 || 30 || Use 5P || For 29 players, ignore 30th player in grid, those sessions are 4P
|-
|-  
| Session 4 - Table 1 (+11) || P1 || P12 || P8 || P4 || P15 || Saturday 2015-05-16 23:59 UTC
| 31 || 35 || Use 5P grid for 35 ||  
|-
|-  
| Session 4 - Table 2 || P11 || P7 || P3 || P14 || P10 || Saturday 2015-05-16 23:59 UTC
| 36 || 40 || Use 5P grid for 40 || Grid can ignore last 5 players.
|-
| Session 4 - Table 3 || P6 || P2 || P13 || P9 || P5 || Saturday 2015-05-16 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 1 (+5) || P1 || P6 || P11 || P5 || P10 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 2 || P15 || P4 || P9 || P14 || P3 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 3 || P8 || P13 || P2 || P7 || P12 || Saturday 2015-05-30 23:59 UTC
|-
| Session 6 - Table 1 (+7) || P1 || P8 || P15 || P7 || P14 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 2 || P6 || P13 || P5 || P12 || P4 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 3 || P11 || P3 || P10 || P2 || P9 || Saturday 2015-06-13 23:59 UTC
|}
|}




==== 25-player season ====
An ideal number of participants would be 25. 24 is easy, 21 to 23 require a minor adjustment.
{| class="wikitable"
|-
! Session and Table !! Player 1 !! Player 2 !! Player 3 !! Player 4 !! Player 5 !! Deadline
|- style="background:#ccf"
| Session 1 - Table 1 (+1) || P1 || P2 || P3 || P4 || P5 || Saturday 2015-04-04 23:59 UTC
|- style="background:#ccf"
| Session 1 - Table 2 || P6 || P7 || P8 || P9 || P10 || Saturday 2015-04-04 23:59 UTC
|- style="background:#ccf"
| Session 1 - Table 3 || P11 || P12 || P13 || P14 || P15 || Saturday 2015-04-04 23:59 UTC
|- style="background:#ccf"
| Session 1 - Table 4 || P16 || P17 || P18 || P19 || P20 || Saturday 2015-04-04 23:59 UTC
|- style="background:#ccf"
| Session 1 - Table 5 || P21 || P22 || P23 || P24 || P25 || Saturday 2015-04-04 23:59 UTC
|-
| Session 2 - Table 1 (-4) || P1 || P22 || P18 || P14 || P10 || Saturday 2015-04-18 23:59 UTC
|-
| Session 2 - Table 2 || P6 || P2 || P23 || P19 || P15 || Saturday 2015-04-18 23:59 UTC
|-
| Session 2 - Table 3 || P11 || P7 || P3 || P24 || P20 || Saturday 2015-04-18 23:59 UTC
|-
| Session 2 - Table 4 || P16 || P12 || P8 || P4 || P25 || Saturday 2015-04-18 23:59 UTC
|-
| Session 2 - Table 5 || P21 || P17 || P13 || P9 || P5 || Saturday 2015-04-18 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 1 (+7) || P1 || P17 || P8 || P24 || P15 || Saturday 2015-05-02 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 2 || P6 || P22 || P13 || P4 || P20 || Saturday 2015-05-02 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 3 || P11 || P2 || P18 || P9 || P25 || Saturday 2015-05-02 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 4 || P16 || P7 || P23 || P14 || P5 || Saturday 2015-05-02 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 5 || P21 || P12 || P3 || P19 || P10 || Saturday 2015-05-02 23:59 UTC
|-
| Session 4 - Table 1 (+11) || P1 || P12 || P23 || P9 || P20 || Saturday 2015-05-16 23:59 UTC
|-
| Session 4 - Table 2 || P6 || P17 || P3 || P14 || P25 || Saturday 2015-05-16 23:59 UTC
|-
| Session 4 - Table 3 || P11 || P22 || P8 || P19 || P5 || Saturday 2015-05-16 23:59 UTC
|-
| Session 4 - Table 4 || P16 || P2 || P13 || P24 || P10 || Saturday 2015-05-16 23:59 UTC
|-
| Session 4 - Table 5 || P21 || P7 || P18 || P4 || P15 || Saturday 2015-05-16 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 1 (+6) || P1 || P7 || P13 || P19 || P25 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 2 || P6 || P12 || P18 || P24 || P5 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 3 || P11 || P17 || P23 || P4 || P10 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 4 || P16 || P22 || P3 || P9 || P15 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 5 || P21 || P2 || P8 || P14 || P20 || Saturday 2015-05-30 23:59 UTC
|-
| Session 6 - Table 1 (+5) || P1 || P6 || P11 || P16 || P21 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 2 || P2 || P7 || P12 || P17 || P22 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 3 || P3 || P8 || P13 || P18 || P23 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 4 || P4 || P9 || P14 || P19 || P24 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 5 || P5 || P10 || P15 || P20 || P25 || Saturday 2015-06-13 23:59 UTC
|}
==== 35-player season ====
Solved via Dutch cycles up to 7 sessions.
==== 40-player season ====
With 40, it has been a problem optimally solved with the "social golfer problem", up to 8 sessions.
{| class="wikitable"
|-
! Session and Table !! Player 1 !! Player 2 !! Player 3 !! Player 4 !! Player 5 !! Deadline
|- style="background:#ccf"
| Session 1 - Table 1 (+8) || P1 || P9 || P17 || P25 || P33 || Saturday 2015-04-04 23:59 UTC
|- style="background:#ccf"
| Session 1 - Table 2 || P2 || P10 || P18 || P26 || P34 || Saturday 2015-04-04 23:59 UTC
|- style="background:#ccf"
| Session 1 - Table 3 || P3 || P11 || P19 || P27 || P35 || Saturday 2015-04-04 23:59 UTC
|- style="background:#ccf"
| Session 1 - Table 4 || P4 || P12 || P20 || P28 || P36 || Saturday 2015-04-04 23:59 UTC
|- style="background:#ccf"
| Session 1 - Table 5 || P5 || P13 || P21 || P29 || P37 || Saturday 2015-04-04 23:59 UTC
|- style="background:#ccf"
| Session 1 - Table 6 || P6 || P14 || P22 || P30 || P38 || Saturday 2015-04-04 23:59 UTC
|- style="background:#ccf"
| Session 1 - Table 7 || P7 || P15 || P23 || P31 || P39 || Saturday 2015-04-04 23:59 UTC
|- style="background:#ccf"
| Session 1 - Table 8 || P8 || P16 || P24 || P32 || P40 || Saturday 2015-04-04 23:59 UTC
|-
| Session 2 - Table 1 || P1 || P10 || P19 || P28 || P37 || Saturday 2015-04-18 23:59 UTC
|-
| Session 2 - Table 2 || P2 || P9 || P20 || P27 || P38 || Saturday 2015-04-18 23:59 UTC
|-
| Session 2 - Table 3 || P3 || P12 || P17 || P26 || P39 || Saturday 2015-04-18 23:59 UTC
|-
| Session 2 - Table 4 || P4 || P11 || P18 || P25 || P40 || Saturday 2015-04-18 23:59 UTC
|-
| Session 2 - Table 5 || P5 || P14 || P23 || P32 || P33 || Saturday 2015-04-18 23:59 UTC
|-
| Session 2 - Table 6 || P6 || P13 || P24 || P31 || P34 || Saturday 2015-04-18 23:59 UTC
|-
| Session 2 - Table 7 || P7 || P16 || P21 || P30 || P35 || Saturday 2015-04-18 23:59 UTC
|-
| Session 2 - Table 8 || P8 || P15 || P22 || P29 || P36 || Saturday 2015-04-18 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 1 || P1 || P11 || P21 || P31 || P36 || Saturday 2015-05-02 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 2 || P2 || P12 || P22 || P32 || P35 || Saturday 2015-05-02 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 3 || P3 || P9 || P23 || P29 || P34 || Saturday 2015-05-02 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 4 || P4 || P10 || P24 || P30 || P33 || Saturday 2015-05-02 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 5 || P5 || P15 || P17 || P27 || P40 || Saturday 2015-05-02 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 6 || P6 || P16 || P18 || P28 || P39 || Saturday 2015-05-02 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 7 || P7 || P13 || P19 || P25 || P38 || Saturday 2015-05-02 23:59 UTC
|- style="background:#ccf"
| Session 3 - Table 8 || P8 || P14 || P20 || P26 || P37 || Saturday 2015-05-02 23:59 UTC
|-
| Session 4 - Table 1 || P1 || P12 || P23 || P30 || P40 || Saturday 2015-05-16 23:59 UTC
|-
| Session 4 - Table 2 || P2 || P11 || P24 || P29 || P39 || Saturday 2015-05-16 23:59 UTC
|-
| Session 4 - Table 3 || P3 || P10 || P21 || P32 || P38 || Saturday 2015-05-16 23:59 UTC
|-
| Session 4 - Table 4 || P4 || P9 || P22 || P31 || P37 || Saturday 2015-05-16 23:59 UTC
|-
| Session 4 - Table 5 || P5 || P16 || P19 || P26 || P36 || Saturday 2015-05-16 23:59 UTC
|-
| Session 4 - Table 6 || P6 || P15 || P20 || P25 || P35 || Saturday 2015-05-16 23:59 UTC
|-
| Session 4 - Table 7 || P7 || P14 || P17 || P28 || P34 || Saturday 2015-05-16 23:59 UTC
|-
| Session 4 - Table 8 || P8 || P13 || P18 || P27 || P33 || Saturday 2015-05-16 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 1 || P1 || P13 || P20 || P32 || P39 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 2 || P2 || P14 || P19 || P31 || P40 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 3 || P3 || P15 || P18 || P30 || P37 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 4 || P4 || P16 || P17 || P29 || P38 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 5 || P5 || P9 || P24 || P28 || P35 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 6 || P6 || P10 || P23 || P27 || P36 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 7 || P7 || P11 || P22 || P26 || P33 || Saturday 2015-05-30 23:59 UTC
|- style="background:#ccf"
| Session 5 - Table 8 || P8 || P12 || P21 || P25 || P34 || Saturday 2015-05-30 23:59 UTC
|-
| Session 6 - Table 1 || P1 || P14 || P18 || P29 || P35 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 2 || P2 || P13 || P17 || P30 || P36 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 3 || P3 || P16 || P20 || P31 || P33 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 4 || P4 || P15 || P19 || P32 || P34 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 5 || P5 || P10 || P22 || P25 || P39 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 6 || P6 || P9 || P21 || P26 || P40 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 7 || P7 || P12 || P24 || P27 || P37 || Saturday 2015-06-13 23:59 UTC
|-
| Session 6 - Table 8 || P8 || P11 || P23 || P28 || P38 || Saturday 2015-06-13 23:59 UTC
|- style="background:#666"
| Session 7 - Table 1 || P1 || P15 || P24 || P26 || P38 || (not played)
|- style="background:#666"
| Session 7 - Table 2 || P2 || P16 || P23 || P25 || P37 || (not played)
|- style="background:#666"
| Session 7 - Table 3 || P3 || P13 || P22 || P28 || P40 || (not played)
|- style="background:#666"
| Session 7 - Table 4 || P4 || P14 || P21 || P27 || P39 || (not played)
|- style="background:#666"
| Session 7 - Table 5 || P5 || P11 || P20 || P30 || P34 || (not played)
|- style="background:#666"
| Session 7 - Table 6 || P6 || P12 || P19 || P29 || P33 || (not played)
|- style="background:#666"
| Session 7 - Table 7 || P7 || P9 || P18 || P32 || P36 || (not played)
|- style="background:#666"
| Session 7 - Table 8 || P8 || P10 || P17 || P31 || P35 || (not played)
|- style="background:#666"
| Session 8 - Table 1 || P1 || P16 || P22 || P27 || P34 || (not played)
|- style="background:#666"
| Session 8 - Table 2 || P2 || P15 || P21 || P28 || P33 || (not played)
|- style="background:#666"
| Session 8 - Table 3 || P3 || P14 || P24 || P25 || P36 || (not played)
|- style="background:#666"
| Session 8 - Table 4 || P4 || P13 || P23 || P26 || P35 || (not played)
|- style="background:#666"
| Session 8 - Table 5 || P5 || P12 || P18 || P31 || P38 || (not played)
|- style="background:#666"
| Session 8 - Table 6 || P6 || P11 || P17 || P32 || P37 || (not played)
|- style="background:#666"
| Session 8 - Table 7 || P7 || P10 || P20 || P29 || P40 || (not played)
|- style="background:#666"
| Session 8 - Table 8 || P8 || P9 || P19 || P30 || P39 || (not played)
|}


==== WAML-relevant summary ====
==== WAML-relevant summary ====
If we can get player blocks of 25♥, 35, 40, 55 (even 65) or sums of their multiples (60♥ = 25♥ + 35; 65 = 25♥ + 40; 70 = 35 + 35; 75yes; 80yes; 85♥♥yes; 90yes; 95yes; 100♥yes; ...) or a number significantly close, 80% + 4 per heart, then we can cover the whole span from <!-- [28, 35], [32,40], [44, 55], [48, 50], [52, 60], [52, 65], [56, 70]... --> 48+ if we stop forming asymmetrical groups after 4 are made. <!-- up to 55 is covered by waiting, 56 is doable with 4 groups of 4 out of 13 [56, 65] ... two 35s [60, 70] ... 35 and 40 for [64, 75] ... 40s [68, 80] --> A fifth group can be drawn at 57 with no dificulty.
If we can get player blocks of 25♥, 35, 40, 55 (even 65) or sums of their multiples (60♥ = 25♥ + 35; 65 = 25♥ + 40; 70 = 35 + 35; 75yes; 80yes; 85♥♥yes; 90yes; 95yes; 100♥yes; ...) or a number significantly close, 80% + 4 per heart, then we can cover the whole span from <!-- [28, 35], [32,40], [44, 55], [48, 50], [52, 60], [52, 65], [56, 70]... --> 48+ if we stop forming asymmetrical groups after 4 are made. <!-- up to 55 is covered by waiting, 56 is doable with 4 groups of 4 out of 13 [56, 65] ... two 35s [60, 70] ... 35 and 40 for [64, 75] ... 40s [68, 80] --> A fifth group can be drawn at 57 with no dificulty.
Senechal
475

edits

Retrieved from "https://riichi.wiki/Special:MobileDiff/13627"