22243156789Hidden onlyoneNaked onlyone22222222212345678919

121212.12.Naked pairs121212.12.12.12.121212.12.12.12.Hidden pairs123123123.123.Naked Triples123123123.123.123Hidden Triples123123123123.123.123.123.123.123.123.123123,1213Hidden Quads12,

22Hidden onlyone22X2X2XIntersection Removal

fishyAAA

EAAX-wingAAASword-fishAAAAJelly-fishESingle's Chains ABCDAEABCDAEA ~E~A B ~C D ~EE5ABCDColouring E

X-cycle X-cycle Grouped X-cycleAAX-wingAAAX-cycleAAGrouped X-cycleXX

Muti-Color B+B+B-B-A-A+A+A+1,B2,A3,A+B+B-4,A-B5,A+BA+B+A+B-=>A-B

ABACBCCY-wingY-wingABBCACBCACCABACBCCY-wing chainsABABY-wing chainsY-wingABEBACBCCXY-chainsAEXY-wingY-wingABEAE-EBY-wing

XY.....ABACBCHidden Y-wingABCYB+B-B-.....ABACBCB+A+Hidden XY-wing chainsXY-loop,XY-cycle.....ABACBCHidden Y-wing chainsorY-cycle,Y-loop.....AB.....AB

XZYZXYZZXYZ-WingXYZXZYZZXZYZWXYZZWXYZ-WingWZXZYZTUVWXYZZWZUZVZTZ

GAE1,ABCDE2,D,~C,B,~A3,AEG Guardians Broken Wings, Turbot-Fish EABCDXY-chains

Bidirection-cycleABABABABABAB,ABA/B.:AB,ABAB,AB.ABA..A..ABABBC..C..CDADADCA

WW-wingWXWX...W-wing()aA,aA. 1:(a)W 2:(a)~W(X)~XXW(A)aAW.XY-chains,XY-chainsWXX..aAWXWXCWXXDaAXY

Unique Rectangles 12121212'Deadly Pattern' 1212x.121212 11241244

ABCABCABAB 2RoofABRoofCRoofCFloorRoofCCABCABABCABC2BABCDABCDABABCDCDCDABDABCABABCDECDECDE

ABCABABCABABDEABABCAB4BCCDABCXABEFABABABM 3Roof3ABMABMM 4()ABCABAB

Empty Rectangle (ER) 4DBACABD -> ~A -> B -> ~D, ~DD

ALS(Amost Lock Set Rule)yaxaAL:axyxyybxaxyaAyxALSAaAyxbByx*ALS:AL(AB)(a)(b)(*)x,yAbaaAyxbByz*xzCc

+-------------------+-------------------+-------------------+ | 459 1 %479 |%78 3 %89 | 2 %58 6 | | 59 569 679 | 278 289 4 |^35 1358 13 | | 8 3 2 | 5 6 1 | 7 9 4 | +-------------------+-------------------+-------------------+ |*139 7 *139 | 6 4 5 | 8 123 1239 | | 6 28 *134 | 9 28 7 |^34 13 5 | | 24 289 5 | 238 1 238 |^49 6 7 | +-------------------+-------------------+-------------------+ | 7 4 39 | 23 259 6 | 1 235 8 | | 12359 2569 1369 | 4 2589 2389 | 3569 7 239 | | 2359 2569 8 | 1 7 239 | 3569 4 239 | +-------------------+-------------------+-------------------+

A={R4C1,R4C3,R5C3} B={R2C7,R5C7,R6C7} C={R1C3,R1C4,R1C6,R1C8} x=9 y=5 z=4

7,8,9 | 4---C---5 : : : : 4 5 / \ 1,3---A B---3,4 \ / 9...*...9

*=r4c9#9,r6c2#9 can be eliminated sudoku.comAr4c1r4c3()r5c3B34r2c7r6c7C789r1c3r1r8Ar4c1r4c39r6c2,r4c99Ar4c1r4c39A4(r5c3)C4,ALC5C5(r1c8=5)B5,ALB9r4c9,r6c29,r4c9,r6c29

Sue-de-Coq(Two-Sector Disjoint Subsets )ABCDEABCDABECDE1,M52,3,5 ABMABCD{EABCD}ABMAB{ABE}ABECDCDE

Aligned Pair Exclusion (APE) X,Y3,23,5 B5,25,5 7,2 A7,5 C3,25,2 X357 Y25

BUG (Bivalue Universal Grave) principle Bivalue Universal Grave (BUG)BUG-Lite BUGBUGpoly-valued cell BUG-LiteLocalized BUG Move (LBM) BUGnon-BUG candidate BUGLBMBUGBUG+n BUGnBUG+1BUGBUGBUGBUG1LBMBUGBUGBUG2BUG3BUG4BUG+15123BUG-Lite

2 9 8 | 47 567 56 | 3 1 45 7 4 5 | 2 1 3 | 6 9 8 1 3 6 | 48 58 9 | 2 7 45 ----------------+----------------+---------------- 5 1 4 | 6 3 8 | 7 2 9 6 2 9 | 17 57 15 | 8 4 3 8 7 3 | 9 4 2 | 1 5 6 ----------------+----------------+---------------- 4 5 2 | 18 68 16 | 9 3 7 3 8 1 | 5 9 7 | 4 6 2 9 6 7 | 3 2 4 | 5 8 1 5BUGR1C5LBM5BUG5BUGBUG+1BUGBUG55.

3 79 57+9 | 1 2 8 | 49 45+9 6 6 4 25 | 3 7 9 | 8 15 12 8 1 29 | 5 6 4 | 7 39 23 -------------------+-------------------+------------------ 9 5 1 | 7 4 3 | 2 6 8 7 3 4 | 2 8 6 | 19 19 5 2 8 6 | 9 1 5 | 3 47 47 -------------------+-------------------+------------------ 4 27 3 | 8 5 1 | 6 27 9 1 6 79 | 4 39 2 | 5 8 37 5 29 8 | 6 39 7 | 14 23+14 14+3 BUG+4BUG1,R1C3=9,R1C8=9,R9C8=1,R9C8=4,R9C9=3R1C85,2,R1C85R1C85

*--------------------------------------------------* | 4 28 19 | 3 6 89 | 5 7 12 | | 5 7 3 | 4 1 2 | 9 6 8 | | 28 6 19 | 89 7 5 | 4 3 12 | |----------------+----------------+----------------| | 6 28 4 | 28 3 1 | 7 5 9 | | 1 9 5 | 7 4 6 | 2 8 3 | | 28 3 7 | 29+8 5 89 | 6 1 4 | |----------------+----------------+----------------| | 9 5 6 | 1 2 3 | 8 4 7 | | 3 4 2 | 6 8 7 | 1 9 5 | | 7 1 8 | 5 9 4 | 3 2 6 | *--------------------------------------------------* BUGR6C4888

Force chain,.:.1,:,;2,:,Kj;3,:K,();

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