The New Sudoku Players' Forum

by **StrmCkr** » Sun Feb 01, 2026 11:47 pm

Mines just Als xz wth a +1 link that falls out of my aic chain walk.
tags names added after.

A side effect of iding Als w wings

by **rjamil** » Wed Feb 11, 2026 2:22 am

I have thoroughly analyze the XY-Wing and XYZ-Wing Transport examplars and overhaul the routines in my RJSudoku.c and RJSukaku.c programs.

Wish to inform that, both the programs are now searched all single-links (strong and weak) Transport moves mentioned in Patterns.txt file:

1) XY-Wing Type 1 Transport (78 examplars)
2) XYZ-Transport (56 examplars)
3) XY-Wing Type 2 Transport (32 examplars)
4) XYZ-Wing Transport (34 exemplars)

Find below statistics of few small known puzzle collections, without guess solving updates:

Code: Select all: With XYZ-Transport ERI Ring examplar 46 added: Ruud's 50K : 20671 +53 17 49158 : 48767 +3 Tarek 6000 : 0 PG 26855 : 12710 +3 PG360 4279 : 1538 PG385 4353 : 1572

R. Jamil

by **pjb** » Mon Feb 16, 2026 3:36 am

While adding this technique to my solver http://www.philsfolly.net.au/Sudoku, I was struck by the huge number of exemplars posted here, but a paucity of actual examples. I went looking for examples of the most common types that are not already posted in this thread, and the results of my searching are in the XYZ Ring help file. It was hard to detect them at a higher SER than 6-7 range. The type with the transport between the arms of the pattern being an empty rectangle were most common. Interestingly, my solver finds the empty recangle type (box 1) firstly in the second puzzle offered by xzfwsf at the start of this thread. There are some types I am yet to discover, so my search goes on.

Phil

by **rjamil** » Wed Feb 18, 2026 2:09 am

Hi all,

Allow me to extract XYZ-Ring moves from XYZ-Transport and XYZ-Wing Transport moves:

Code: Select all: XYZ-Transport: Line Ring (multiple removals) 13 ---------------+---------------+--------------- ---------------+---------------+--------------- 41) . -YZ . | . . . | . -Z . 42) . -Y . | . / . | . . . \ -X xyz -X | -X -X -X | -X xz -X \ -XZ xyz -XZ |-XZ +Z-X -XZ | -XZ xz -XZ . -YZ . | . . . | . -Z . . -Y . | . / . | . . . 03---------------+---------------+---------------03---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y . | . / . | . . . / +Z-Y / | / / / | / +Z / . -Y . | . / . | . . . . -YZ . | . . . | . -Z . . -Y . | . / . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y . | . / . | . . . . yz . | . . . | . (-Z) . -Z yz -Z | -Z +Z -Z | -Z (-Z) -Z . -YZ . | . . . | . -Z . . -Y . | . / . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ERI Ring (multiple removals) ---------------+---------------+--------------- ---------------+---------------+--------------- 43) . -YZ . | . . . | . -Z . 44) . -Y . | / +z / | . . . \ -X xyz -X | -X -X -X | -X xz -X \ -XZ xyz -XZ |+z-X -XZ +z-X | -XZ xz -XZ . -YZ . | . . . | . -Z . . -Y . | / +z / | . . . 03---------------+---------------+---------------03---------------+---------------+--------------- / +z-Y / | . . . | / +z / . -Y . | . -Z . | . . . +z -YZ +z | -Z -Z -Z | +z -Z +z . -Y . | . -Z . | . . . / +z-Y / | . . . | / +z / . -Y . | . -Z . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y . | / +z / | . . . . yz . | . . . | . (-Z) . -Z yz -Z | +z -Z +z | -Z (-Z) -Z . -YZ . | . . . | . -Z . . -Y . | / +z / | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 45) / +z-Y / | . . . | . . . 46) . -Y . | . . . | . [.] . +z-X xyz +z-X | -XZ -XZ -XZ | -XZ xz -XZ \ -X xyz -X | -X -X -X | -X xz -X / +z-Y / | . . . | . . . . -Y . | . . . | . [.] . 01---------------+---------------+---------------01---------------+---------------+--------------- . -YZ . | . . . | . . . . -Y . | . . . | . [.] . . -YZ . | . . . | . . . . -Y . | . . . | . [.] . . -YZ . | . . . | . . . . -Y . | . . . | . [.] . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . . . . -Y . | . . . | / +z / . yz . | . . . | . . . [.] yz [.] | [.] [.] [.] | +z . +z . -YZ . | . . . | . . . . -Y . | . . . | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- Reduced Line Ring (multiple removals) 15 ---------------+---------------+--------------- ---------------+---------------+--------------- 59) . -YZ . | . . . | -Z -Z -Z 60) . -Y / | . . . | . . . -X xyz -X | -X -X -X |-XZ xz -XZ -XZ xyz +Z-X | -XZ -XZ -XZ |-XZ xz -XZ / +Z-Y / | / / / | +z +z +z . -Y / | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . -YZ . | . . . | . . . . -Y / | . . . | . . . . -YZ . | . . . | . . . . -Y / | . . . | . . . . -YZ . | . . . | . . . . -Y / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . . . -Z -YZ +z | . . . | . . . . yz . | . . . | . . . -Z yz +z | . . . | . . . . -YZ . | . . . | . . . -Z -YZ +z | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- 15 ---------------+---------------+--------------- ---------------+---------------+--------------- 61) . -Y . | . . . | . (.) . 62) . -Y . | . . . | +z (.) (.) \ -X xyz -X | -X -X -X | -X xz -X \ -X xyz -X | -X -X -X |+z-X xz -XZ . -Y . | . . . | . (.) . . -Y . | . . . | +z (.) (.) 02---------------+---------------+---------------02---------------+---------------+--------------- . -Y . | . . . | . (.) . . -Y . | . . . | / . . . -Y . | . . . | . (.) . . -Y . | . . . | / . . . -Y . | . . . | . (.) . . -Y . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- +z +z-Y +z | / / / | / +Z / . -Y . | . . . | / . . (.) yz (.) | . . . | . (.) . (.) yz (.) | (.) (.) (.) | +Z (.) (.) (.) -YZ (.) | . . . | . (.) . . -Y . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 63) . -YZ . | . . . | -Z -Z -Z 64) . -Y / | . . . | . . . \ -X xyz -X | -X -X -X | -XZ xz -XZ \ -XZ xyz +Z-X | -XZ -XZ -XZ | -XZ xz -XZ / +Z-Y / | / / / | / +Z / . -Y / | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y / | . . . | . . . . -YZ . | . . . | . -Z . . -Y / | . . . | . . . . -YZ . | . . . | . -Z . . -Y / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . -Z . -Z -YZ / | . . . | . . . . yz . | . . . | . (-Z) . -Z yz +Z | -Z -Z -Z | -Z (-Z) -Z . -YZ . | . . . | . -Z . -Z -YZ / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 65) . -YZ . | . . . | . -Z . 66) . -Y . | . . . | / (.) (.) \ -X xyz -X | -X -X -X | -X xz -X \ -XZ xyz -XZ | -XZ -XZ -XZ |+Z-X xz -XZ . -YZ . | . . . | . -Z . . -Y . | . . . | / (.) (.) 02---------------+---------------+---------------02---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y . | . . . | / . . . -YZ . | . . . | . -Z . . -Y . | . . . | / . . . -YZ . | . . . | . -Z . . -Y . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- / +Z-Y / | / / / | / +Z / . -Y . | . . . | / . . (.) yz (.) | . . . | . (-Z) . -Z yz -Z | -Z -Z -Z | +Z (-Z) -Z (.) -YZ (.) | . . . | . -Z . . -Y . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- XYZ-Hybrid (Row-Column wise) (2 exemplars, up to 7 removals): (ZH done) ---------------+---------------+--------------- ---------------+---------------+--------------- 01) . . . | . . . | . / . 02) . -Z . | . . . | . . . -Z xyz -Z | -Z -Z -Z | -Z xZ - Z . xyz . | . . . | . xz . . . . | . . . | . / . . -Z . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . / . . -Z . | . . . | . . . . . . | . . . | . / . . -Z . | . . . | . . . . . . | . . . | . / . . -Z . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . / . . -Z . | . . . | . . . . yz . | . . . | . +Z . / yZ / | / / / | / +Z / . . . | . . . | . / . . -Z . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Dual XYZ-Hybrid: (Row-Column wise) (1 exemplar, up to 14 removals): (ZH done) ---------------+---------------+--------------- 01) . -Z . | . . . | . / . -Z xyz -Z | -Z -Z -Z | -Z xZ - Z . -Z . | . . . | . / . ---------------+---------------+--------------- . -Z . | . . . | . / . . -Z . | . . . | . / . . -Z . | . . . | . / . ---------------+---------------+--------------- . -Z . | . . . | . / . / yZ / | / / / | / +Z / . -Z . | . . . | . / . ---------------+---------------+---------------

Code: Select all: XYZ-Wing Transport: Line Ring 09 Box Ring 10 ---------------+---------------+--------------- ---------------+---------------+--------------- 05)-XYz xyz -XYz | -XZ xz -XZ | -X -X -X 06)-XYz xyz -XYz | -XZ xz -XZ |+z-X +z-X +z-X \ +z-Y +z-Y +z-Y | +z +z +z | / / / \ -Y -Y -Y | . . . | / / / -YZ -YZ yz |(-Z) (-Z) (-Z) | . . . -YZ -YZ yz |(-Z) (-Z) (-Z) | +z +z +z 01---------------+---------------+---------------01---------------+---------------+--------------- Line Ring 11 Box Ring 12 ---------------+---------------+--------------- ---------------+---------------+--------------- 07)-XYz -XYz xyz | -XZ xz -XZ | -X -X -X 08)-XYz -XYz xyz | -XZ xz -XZ |+z-X +z-X +z-X +z-Y +z-Y +z-Y | +z +z +z | / / / -Y -Y -Y | . . . | / / / -YZ -YZ yz |(-Z) (-Z) (-Z) | . . . -YZ -YZ yz |(-Z) (-Z) (-Z) | +z +z +z 01---------------+---------------+---------------01---------------+---------------+--------------- . . -Y | . . . | . . . . . -Y | . . . | . . . . . -Y | . . . | . . . . . -Y | . . . | . . . . . -Y | . . . | . . . . . -Y | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . -Y | . . . | . . . . . -Y | . . . | . . . . . -Y | . . . | . . . . . -Y | . . . | . . . . . -Y | . . . | . . . . . -Y | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Reduced Line Ring 14 15 ---------------+---------------+--------------- ---------------+---------------+--------------- 09)-XYz -XYz xyz | -XZ xz -XZ | -X -X -X 10)-XYz xyz -XYz | -XZ xz -XZ | -X -X -X \ /-Y /-Y +Z-Y | +z +z +z | / / / \ +z-Y +z-Y +z-Y | / +Z / | / / / -YZ -YZ yz |(-Z) (-Z) (-Z) | . . . -YZ -YZ yz |(-Z) (-Z) (-Z) | . . . 01---------------+---------------+---------------01---------------+---------------+--------------- . . -YZ | . . . | . . . . . . | . -Z . | . . . . . -YZ | . . . | . . . . . . | . -Z . | . . . . . -YZ | . . . | . . . . . . | . -Z . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . -YZ | . . . | . . . . . . | . -Z . | . . . . . -YZ | . . . | . . . . . . | . -Z . | . . . . . -YZ | . . . | . . . . . . | . -Z . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- 16 18 ---------------+---------------+--------------- ---------------+---------------+--------------- 11)-XYz -XYz xyz | -XZ xz -XZ | -X -X -X 12)-XYz -XYz xyz | -XZ xz -XZ | -X -X -X \ +z-Y +z-Y +z-Y | / +Z / | / / / /-Y /-Y +Z-Y | / +Z / | / / / -YZ -YZ yz |(-Z) (-Z) (-Z) | . . . -YZ -YZ yz |(-Z) (-Z) (-Z) | . . . 01---------------+---------------+---------------01---------------+---------------+--------------- . . -Y | . -Z . | . . . . . -YZ | . -Z . | . . . . . -Y | . -Z . | . . . . . -YZ | . -Z . | . . . . . -Y | . -Z . | . . . . . -YZ | . -Z . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . -Y | . -Z . | . . . . . -YZ | . -Z . | . . . . . -Y | . -Z . | . . . . . -YZ | . -Z . | . . . . . -Y | . -Z . | . . . . . -YZ | . -Z . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Line Ring 19 20 ---------------+---------------+--------------- ---------------+---------------+--------------- 13)-XYz xyz -XYz | -X xz -X | -X -X -X 14)-XYz -XYz xyz | -XZ xz -XZ | -X -X -X \ -Y -Y -YZ | . (.) . | . . . \ -Y -Y -YZ | . -Z . | . . . -Y -Y yz | . . . | . . . -Y -Y yz | . (-Z) . | . . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . (.) | . (.) . | . . . . . -YZ | . -Z . | . . . / / +Z | / +Z / | / / / / / +Z | / +Z / | / / / . . (.) | . (.) . | . . . . . -YZ | . -Z . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . (.) | . (.) . | . . . . . -YZ | . -Z . | . . . . . (.) | . (.) . | . . . . . -YZ | . -Z . | . . . . . (.) | . (.) . | . . . . . -YZ | . -Z . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ERI Ring 21 22 ---------------+---------------+--------------- ---------------+---------------+--------------- 15)-XYz xyz -XYz | -X xz -X | -X -X -X 16)-XYz -XYz xyz | -XZ xz -XZ | -X -X -X \ -Y -Y -YZ | . (.) . | . . . \ -Y -Y -YZ | . -Z . | . . . -Y -Y yz | . . . | . . . -Y -Y yz | . (-Z) . | . . . 06---------------+---------------+---------------06---------------+---------------+--------------- / / +z | / +z / | . . . / / +z | / +z / | . . . +z +z (.) | +z (.) +z |(.) (.) (.) +z +z -YZ | +z -Z +z | -Z -Z -Z / / +z | / +z / | . . . / / +z | / +z / | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . (.) | . (.) . | . . . . . -YZ | . -Z . | . . . . . (.) | . (.) . | . . . . . -YZ | . -Z . | . . . . . (.) | . (.) . | . . . . . -YZ | . -Z . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- XYZ-Wing Hybrid: Reduced Line ---------------+---------------+--------------- 1a)-z -z xyz | . xz . | . . . / -Z -Z -Z | . . . | . . . / / yz | +z +z +z | / / / 01---------------+---------------+--------------- . . -Z | . . . | . . . . . -Z | . . . | . . . . . -Z | . . . | . . . ---------------+---------------+--------------- . . -Z | . . . | . . . . . -Z | . . . | . . . . . -Z | . . . | . . . ---------------+---------------+---------------

Please note that the above mentioned known examplars are incorporated in to my solvers.

R. Jamil

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