## What is maximum number of eliminations with one technique?

Everything about Sudoku that doesn't fit in one of the other sections

### What is maximum number of eliminations with one technique?

Carcul (in the Effortless Extremes thread) wrote:
Ocean wrote:What is the maximum number of eliminations with one technique?

My "personal record" is 18. It would be interesting to see other examples of more than, let's say, 10 eliminations.

Carcul

Here are some puzzles with 10 or more eliminations.
Certain techniques (fishes, coloring, bidirectional cycles, others?) can sometimes lead to a high number of candidate eliminations. The examples below are all xy-ring eliminiations, which is a subset of bidirectional cycles. The puzzles are divided in two groups: A. Puzzles that can be solved with basics + one xy-ring. B. More than one advanced technique is "needed" (- or maybe room for improvement?)

Examples:

Code: Select all
`Example A: *-----------* |...|...|.12| |...|...|345| |...|..3|67.| |---+---+---| |...|.36|8..| |...|498|...| |..4|51.|...| |---+---+---| |.42|1..|...| |891|...|...| |67.|...|...| *-----------*# After basic techniques: xy-ring (8-ring) with 12 eliminations. *--------------------------------------------------------------------* | 3457   356    35678  | 678    45678  457    | 9      1      2      | | 279    26     6789   | 26789  2678   1      | 3      4      5      | | 12459  125   #59     |#29     245    3      | 6      7      8      | |----------------------+----------------------+----------------------| | 12579  125    579    |#27     3      6      | 8      259    4      | | 2357   2356   3567   | 4      9      8      | 1257   235    137    | | 39     8      4      | 5      1     #27     |#27     369    369    | |----------------------+----------------------+----------------------| |#35     4      2      | 1      5678   579    |#57     35689  3679   | | 8      9      1      | 2367   24567  2457   | 2457   2356   367    | | 6      7     #35     | 238    2458   2459   | 1245   23589  139    | *--------------------------------------------------------------------*# Then one xy-wing solves the puzzle.Example B: *-----------* |...|...|.12| |...|...|345| |...|..1|67.| |---+---+---| |...|.18|7..| |...|379|...| |..9|25.|...| |---+---+---| |.82|5..|...| |175|...|...| |63.|...|...| *-----------* # After basic techniques: xy-ring (6-ring) with 12 eliminations. *--------------------------------------------------------------------* | 348    469    3678   | 46789  34689  5      | 89     1      2      | |#28     1269   1678   | 6789   2689  #26     | 3      4      5      | | 23458  2459  #38     | 489    23489  1      | 6      7      89     | |----------------------+----------------------+----------------------| | 2345   2456  #36     |#46     1      8      | 7      2569   469    | | 2458   12456  168    | 3      7      9      | 1245   256    146    | | 7      146    9      | 2      5     #46     | 148    368    13468  | |----------------------+----------------------+----------------------| | 9      8      2      | 5      46     3467   | 14     36     13467  | | 1      7      5      | 4689   24689  2346   | 2489   23689  34689  | | 6      3      4      | 1      289    27     | 2589   2589   789    | *--------------------------------------------------------------------*# Not enough. More chains are needed. What is the simplest way?`

Puzzles:

A. One xy-ring (+ basic techniques) is enough to solve the puzzle.

Code: Select all
`# RA-01   *-----------* |..1|2.3|4..| |...|...|...| |.5.|6.1|.3.| |---+---+---| |3..|...|..6| |7.4|...|2.8| |6..|...|..9| |---+---+---| |.8.|9.6|.5.| |...|...|...| |..2|8.7|6..| *-----------*# RA-02 *-----------* |.1.|2.3|.4.| |...|5.6|...| |3..|...|..7| |---+---+---| |4.3|...|8.1| |...|...|...| |7.6|...|5.4| |---+---+---| |1..|...|..6| |...|7.4|...| |.5.|6.8|.7.| *-----------*# RA-03 *-----------* |1..|.2.|..3| |.4.|.5.|.1.| |..6|...|4..| |---+---+---| |7..|5.6|..2| |...|...|...| |8..|9.3|..7| |---+---+---| |..5|...|3..| |.1.|.3.|.5.| |2..|.8.|..6| *-----------*# RA-04 *-----------* |...|.1.|.2.| |..3|...|..4| |.5.|..6|1..| |---+---+---| |...|..7|5..| |2..|...|..8| |..9|5..|...| |---+---+---| |..7|2..|.9.| |1..|...|7..| |.4.|.8.|...| *-----------*# RA-05 (4-ring: 15 eliminations) *-----------* |.1.|2..|.3.| |4..|.5.|...| |...|..6|2.7| |---+---+---| |6..|..8|..4| |.5.|...|..8| |..2|5..|..6| |---+---+---| |..1|...|.7.| |3..|...|8..| |..5|794|...| *-----------*`

B. XY-ring with many eliminations, but one or more extra 'advanced' techniques are needed to solve the puzzle.
Code: Select all
`# RB-01 *-----------* |...|.1.|...| |2..|3.4|..5| |6.4|...|7.2| |---+---+---| |..8|...|4..| |3..|...|..1| |..6|...|2..| |---+---+---| |9.7|...|8.3| |1..|6.3|..9| |...|.4.|...| *-----------*# RB-02 *-----------* |...|1.2|...| |.1.|.3.|.4.| |5..|...|..6| |---+---+---| |7.2|...|8.4| |...|4.9|...| |8.5|...|9.3| |---+---+---| |1..|...|..9| |.6.|.9.|.7.| |...|3.8|...| *-----------*# RB-03 *-----------* |...|1.2|...| |.3.|...|.4.| |..5|6.7|1..| |---+---+---| |8..|.5.|..1| |.7.|...|.3.| |2..|.7.|..8| |---+---+---| |..4|9.5|7..| |.6.|...|.5.| |...|2.3|...| *-----------*# RB-04 *-----------* |...|1.2|...| |.3.|.4.|.5.| |6..|...|..7| |---+---+---| |.53|...|87.| |...|9.7|...| |.26|...|43.| |---+---+---| |1..|...|..8| |.4.|.5.|.6.| |...|8.6|...| *-----------*# RB-05 *-----------* |...|123|...| |.4.|...|.1.| |5..|...|..6| |---+---+---| |7..|.4.|..3| |8..|3.6|..5| |4..|.8.|..9| |---+---+---| |3..|...|..7| |.5.|...|.9.| |...|574|...| *-----------*# RB-06 *-----------* |..1|...|2..| |3.4|...|5.6| |...|6.7|...| |---+---+---| |.8.|2.9|.1.| |...|...|...| |.9.|1.5|.6.| |---+---+---| |...|7.2|...| |5.2|...|8.3| |..9|...|1..| *-----------*# RB-07 *-----------* |.1.|...|.2.| |...|3.4|...| |5..|1.6|..3| |---+---+---| |.7.|...|.8.| |..9|4.2|7..| |.8.|...|.5.| |---+---+---| |4..|7.9|..2| |...|6.8|...| |.3.|...|.4.| *-----------*# RB-08 *-----------* |.1.|.2.|.3.| |...|4.5|...| |..6|...|7..| |---+---+---| |..5|2.7|6..| |2..|...|..8| |..4|1.6|2..| |---+---+---| |..9|...|5..| |...|8.3|...| |.8.|.4.|.1.| *-----------*# RB-09 *-----------* |.12|...|34.| |.5.|6.4|.7.| |...|...|...| |---+---+---| |8..|7.6|..4| |...|...|...| |4..|8.9|..3| |---+---+---| |...|...|...| |.9.|4.7|.1.| |.34|...|25.| *-----------*# RB-10 *-----------* |1..|...|..2| |..2|3.4|5..| |.3.|.6.|.7.| |---+---+---| |8..|.7.|..3| |...|...|...| |7..|.9.|..1| |---+---+---| |.8.|.2.|.4.| |..7|8.1|6..| |5..|...|..7| *-----------*# RB-11 *-----------* |1..|2.3|..4| |...|...|...| |.56|...|78.| |---+---+---| |..2|.9.|8..| |...|4.6|...| |..3|.7.|6..| |---+---+---| |.17|...|35.| |...|...|...| |2..|5.9|..7| *-----------*# RB-12 *-----------* |1..|2.3|..4| |.4.|...|.5.| |..6|...|7..| |---+---+---| |..8|.7.|3..| |.5.|...|.7.| |..4|.5.|9..| |---+---+---| |..3|...|8..| |.6.|...|.2.| |8..|1.9|..3| *-----------*`

Fishermen, Color artists and Chainsmiths are wanted for other examples.
Ocean

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Joined: 29 August 2005