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.
