The Effortless Extremes thread

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

The Effortless Extremes thread

Postby RW » Sun Apr 02, 2006 5:55 pm

Seems there's lots of people who like to manufacture puzzles around here and some nice databases are building up on this forum. I would be interested in yet another kind of puzzles, puzzles that can be classified "extreme", but still have a simple solution. The rules for a puzzle like this would be:

1. It shall not be solvable through use of the following techniques alone:

-locked candidates
-pairs, triplets, quads (naked or hidden)
-x-wing, swordfish
-colors, multiple colors
-xy-wing

[edit: I decided to count Uniqueness rectangles as an "advanced technique"]

2. It must be solvable through use of:

-locked candidates
-pairs & triplets (naked or hidden)
+ one move with a more advanced technique

The easier this "advanced" move is to recognize for a human solver, the better. The puzzle should preferrably have some kind of symmetry also. I think puzzles like this would be very valuable for people who wish to learn to apply advanced techniques.

[Edit: 4.7.2006: from this day on, all submitted puzzles must have some kind of symmetry.]

Here's an example to show what I mean (I apologize the faulty symmetry, don't have a generator and handcrafting a puzzle like this is hard enough for me without symmetry...)

Code: Select all
 *-----------*
 |...|.7.|5..|
 |...|..1|.6.|
 |.4.|56.|31.|
 |---+---+---|
 |.12|...|6..|
 |...|...|1.3|
 |..9|...|42.|
 |---+---+---|
 |.81|.4.|73.|
 |.5.|7..|...|
 |..6|.38|...|
 *-----------*


After solving all singles that can be found through pairs and triplets, you could a) go on with two swordfishes, some coloring, solve a few singles and get stuck or b) make one reduction based on a reverse-BUG and solve the rest of the puzzle as singles.

When you send your puzzles, please mention what technique the advanced move applies and I'll try to organize the puzzles by technique. I'll add some more puzzles myself when I get better at preserving symmetry.

RW

Puzzles:

XYZ-wing

Code: Select all
1. Mike Barker
 *-----------*
 |..1|...|.5.|
 |...|.85|.74|
 |..3|9..|8..|
 |---+---+---|
 |5..|7.8|1..|
 |.8.|.6.|..5|
 |...|4..|.2.|
 |---+---+---|
 |...|...|...|
 |6.7|.4.|...|
 |..5|..9|..3|
 *-----------*

2. Mike Barker
 *-----------*
 |...|8..|6..|
 |.1.|9..|82.|
 |..5|6..|3..|
 |---+---+---|
 |.52|...|..3|
 |8..|..4|.1.|
 |...|.5.|2..|
 |---+---+---|
 |2..|...|1..|
 |..6|4..|...|
 |5..|.27|..4|
 *-----------*

3. Mike Barker
 *-----------*
 |..4|...|.87|
 |..3|8.2|..6|
 |.6.|..5|...|
 |---+---+---|
 |.5.|.9.|1..|
 |...|3..|...|
 |...|.1.|8.2|
 |---+---+---|
 |..5|...|.6.|
 |...|126|7..|
 |..1|...|9..|
 *-----------*

4. Ocean
 *-----------*
 |8..|762|..3|
 |.74|1.3|89.|
 |.3.|...|.6.|
 |---+---+---|
 |28.|...|.36|
 |7..|...|..1|
 |14.|...|.59|
 |---+---+---|
 |.6.|...|.1.|
 |.21|6.5|97.|
 |4..|391|..8|
 *-----------*

5. Ocean
 *-----------*
 |..4|2.7|6..|
 |.6.|.1.|.2.|
 |2..|6.3|..4|
 |---+---+---|
 |4.8|...|9.7|
 |.9.|...|.6.|
 |5.6|...|4.3|
 |---+---+---|
 |9..|4.1|..6|
 |.3.|.6.|.4.|
 |..5|8.9|2..|
 *-----------*

6. ab
 *-----------*
 |..4|.3.|682|
 |...|9..|..7|
 |7..|.4.|..3|
 |---+---+---|
 |.3.|...|...|
 |5.7|...|1.8|
 |...|...|.4.|
 |---+---+---|
 |8..|.5.|..4|
 |9..|..7|...|
 |413|.9.|7..|
 *-----------*

7. wapati
 *-----------*
 |...|...|5..|
 |...|63.|...|
 |..5|.8.|9.1|
 |---+---+---|
 |...|8.6|...|
 |4..|...|32.|
 |.21|..9|.8.|
 |---+---+---|
 |7..|4..|8..|
 |25.|7..|...|
 |938|.6.|...|
 *-----------*


[url=http://forum.enjoysudoku.com/viewtopic.php?t=1169[/url]VWXYZ-wing[/url]

Code: Select all
1. Mike Barker
 *-----------*
 |.76|3..|...|
 |...|.9.|..2|
 |...|.84|...|
 |---+---+---|
 |..3|...|16.|
 |...|...|.4.|
 |2..|...|.8.|
 |---+---+---|
 |1..|...|.2.|
 |6.9|.75|...|
 |..2|4.9|..5|
 *-----------*

2. Mike Barker
 *-----------*
 |...|..5|6.2|
 |.3.|.98|.17|
 |..9|...|...|
 |---+---+---|
 |..1|..3|...|
 |2..|4..|.8.|
 |...|8..|...|
 |---+---+---|
 |.1.|5..|...|
 |3..|.42|.5.|
 |..6|...|9.1|
 *-----------*


XY-ring

Code: Select all
1. Ocean
 *-----------*
 |...|...|...|
 |..1|.2.|3..|
 |.3.|1.4|.5.|
 |---+---+---|
 |..6|...|2..|
 |.4.|...|.7.|
 |..8|...|9..|
 |---+---+---|
 |.1.|3.7|.4.|
 |..2|.9.|8..|
 |...|...|...|
 *-----------*

2. Mike Barker
 *-----------*
 |.13|...|..4|
 |...|61.|..2|
 |.2.|...|8..|
 |---+---+---|
 |4..|.5.|..1|
 |..5|.4.|23.|
 |6..|...|5.9|
 |---+---+---|
 |..1|.28|...|
 |.9.|4..|...|
 |...|9..|.7.|
 *-----------*

3. Mike Barker
 *-----------*
 |...|...|..4|
 |...|8..|7..|
 |.76|...|.15|
 |---+---+---|
 |1..|..2|.56|
 |.2.|93.|...|
 |4..|...|...|
 |---+---+---|
 |..9|...|4.7|
 |2..|.6.|3..|
 |...|.1.|...|
 *-----------*

4. Mike Barker
 *-----------*
 |...|9..|...|
 |35.|.2.|6..|
 |..7|..4|...|
 |---+---+---|
 |.26|7..|5..|
 |5.9|...|3..|
 |...|1..|...|
 |---+---+---|
 |..8|...|..9|
 |...|.67|.1.|
 |1..|..9|.56|
 *-----------*

5. Ocean
 *-----------*
 |...|...|...|
 |..1|...|2..|
 |.2.|3.4|.5.|
 |---+---+---|
 |..2|.6.|7..|
 |...|4.8|...|
 |..6|.1.|9..|
 |---+---+---|
 |.8.|2.5|.4.|
 |..7|...|1..|
 |...|...|...|
 *-----------*

6. Ocean
 *-----------*
 |...|..1|2..|
 |..3|.42|...|
 |5..|...|.6.|
 |---+---+---|
 |72.|...|...|
 |.6.|...|.5.|
 |...|...|.84|
 |---+---+---|
 |.1.|...|..8|
 |...|75.|9..|
 |..6|4..|...|
 *-----------*

7. Mike Barker
 *-----------*
 |8.4|.52|.1.|
 |7.2|.4.|...|
 |...|1..|.49|
 |---+---+---|
 |.3.|7..|...|
 |5..|...|.82|
 |...|..1|.3.|
 |---+---+---|
 |..7|6..|...|
 |...|..5|1.6|
 |...|.7.|...|
 *-----------*

8. Ocean
 *-----------*
 |..1|..2|...|
 |.3.|.4.|.5.|
 |2..|6..|7..|
 |---+---+---|
 |..7|...|..8|
 |.1.|...|.3.|
 |6..|...|5..|
 |---+---+---|
 |..6|..8|..2|
 |.8.|.9.|.1.|
 |...|5..|9..|
 *-----------*


XY-chains (n)=cycle length

Code: Select all
1. Ocean (5):
[Edit: moved to BUG+1]

2. Ocean (5):
 *-----------*
 |2.5|.1.|8.3|
 |.4.|...|.7.|
 |7.3|2.4|5.9|
 |---+---+---|
 |..4|...|3..|
 |9..|...|..7|
 |..7|...|2..|
 |---+---+---|
 |6.1|3.8|9.4|
 |.3.|...|.5.|
 |8.2|.7.|1.6|
 *-----------*

3. Ocean (6):
[Edit: moved to XYZ-wing]

4. Ocean (6):
*-----------*
 |7..|5.8|..3|
 |.42|3.6|78.|
 |.8.|.4.|.2.|
 |---+---+---|
 |85.|...|.79|
 |..7|...|5..|
 |41.|...|.32|
 |---+---+---|
 |.3.|.5.|.9.|
 |.24|8.9|36.|
 |9..|6.2|..4|
 *-----------*

5. Ocean (6):
*-----------*
 |.1.|4.8|.6.|
 |7..|.6.|..1|
 |..3|...|2..|
 |---+---+---|
 |1..|524|..7|
 |.7.|6.1|.4.|
 |8..|397|..2|
 |---+---+---|
 |..7|...|1..|
 |4..|.5.|..3|
 |.2.|7.9|.5.|
 *-----------*

6. Ocean (6):
 *-----------*
 |..4|659|7..|
 |...|4.3|...|
 |9..|.7.|..8|
 |---+---+---|
 |41.|...|.75|
 |2.7|...|4.6|
 |56.|...|.13|
 |---+---+---|
 |3..|.6.|..4|
 |...|1.2|...|
 |..1|834|5..|
 *-----------*

7. Ocean (6):
[Edit: removed, solved with XYZ-wing + XY-wing]

8. Ocean (6):
[Edit: removed, solved with UR+1]

9. Ocean (6):
 *-----------*
 |..5|4.3|2..|
 |...|179|...|
 |9..|...|..7|
 |---+---+---|
 |78.|3.1|.95|
 |.5.|...|.2.|
 |19.|8.4|.36|
 |---+---+---|
 |8..|...|..4|
 |...|618|...|
 |..7|9.5|6..|
 *-----------*

10. Ocean (6):
[Edit: moved to UR]

11. Ocean (6):
 *-----------*
 |...|...|...|
 |.37|1.6|29.|
 |.5.|.9.|.1.|
 |---+---+---|
 |.9.|5.3|.2.|
 |..8|.6.|9..|
 |.4.|9.7|.3.|
 |---+---+---|
 |.8.|.3.|.4.|
 |.61|2.4|58.|
 |...|...|...|
 *-----------*

12. Ocean (7):
 *-----------*
 |1..|2.3|..4|
 |..3|.7.|6..|
 |.4.|.1.|.9.|
 |---+---+---|
 |9..|...|..1|
 |.16|...|45.|
 |4..|...|..7|
 |---+---+---|
 |.2.|.5.|.3.|
 |..9|.8.|7..|
 |5..|9.2|..6|
 *-----------*

13. Ocean (7):
[Edit: moved to XYZ-wing]

14. Ocean (7):
 *-----------*
 |..4|.9.|7..|
 |...|6.7|...|
 |5.7|...|9.6|
 |---+---+---|
 |.1.|3.6|.8.|
 |3..|...|..5|
 |.2.|8.4|.9.|
 |---+---+---|
 |9.6|...|4.2|
 |...|2.1|...|
 |..1|.6.|3..|
 *-----------*

15. Ocean (7):
 *-----------*
 |.93|...|65.|
 |2..|5.9|..3|
 |1..|...|..7|
 |---+---+---|
 |.8.|.9.|.6.|
 |...|2.1|...|
 |.2.|.4.|.1.|
 |---+---+---|
 |8..|...|..6|
 |3..|4.8|..5|
 |.54|...|82.|
 *-----------*

16. Ocean (7):
 *-----------*
 |6..|8.9|..7|
 |..4|...|6..|
 |.9.|6.2|.3.|
 |---+---+---|
 |2.3|.9.|1.6|
 |...|3.7|...|
 |8.9|.6.|7.3|
 |---+---+---|
 |.2.|9.6|.7.|
 |..1|...|2..|
 |9..|2.5|..8|
 *-----------*

17. Ocean (11):
 *-----------*
 |52.|.4.|.91|
 |17.|...|.54|
 |..4|...|2..|
 |---+---+---|
 |...|958|...|
 |6..|4.7|..2|
 |...|162|...|
 |---+---+---|
 |..8|...|4..|
 |45.|...|.38|
 |31.|.8.|.69|
 *-----------*

18. Mike Barker (5)
 *-----------*
 |3.2|.6.|7..|
 |1.4|..7|.2.|
 |..5|...|.3.|
 |---+---+---|
 |4..|3..|..5|
 |...|...|2..|
 |...|..9|..8|
 |---+---+---|
 |...|..2|8..|
 |.56|..4|...|
 |7..|.5.|1..|
 *-----------*

19. Mike Barker (5)
 *-----------*
 |..8|.1.|..7|
 |3..|.72|4..|
 |...|...|98.|
 |---+---+---|
 |...|..5|..4|
 |.4.|.3.|5..|
 |..9|...|13.|
 |---+---+---|
 |2..|...|...|
 |.5.|9.4|..8|
 |.1.|2..|...|
 *-----------*


Jellyfish

Code: Select all
1. Wapati
 *-----------*
 |..2|5.7|6..|
 |.4.|...|.5.|
 |..5|9.4|2..|
 |---+---+---|
 |8.9|...|1.2|
 |.5.|...|.7.|
 |3.4|...|5.6|
 |---+---+---|
 |..7|4.9|8..|
 |.6.|...|.2.|
 |..1|2.6|7..|
 *-----------*


Empty Rectangle

Code: Select all
1. Mike Barker
 *-----------*
 |...|...|.8.|
 |.4.|3..|...|
 |..6|.75|..9|
 |---+---+---|
 |7..|...|6..|
 |..8|...|.7.|
 |.9.|1..|..5|
 |---+---+---|
 |...|.6.|9.1|
 |2.7|...|...|
 |.39|.2.|4..|
 *-----------*


Finned Swordfish

Code: Select all
1. Miker Barker
 *-----------*
 |...|.2.|6.8|
 |...|...|.15|
 |.57|...|.4.|
 |---+---+---|
 |...|...|...|
 |6.8|.4.|...|
 |.32|..7|9..|
 |---+---+---|
 |.9.|2..|37.|
 |...|.18|...|
 |36.|...|...|
 *-----------*

2. Miker Barker
 *-----------*
 |..8|..7|964|
 |..9|6..|...|
 |...|...|7..|
 |---+---+---|
 |...|..1|.3.|
 |7..|2.4|1..|
 |.6.|5..|...|
 |---+---+---|
 |...|.5.|...|
 |5..|..2|.83|
 |.46|3..|..7|
 *-----------*


Franken Swordfish

Code: Select all
1. Mike Barker
 *-----------*
 |..7|..2|19.|
 |..5|...|..8|
 |...|9..|2..|
 |---+---+---|
 |.3.|6..|.2.|
 |...|..7|..9|
 |...|.25|...|
 |---+---+---|
 |6..|23.|...|
 |9..|4..|31.|
 |5..|...|6..|
 *-----------*


ALS-XZ

Code: Select all
1. tarek:
 *-----------*
 |...|..8|...|
 |..9|...|...|
 |52.|.4.|3..|
 |---+---+---|
 |..5|.6.|..7|
 |976|5.2|1..|
 |1..|...|..9|
 |---+---+---|
 |..7|..5|...|
 |2..|.93|..4|
 |31.|...|6..|
 *-----------*

2. Mike Barker
 *-----------*
 |7..|3..|.6.|
 |...|.1.|..4|
 |.3.|..5|2..|
 |---+---+---|
 |...|.64|9..|
 |9.6|1..|...|
 |...|8..|...|
 |---+---+---|
 |..3|.2.|.5.|
 |2..|...|.1.|
 |.15|4..|.7.|
 *-----------*

3. Mike Barker
 *-----------*
 |9..|2..|.8.|
 |24.|...|...|
 |..8|.4.|..9|
 |---+---+---|
 |...|...|3.8|
 |...|...|.7.|
 |...|591|...|
 |---+---+---|
 |6..|.7.|...|
 |...|8..|6..|
 |.71|..6|.54|
 *-----------*

4. Mike Barker
 *-----------*
 |...|...|9..|
 |...|...|.67|
 |42.|...|3..|
 |---+---+---|
 |.5.|..4|..3|
 |...|1.2|...|
 |.87|.9.|...|
 |---+---+---|
 |..2|.81|...|
 |..6|4..|.5.|
 |...|...|274|
 *-----------*

5. Mike Barker
 *-----------*
 |...|4..|...|
 |..5|...|.3.|
 |...|.3.|8.1|
 |---+---+---|
 |..9|..8|..5|
 |.5.|..3|..2|
 |8.6|..1|4..|
 |---+---+---|
 |24.|...|..8|
 |...|.7.|...|
 |.1.|26.|...|
 *-----------*

6. Mike Barker
 *-----------*
 |..8|...|.95|
 |19.|...|.7.|
 |.5.|6..|...|
 |---+---+---|
 |2.3|7..|..1|
 |...|.2.|..4|
 |...|..3|..9|
 |---+---+---|
 |.3.|...|1..|
 |..6|47.|...|
 |.8.|.5.|2..|
 *-----------*

7. Ruud
 *-----------*
 |...|97.|..3|
 |...|..1|8..|
 |97.|8.4|.1.|
 |---+---+---|
 |..9|7.2|.6.|
 |13.|...|..9|
 |28.|.1.|.7.|
 |---+---+---|
 |...|6.8|...|
 |.61|...|...|
 |4..|...|.3.|
 *-----------*

8. Ruud
 *-----------*
 |.34|...|.1.|
 |1..|7..|5..|
 |...|6..|...|
 |---+---+---|
 |...|...|...|
 |.7.|..2|3..|
 |62.|.3.|.59|
 |---+---+---|
 |..7|.59|..2|
 |39.|...|.85|
 |.8.|..1|.7.|
 *-----------*


Nice loops

Code: Select all
1. Mike Barker
 *-----------*
 |...|..7|3..|
 |.9.|...|...|
 |...|.16|.58|
 |---+---+---|
 |3..|...|1..|
 |72.|1..|.9.|
 |...|...|.26|
 |---+---+---|
 |.14|.8.|27.|
 |...|2.5|...|
 |..9|7..|...|
 *-----------*

2. Mike Barker
 *-----------*
 |.63|.4.|..1|
 |...|...|...|
 |129|...|8..|
 |---+---+---|
 |...|.38|...|
 |.17|...|..8|
 |..8|...|6..|
 |---+---+---|
 |..2|1..|9..|
 |8..|42.|.3.|
 |5..|..3|7..|
 *-----------*

3. Mike Barker
 *-----------*
 |6..|1..|...|
 |.5.|...|9..|
 |7.3|...|..4|
 |---+---+---|
 |3..|8..|.1.|
 |.8.|6..|59.|
 |..6|...|2..|
 |---+---+---|
 |.4.|..1|8..|
 |...|.6.|7.5|
 |..9|..5|...|
 *-----------*

4. Mike Barker
 *-----------*
 |.69|.3.|.8.|
 |.1.|...|...|
 |...|2..|.9.|
 |---+---+---|
 |.91|.4.|.2.|
 |7..|...|4..|
 |.2.|..9|..7|
 |---+---+---|
 |...|7..|91.|
 |..3|.5.|...|
 |...|..2|..6|
 *-----------*

5. Mike Barker
 *-----------*
 |.43|...|7..|
 |...|.6.|...|
 |68.|.79|...|
 |---+---+---|
 |...|...|..8|
 |..1|.8.|3..|
 |...|5..|1.4|
 |---+---+---|
 |...|..1|.6.|
 |.5.|..2|..3|
 |9.7|...|8..|
 *-----------*

6. Mike Barker
 *-----------*
 |.5.|...|3.2|
 |.9.|...|7..|
 |.7.|2..|.8.|
 |---+---+---|
 |...|6.1|...|
 |..9|.3.|..7|
 |..2|...|.64|
 |---+---+---|
 |..8|35.|...|
 |51.|8.6|...|
 |...|...|.3.|
 *-----------*

7. Ocean
 *-----------*
 |...|..1|.2.|
 |.1.|...|..3|
 |..4|.5.|...|
 |---+---+---|
 |...|6..|..7|
 |..8|.4.|9..|
 |5..|..3|...|
 |---+---+---|
 |...|.9.|4..|
 |3..|...|.5.|
 |.7.|4..|...|
 *-----------*

8. Ocean
 *-----------*
 |..6|...|5..|
 |.7.|.3.|.9.|
 |4..|...|..6|
 |---+---+---|
 |1..|...|..2|
 |.2.|...|.3.|
 |..4|.5.|6..|
 |---+---+---|
 |...|1.7|...|
 |.8.|.9.|.7.|
 |...|4.5|...|
 *-----------*

9. Ocean
 *-----------*
 |..1|..2|...|
 |.3.|.4.|.5.|
 |5..|6..|7..|
 |---+---+---|
 |..8|...|..6|
 |.1.|...|.9.|
 |6..|...|8..|
 |---+---+---|
 |..6|..7|..4|
 |.9.|.1.|.3.|
 |...|5..|2..|
 *-----------*


Gurths symmetrical placement

Code: Select all
1. ravel
 *-----------*
 |..7|...|...|
 |...|.34|.76|
 |...|1.7|5.3|
 |---+---+---|
 |2..|3..|..8|
 |8..|...|..5|
 |5..|..6|..1|
 |---+---+---|
 |6.8|4.2|...|
 |34.|76.|...|
 |...|...|4..|
 *-----------*

2. ravel
 *-----------*
 |..1|5.2|.3.|
 |...|..1|..9|
 |4..|7..|.2.|
 |---+---+---|
 |..2|.6.|..8|
 |6..|...|..1|
 |8..|.1.|4..|
 |---+---+---|
 |.4.|..9|..2|
 |7..|6..|...|
 |.5.|4.3|6..|
 *-----------*

3. ravel
 *-----------*
 |5..|2.1|..3|
 |9..|3..|.81|
 |..4|...|...|
 |---+---+---|
 |...|9..|528|
 |...|...|...|
 |639|..5|...|
 |---+---+---|
 |...|...|1..|
 |46.|..2|..5|
 |2..|4.3|..9|
 *-----------*

4. ravel
 *-----------*
 |..3|..6|8..|
 |.1.|3..|...|
 |..5|.1.|3.4|
 |---+---+---|
 |87.|..2|...|
 |...|...|...|
 |...|1..|.39|
 |---+---+---|
 |6.7|.2.|5..|
 |...|..7|.2.|
 |..9|4..|7..|
 *-----------*


BUG-lite

Code: Select all
1. Mike Barker
[Edit: moved to Layered BUG-lite]

2. Mike Barker
 *-----------*
 |..8|...|2..|
 |9..|...|..7|
 |2.7|...|.93|
 |---+---+---|
 |4..|.9.|..6|
 |...|.2.|...|
 |...|..3|1.5|
 |---+---+---|
 |...|..8|...|
 |.5.|43.|...|
 |.6.|..7|.84|
 *-----------*

3. Mike Barker
 *-----------*
 |3..|...|4..|
 |...|...|.8.|
 |.9.|.4.|1..|
 |---+---+---|
 |...|...|.7.|
 |..8|..6|...|
 |..4|.79|6..|
 |---+---+---|
 |.7.|9.8|3..|
 |.4.|32.|...|
 |25.|..1|...|
 *-----------*

4. Mike Barker
[Edit: removed, solved with UR+1]

5. Mike Barker
[Edit: moved to Layered BUG-lite]

6. Mike Barker
 *-----------*
 |...|..1|.54|
 |.9.|.3.|2..|
 |374|...|..1|
 |---+---+---|
 |...|.2.|.8.|
 |5.9|46.|...|
 |2.8|.1.|...|
 |---+---+---|
 |...|9..|...|
 |.4.|6..|.1.|
 |..6|...|..5|
 *-----------*

7. Mike Barker
 *-----------*
 |.4.|9..|.2.|
 |...|...|.61|
 |2..|..4|5..|
 |---+---+---|
 |..6|3.2|8..|
 |..7|..1|..2|
 |5..|...|...|
 |---+---+---|
 |.2.|.5.|..3|
 |95.|.48|...|
 |...|...|18.|
 *-----------*

8. Mike Barker
 *-----------*
 |...|1..|...|
 |.3.|.5.|.12|
 |41.|23.|.5.|
 |---+---+---|
 |...|..2|..3|
 |16.|...|..9|
 |.2.|37.|..8|
 |---+---+---|
 |..9|...|..5|
 |..8|...|...|
 |24.|...|8..|
 *-----------*

9. RW
 *-----------*
 |...|7.4|...|
 |..1|.8.|7..|
 |.75|2.3|81.|
 |---+---+---|
 |9.4|...|3.5|
 |.6.|...|.4.|
 |5.7|...|6.9|
 |---+---+---|
 |.42|8.7|93.|
 |..8|.3.|4..|
 |...|4.1|...|
 *-----------*

10. wapati
 *-----------*
 |24.|.5.|.89|
 |9..|4.8|..5|
 |..8|...|3..|
 |---+---+---|
 |.8.|527|.3.|
 |4..|3.6|..7|
 |.3.|849|.5.|
 |---+---+---|
 |..2|...|9..|
 |8..|9.5|..2|
 |19.|.8.|.73|
 *-----------*


Layered BUG-lite

Code: Select all
1. Mike Barker
 *-----------*
 |.9.|.8.|.7.|
 |...|3..|.52|
 |65.|4..|...|
 |---+---+---|
 |8.7|..3|1.6|
 |1..|...|...|
 |9..|8.4|...|
 |---+---+---|
 |...|.6.|4.7|
 |78.|...|...|
 |...|2..|...|
 *-----------*

2. Mike Barker
 *-----------*
 |.78|...|2..|
 |..4|.9.|.3.|
 |.6.|4..|9..|
 |---+---+---|
 |3..|..6|.15|
 |8..|.1.|...|
 |61.|..5|...|
 |---+---+---|
 |4..|...|...|
 |...|..2|8.9|
 |...|...|.27|
 *-----------*


Advanced BUG-lite

Code: Select all
1. RW
 *-----------*
 |..3|6.4|9..|
 |...|7.2|...|
 |6..|...|..4|
 |---+---+---|
 |35.|...|.98|
 |...|...|...|
 |82.|...|.75|
 |---+---+---|
 |5..|...|..6|
 |...|9.7|...|
 |..1|2.6|8..|
 *-----------*


BUG+1

Code: Select all
1. Mike Barker
 *-----------*
 |.1.|2..|.4.|
 |.9.|...|.3.|
 |5..|4..|...|
 |---+---+---|
 |...|...|...|
 |..7|5..|1.8|
 |..6|8.1|...|
 |---+---+---|
 |3..|.2.|8..|
 |...|.6.|.2.|
 |85.|.4.|..3|
 *-----------*

2. Mike Barker
 *-----------*
 |...|.12|6.7|
 |.59|...|.32|
 |...|...|.8.|
 |---+---+---|
 |7..|...|...|
 |..8|4..|.7.|
 |..5|8.9|12.|
 |---+---+---|
 |.9.|758|2..|
 |..6|.4.|..5|
 |.4.|...|...|
 *-----------*

3. Mike Barker
moved to BUG+2

4. Mike Barker
 *-----------*
 |3..|96.|.8.|
 |...|...|..2|
 |1..|..5|.3.|
 |---+---+---|
 |...|3..|...|
 |..1|...|.9.|
 |.47|21.|...|
 |---+---+---|
 |...|..8|..7|
 |..8|1..|5..|
 |..9|..6|1..|
 *-----------*

5. Mike Barker
 *-----------*
 |...|...|56.|
 |9..|...|2..|
 |.8.|.2.|...|
 |---+---+---|
 |2.9|..4|..5|
 |3..|..9|..7|
 |1..|..2|.36|
 |---+---+---|
 |...|46.|...|
 |4..|...|.1.|
 |...|5.1|..3|
 *-----------*

6. Mike Barker
 *-----------*
 |1.9|...|...|
 |6..|58.|...|
 |...|72.|.4.|
 |---+---+---|
 |...|37.|..2|
 |...|...|4.7|
 |..3|1..|.9.|
 |---+---+---|
 |8.2|4..|...|
 |...|...|...|
 |.5.|..2|9.1|
 *-----------*

7. tso
 *-----------*
 |.15|24.|...|
 |.2.|.18|645|
 |.6.|...|..8|
 |---+---+---|
 |.3.|...|..6|
 |69.|...|.73|
 |5..|...|.8.|
 |---+---+---|
 |4..|...|.5.|
 |289|73.|.6.|
 |...|.21|89.|
 *-----------*

8. Ocean
 *-----------*
 |9..|.7.|..2|
 |..4|.8.|7..|
 |.6.|9.3|.4.|
 |---+---+---|
 |..7|...|2..|
 |84.|...|.31|
 |..9|...|4..|
 |---+---+---|
 |.9.|4.7|.6.|
 |..6|.1.|9..|
 |2..|.6.|..4|
 *-----------*

9. wapati
 *-----------*
 |...|...|...|
 |7..|.9.|..6|
 |89.|...|.45|
 |---+---+---|
 |9..|368|..2|
 |...|...|...|
 |.56|.7.|91.|
 |---+---+---|
 |16.|4.2|.79|
 |.2.|5.7|.8.|
 |...|.8.|...|
 *-----------*

10. wapati
 *-----------*
 |..1|.5.|8..|
 |.2.|...|.7.|
 |3..|.17|2.5|
 |---+---+---|
 |...|4..|5..|
 |9.3|...|4.2|
 |..6|..1|...|
 |---+---+---|
 |5.4|69.|..7|
 |.3.|...|.4.|
 |..7|.4.|3..|
 *-----------*

11. wapati
 *-----------*
 |97.|...|.45|
 |5..|834|..7|
 |..6|9.5|8..|
 |---+---+---|
 |.69|...|52.|
 |.2.|...|.8.|
 |.53|...|16.|
 |---+---+---|
 |..4|2.7|9..|
 |2..|369|..1|
 |69.|...|.38|
 *-----------*


BUG+2

Code: Select all
1. Mike Barker
 *-----------*
 |.6.|.98|.4.|
 |31.|...|...|
 |5.8|...|.3.|
 |---+---+---|
 |..1|..6|...|
 |...|...|4..|
 |...|182|5..|
 |---+---+---|
 |...|245|..7|
 |...|9..|6.1|
 |..7|...|2..|
 *-----------*

2. Mike Barker
 *-----------*
 |1..|.6.|...|
 |6..|8..|..5|
 |...|.52|...|
 |---+---+---|
 |.9.|...|4.8|
 |86.|...|.9.|
 |...|..3|.1.|
 |---+---+---|
 |7.2|.4.|.6.|
 |...|5.8|3..|
 |.5.|...|...|
 *-----------*

3. Mike Barker
[Edit: removed, solved with UR+1]

4. Mike Barker
 *-----------*
 |.9.|..1|..5|
 |.4.|...|37.|
 |.1.|2..|..9|
 |---+---+---|
 |6..|...|5..|
 |.5.|.2.|9.7|
 |...|3..|...|
 |---+---+---|
 |8..|..2|...|
 |...|.59|768|
 |4.9|.6.|...|
 *-----------*

5. wapati
 *-----------*
 |6..|...|..2|
 |..2|691|4..|
 |.9.|5.3|.7.|
 |---+---+---|
 |.23|...|78.|
 |.7.|...|.5.|
 |.14|...|26.|
 |---+---+---|
 |.4.|7.2|.9.|
 |..7|948|3..|
 |2..|...|..7|
 *-----------*

6. Mike Barker
 *-----------*
 |2.9|...|7..|
 |.8.|.49|...|
 |...|...|...|
 |---+---+---|
 |..4|1..|.9.|
 |.63|9..|4..|
 |5.8|2..|...|
 |---+---+---|
 |.32|81.|...|
 |...|...|6.5|
 |...|43.|..1|
 *-----------*

7. wapati
 *-----------*
 |...|...|4.3|
 |.7.|...|58.|
 |...|..2|.61|
 |---+---+---|
 |...|.5.|.9.|
 |...|1.7|...|
 |..6|.4.|1.5|
 |---+---+---|
 |86.|..3|.5.|
 |.37|8..|9..|
 |9.4|..6|...|
 *-----------*


BUG+3

Code: Select all
1. Mike Barker
 *-----------*
 |.29|...|.15|
 |...|...|..3|
 |15.|..7|..4|
 |---+---+---|
 |...|1..|..8|
 |4..|...|.9.|
 |...|5..|...|
 |---+---+---|
 |6..|31.|.4.|
 |.8.|...|73.|
 |5..|.6.|8..|
 *-----------*

2. Mike Barker
 *-----------*
 |...|.6.|.3.|
 |.84|9..|...|
 |...|...|8.1|
 |---+---+---|
 |...|2.8|...|
 |..5|...|..4|
 |..6|..3|..7|
 |---+---+---|
 |1..|.8.|.7.|
 |2..|.4.|..5|
 |.7.|..1|4..|
 *-----------*

3. Mike Barker
 *-----------*
 |.14|8.2|9..|
 |...|...|...|
 |8.2|6..|...|
 |---+---+---|
 |.78|..4|..9|
 |.2.|...|.4.|
 |...|5.1|...|
 |---+---+---|
 |56.|...|...|
 |7..|.9.|.16|
 |.8.|.3.|..7|
 *-----------*


BUG+4

Code: Select all
1. Mike Barker
 *-----------*
 |...|.12|...|
 |8..|.7.|...|
 |...|.95|3.7|
 |---+---+---|
 |..4|...|78.|
 |.5.|...|1..|
 |...|.5.|..9|
 |---+---+---|
 |.1.|...|.3.|
 |.2.|.8.|9..|
 |.73|.4.|.6.|
 *-----------*


Reverse-BUG

Code: Select all
1. RW
 *-----------*
 |.7.|...|3..|
 |6.2|1.9|4..|
 |...|..6|..8|
 |---+---+---|
 |..7|56.|..4|
 |...|8.7|...|
 |5..|.34|6..|
 |---+---+---|
 |7..|6..|...|
 |..9|4.8|7.5|
 |..5|...|.6.|
 *-----------*


Uniqueness Rectangles

Code: Select all
1. Ocean:
 *-----------*
 |...|825|...|
 |.4.|...|.1.|
 |..2|.1.|5..|
 |---+---+---|
 |8..|7.1|..9|
 |4.9|...|3.1|
 |7..|9.3|..8|
 |---+---+---|
 |..3|.9.|1..|
 |.8.|...|.6.|
 |...|567|...|
 *-----------*

2. Ocean:
 *-----------*
 |2..|...|..8|
 |.64|.5.|21.|
 |.19|...|65.|
 |---+---+---|
 |...|237|...|
 |.3.|4.6|.8.|
 |...|185|...|
 |---+---+---|
 |.21|...|43.|
 |.83|.4.|56.|
 |9..|...|..1|
 *-----------*

3. RW:
 *-----------*
 |...|123|...|
 |..8|.9.|4..|
 |.3.|...|.5.|
 |---+---+---|
 |9..|...|..6|
 |8..|.1.|..7|
 |7..|3.4|..8|
 |---+---+---|
 |.6.|.8.|.9.|
 |..5|...|1..|
 |.9.|432|.6.|
 *-----------*

4. RW:
 *-----------*
 |...|123|...|
 |..8|...|4..|
 |.3.|...|.5.|
 |---+---+---|
 |9..|.4.|..6|
 |8..|3.9|..7|
 |7..|...|..8|
 |---+---+---|
 |.6.|...|.9.|
 |3.5|.7.|1.4|
 |...|432|...|
 *-----------*

5. Mike Barker
 *-----------*
 |.7.|5..|...|
 |4..|19.|...|
 |51.|...|.9.|
 |---+---+---|
 |.43|.2.|.1.|
 |..8|...|.26|
 |.2.|3..|..5|
 |---+---+---|
 |...|...|.8.|
 |...|7..|.51|
 |79.|...|..2|
 *-----------*

6. Mike Barker
 *-----------*
 |..3|2..|...|
 |4..|...|...|
 |...|8.7|..5|
 |---+---+---|
 |...|675|...|
 |95.|4..|7..|
 |8.1|.3.|.6.|
 |---+---+---|
 |...|.96|.7.|
 |..7|...|8..|
 |.9.|...|..2|
 *-----------*

7. Mike Barker
 *-----------*
 |.47|...|...|
 |...|9..|..6|
 |98.|..5|.72|
 |---+---+---|
 |..5|.7.|.6.|
 |3.4|...|...|
 |27.|5..|...|
 |---+---+---|
 |...|...|.9.|
 |...|.16|..7|
 |.62|..8|4..|
 *-----------*

8. Mike Barker
 *-----------*
 |...|9.7|..8|
 |...|.6.|...|
 |72.|5..|.9.|
 |---+---+---|
 |.83|...|6..|
 |..2|...|.3.|
 |4..|..3|7..|
 |---+---+---|
 |.9.|...|14.|
 |.1.|..2|..6|
 |...|.56|...|
 *-----------*

9. Mike Barker
 *-----------*
 |896|.4.|...|
 |...|...|7.2|
 |...|9..|.6.|
 |---+---+---|
 |.18|..9|.24|
 |6..|3..|.8.|
 |.3.|.1.|...|
 |---+---+---|
 |...|4..|2..|
 |3..|..6|...|
 |..5|.3.|.1.|
 *-----------*

10. Mike Barker
 *-----------*
 |...|...|...|
 |...|3..|6..|
 |...|.74|2..|
 |---+---+---|
 |.34|.5.|9.2|
 |.7.|4..|5.1|
 |...|...|...|
 |---+---+---|
 |8.5|.16|..3|
 |6..|...|...|
 |..7|.9.|..8|
 *-----------*

11. Mike Barker
 *-----------*
 |...|4.3|.7.|
 |53.|...|...|
 |...|...|.46|
 |---+---+---|
 |9..|...|...|
 |8..|..7|4.2|
 |...|36.|.1.|
 |---+---+---|
 |.7.|18.|.6.|
 |.5.|.2.|...|
 |.4.|..5|7..|
 *-----------*

12. Mike Barker
 *-----------*
 |8..|3..|..1|
 |9.2|...|...|
 |...|56.|..4|
 |---+---+---|
 |..8|..4|.65|
 |...|7..|..3|
 |2.6|...|...|
 |---+---+---|
 |...|.1.|...|
 |...|.8.|542|
 |7..|...|...|
 *-----------*

13. Mike Barker
 *-----------*
 |.2.|..8|...|
 |..5|...|2..|
 |7..|.1.|..6|
 |---+---+---|
 |...|...|.2.|
 |938|.2.|...|
 |..7|4.5|8..|
 |---+---+---|
 |...|1.9|7..|
 |..9|5..|6..|
 |6..|.83|..4|
 *-----------*

14. Mike Barker
 *-----------*
 |...|..2|..4|
 |..1|7..|8..|
 |.4.|.6.|.3.|
 |---+---+---|
 |4.6|...|..5|
 |3.7|...|.8.|
 |...|..9|...|
 |---+---+---|
 |..9|.18|..2|
 |1..|...|.5.|
 |.5.|..4|76.|
 *-----------*

15. Mike Barker
 *-----------*
 |2.1|...|..8|
 |...|..3|...|
 |...|...|.62|
 |---+---+---|
 |6.3|..7|...|
 |.52|.94|7..|
 |7..|3..|1..|
 |---+---+---|
 |4..|..6|.51|
 |9..|5..|.4.|
 |..7|.1.|...|
 *-----------*

16. Mike Barker
 *-----------*
 |...|..1|5..|
 |.45|3..|...|
 |...|.9.|468|
 |---+---+---|
 |..8|..3|..9|
 |9..|2.7|...|
 |...|.5.|.26|
 |---+---+---|
 |6..|...|.41|
 |42.|...|...|
 |..9|...|..3|
 *-----------*

17. Mike Barker
 *-----------*
 |...|...|..7|
 |2..|...|...|
 |..3|79.|.1.|
 |---+---+---|
 |4.6|...|25.|
 |...|.5.|...|
 |...|.76|..3|
 |---+---+---|
 |85.|9.7|...|
 |.4.|...|8.6|
 |...|4.8|.2.|
 *-----------*

18. Mike Barker
 *-----------*
 |8.2|..3|...|
 |...|...|7..|
 |6.1|...|.8.|
 |---+---+---|
 |...|78.|.2.|
 |75.|.91|34.|
 |.9.|.5.|...|
 |---+---+---|
 |...|.3.|5..|
 |4..|..9|...|
 |1..|8..|6..|
 *-----------*

19. Mike Barker
 *-----------*
 |...|.6.|71.|
 |..3|8..|.45|
 |.5.|..2|..3|
 |---+---+---|
 |.1.|..3|...|
 |.8.|..7|.6.|
 |3.7|...|.5.|
 |---+---+---|
 |..6|.2.|.91|
 |...|...|...|
 |4.1|.98|...|
 *-----------*

20. Mike Barker
[Edit: removed, also required XY-wing]

21. Mike Barker
 *-----------*
 |.4.|7..|62.|
 |1..|.4.|..3|
 |...|.1.|.8.|
 |---+---+---|
 |...|1..|.9.|
 |9.5|...|..8|
 |..8|4..|...|
 |---+---+---|
 |...|...|7.2|
 |...|3..|.4.|
 |.2.|.5.|.19|
 *-----------*

22. Mike Barker
[Edit: removed, solvable with XY-wing]

23. Mike Barker
 *-----------*
 |...|..4|9.6|
 |23.|7..|...|
 |...|5..|..1|
 |---+---+---|
 |1..|...|...|
 |.4.|...|8..|
 |.5.|..3|6.9|
 |---+---+---|
 |9..|..8|...|
 |...|1..|3.7|
 |..2|..9|.4.|
 *-----------*

24. Mike Barker
 *-----------*
 |...|...|7..|
 |6..|8..|.5.|
 |..8|.91|..2|
 |---+---+---|
 |...|6..|.4.|
 |.54|...|...|
 |82.|3..|...|
 |---+---+---|
 |...|..8|..9|
 |.3.|..7|.6.|
 |5.9|.3.|...|
 *-----------*

25. Mike Barker
 *-----------*
 |..7|...|.4.|
 |.2.|.67|...|
 |9..|4..|..1|
 |---+---+---|
 |...|3.1|...|
 |..4|.2.|67.|
 |...|...|..8|
 |---+---+---|
 |...|...|35.|
 |..5|..9|...|
 |.3.|6.4|.2.|
 *-----------*

 26. Mike Barker
 *-----------*
 |.8.|..5|.7.|
 |.4.|.3.|9..|
 |.1.|...|.2.|
 |---+---+---|
 |.2.|.9.|...|
 |7..|.48|..5|
 |63.|.5.|8..|
 |---+---+---|
 |...|3.2|...|
 |...|...|1..|
 |...|...|.34|
 *-----------*

27. Mike Barker
 *-----------*
 |67.|5.8|.9.|
 |...|...|...|
 |...|3..|.2.|
 |---+---+---|
 |5..|...|..9|
 |...|.4.|2..|
 |.4.|..1|.8.|
 |---+---+---|
 |..1|47.|..3|
 |.2.|..3|1..|
 |49.|...|5..|
 *-----------*

28. Mike Barker
 *-----------*
 |...|...|...|
 |24.|.51|93.|
 |9..|4..|...|
 |---+---+---|
 |...|..3|.7.|
 |.8.|.7.|421|
 |...|.1.|..5|
 |---+---+---|
 |.5.|.94|...|
 |.28|...|6..|
 |36.|..2|...|
 *-----------*

29. Mike Barker
 *-----------*
 |...|..8|.1.|
 |..5|1..|7..|
 |...|92.|...|
 |---+---+---|
 |...|.6.|...|
 |.73|...|94.|
 |...|8..|6.7|
 |---+---+---|
 |42.|..5|...|
 |.3.|.4.|16.|
 |..1|...|.5.|
 *-----------*

30. Mike Barker
 *-----------*
 |14.|.3.|...|
 |...|...|.6.|
 |...|845|...|
 |---+---+---|
 |.2.|...|.9.|
 |.18|...|...|
 |9.6|...|.78|
 |---+---+---|
 |.5.|7..|9..|
 |372|.1.|..4|
 |..4|...|..2|
 *-----------*

31. Mike Barker
 *-----------*
 |...|1.4|9..|
 |7..|9..|42.|
 |...|7..|6..|
 |---+---+---|
 |.6.|...|...|
 |.2.|..5|...|
 |8..|.3.|..4|
 |---+---+---|
 |.8.|...|.7.|
 |...|5..|...|
 |231|.6.|..5|
 *-----------*

32. Mike Barker
 *-----------*
 |.9.|..4|...|
 |4..|38.|...|
 |...|.5.|1.7|
 |---+---+---|
 |..4|...|9..|
 |...|..9|..3|
 |...|2.3|.64|
 |---+---+---|
 |.8.|...|...|
 |..6|71.|8.2|
 |..2|...|.3.|
 *-----------*

33. Mike Barker
 *-----------*
 |.4.|36.|1..|
 |...|...|7..|
 |.8.|19.|..2|
 |---+---+---|
 |2.5|...|...|
 |...|...|3..|
 |...|2..|..6|
 |---+---+---|
 |61.|...|.98|
 |95.|.4.|...|
 |7..|6..|2..|
 *-----------*

34. gsf
 *-----------*
 |5..|6..|...|
 |94.|2..|3..|
 |.6.|7.8|.4.|
 |---+---+---|
 |3.9|...|8..|
 |4..|...|...|
 |..6|...|132|
 |---+---+---|
 |...|9.5|...|
 |...|...|21.|
 |...|.36|.57|
 *-----------*

35. Ocean
 *-----------*
 |8..|...|..9|
 |..2|9.6|3..|
 |.9.|8.1|.6.|
 |---+---+---|
 |.51|.2.|93.|
 |...|3.8|...|
 |.28|.1.|74.|
 |---+---+---|
 |.7.|1.4|.9.|
 |..4|7.5|6..|
 |6..|...|..7|
 *-----------*

36. Mike Barker
 *-----------*
 |123|9..|...|
 |...|1..|.5.|
 |..7|...|...|
 |---+---+---|
 |..8|3..|64.|
 |..9|..8|..5|
 |.1.|.65|.3.|
 |---+---+---|
 |8..|.9.|..3|
 |...|.21|...|
 |..5|...|8.4|
 *-----------*
Last edited by RW on Tue Nov 28, 2006 3:20 am, edited 33 times in total.
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Re: The Effortless Extremes thread

Postby Ocean » Wed Apr 12, 2006 1:24 am

I liked this challenge, but it took a while to handle it.
Here is an 'effortless' extreme:

Code: Select all
 . . . | 8 2 5 | . . .
 . 4 . | . . . | . 1 .
 . . 2 | . 1 . | 5 . .
-------+-------+------
 8 . . | 7 . 1 | . . 9
 4 . 9 | . . . | 3 . 1
 7 . . | 9 . 3 | . . 8
-------+-------+------
 . . 3 | . 9 . | 1 . .
 . 8 . | . . . | . 6 .
 . . . | 5 6 7 | . . .

Extreme technique: xy-chain length 4.


Same techinque for these (xy-chain length 4):
700000006032000710050801030003090600000702000007060500010509070078000920900000003
900070002004080700060903040007000200840000031009000400090407060006010900200060004
205010803040000070703204509004000300900000007007000200601308904030000050802070106



This one is slightly harder:
Code: Select all
 2 . . | . . . | . . 8
 . 6 4 | . 5 . | 2 1 . 
 . 1 9 | . . . | 6 5 .
-------+-------+------
 . . . | 2 3 7 | . . .
 . 3 . | 4 . 6 | . 8 .
 . . . | 1 8 5 | . . .
-------+-------+------
 . 2 1 | . . . | 4 3 .
 . 8 3 | . 4 . | 5 6 .
 9 . . | . . . | . . 1

Extreme technique: xy-chain length 8.


Code: Select all
 . . 4 | 2 . 7 | 6 . .
 . 6 . | . 1 . | . 2 .
 2 . . | 6 . 3 | . . 4
-------+-------+------
 4 . 8 | . . . | 9 . 7
 . 9 . | . . . | . 6 . 
 5 . 6 | . . . | 4  .3
-------+-------+------
 9 . . | 4 . 1 | . . 6
 . 3 . | . 6 . | . 4 . 
 . . 5 | 8 . 9 | 2 . .

Extreme technique: xy-chain length 5
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Re: The Effortless Extremes thread

Postby gsf » Wed Apr 12, 2006 5:04 am

Code: Select all
# 27 clue pi symmetric (symmetrially minimal)
# length 13 x cycle on 8's
# [16][19][99]-[94][64]-[62][72][71][51][58][47][87][86]-

. 4 .  . 3 .  . . .
5 . .  . . .  . . 3
. 3 8  1 6 .  2 . .

. . 6  7 . .  . . 2
. . .  4 5 6  . . .
7 . .  . . 3  5 . .

. . 2  . 7 5  6 9 .
3 . .  . . .  . . 7
. . .  . 9 .  . 5 .
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Re: The Effortless Extremes thread

Postby Ocean » Wed Apr 12, 2006 8:53 am

Here is also a candidate. When 55 clues are filled in, nice loops of length 5 and 7 lead to 5 possible eliminations. (Three of the eliminations lead to 'nothing', while any choice of the other two leads to simple solution of the puzzle).

Code: Select all
 7 . . | 5 . 8 | . . 3
 . 4 2 | 3 . 6 | 7 8 .
 . 8 . | . 4 . | . 2 .
-------+-------+------
 8 5 . | . . . | . 7 9
 . . 7 | . . . | 5 . .
 4 1 . | . . . | . 3 2
-------+-------+------
 . 3 . | . 5 . | . 9 .
 . 2 4 | 8 . 9 | 3 6 .
 9 . . | 6 . 2 | . . 4

Extreme technique: xy-chain length 5 or 7.
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Postby RW » Wed Apr 12, 2006 11:32 am

Hi guys

Thanks for your submissions. Seems this is a lot harder than I intended it to be. Only half of the submitted puzzles this far has passed the original demands.

gsf:
Code: Select all
 *-----------*
 |.4.|.3.|...|
 |5..|...|..3|
 |.38|16.|2..|
 |---+---+---|
 |..6|7..|..2|
 |...|456|...|
 |7..|..3|5..|
 |---+---+---|
 |..2|.75|69.|
 |3..|...|..7|
 |...|.9.|.5.|
 *-----------*

Nice puzzle, but solvable with simple coloring.

Ocean: 4 good puzzles, this one

700000006032000710050801030003090600000702000007060500010509070078000920900000003

can be solved with multiple colors and two of your puzzles were solvable with quite obvious uniqueness rectangles.

I hereby made a desicion that I'll count uniqueness rectangles as an "advanced technique", even though I find it a lot easier to use than for example X-wing. Apparently these uniqueness rectangles aren't as obvious to everybody else, so I thought it could be good to have a collection of puzzles for people to practise on. Ocean, I took the liberty to add the two of your puzzles to that category, hope you don't mind. I also added a couple of my own designs, this time they at least have some kind of symmetry.

What do you think in general, should I also consider coloring and multiple colors "advanced techniques" and make lists for puzzles that require these techniques as well?

RW
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Postby Ruud » Wed Apr 12, 2006 12:19 pm

Hi RW,

There must be a few examples in my Benchmark Sudoku List that you can use.

Actually, I posted the list on this forum, so it can be used as source for solving technique samples. We could join forces and complete the list with advanced solving techniques that are still missing.

Ruud.
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Postby Ocean » Thu Apr 13, 2006 7:47 am

RW wrote:Ocean: 4 good puzzles, this one

700000006032000710050801030003090600000702000007060500010509070078000920900000003

can be solved with multiple colors and two of your puzzles were solvable with quite obvious uniqueness rectangles.

Thank you for analyzing the submissions! I have not included all possible techniques in my solver/analyzer. After writing the "XY-chain" part, I decided to kick this thread alive... without further delay. (I'm a very slow programmer - the techniques for 'colouring' and detecting 'uniqueness rectangles' are not yet implemented, and it might take a while to write those, if I ever do). I checked colouring manually, but forgot to check uniqueness arguments. Checking again now, I also find that the puzzle listed as #1 under XY-chains (length 4) has an alternative (simpler?) solution strategy, as it almost falls in the "bivalue universal grave" (BUG).

RW wrote:I hereby made a desicion that I'll count uniqueness rectangles as an "advanced technique", even though I find it a lot easier to use than for example X-wing. Apparently these uniqueness rectangles aren't as obvious to everybody else, so I thought it could be good to have a collection of puzzles for people to practise on. Ocean, I took the liberty to add the two of your puzzles to that category, hope you don't mind. I also added a couple of my own designs, this time they at least have some kind of symmetry.

What do you think in general, should I also consider coloring and multiple colors "advanced techniques" and make lists for puzzles that require these techniques as well?

RW

Fine. I agree that uniqueness rectangles are often quite easy to use. (The dilemma for a solver/analyzer is that it's only a valid method when you already 'know' the puzzle has a single solution). Your puzzles are good examples of this technique, and the rectangles are easy to spot when you know they are there.

Whether coloring and multiple colors should be considered as "advanced techniques" is probably a matter of taste. It's obviously not the first technique you try, and you can certainly use coloring methods on a quite 'advanced' level.

Here are some new candidates. I checked manually that they should not be solvable by colouring, uniqueness rectangles or simple BUGs, but I might of course have overlooked something. Some of the puzzles can eliminate candidates by a Swordfish or by Colouring, but without reaching the solution. The XY-chains are found and measured by a newly written analyzer, which analyzes the whole bivalue graph.

Code: Select all
 XY-chain (5)
 *-----------*
 |.1.|4.8|.6.|
 |7..|.6.|..1|
 |..3|...|2..|
 |---+---+---|
 |1..|524|..7|
 |.7.|6.1|.4.|
 |8..|397|..2|
 |---+---+---|
 |..7|...|1..|
 |4..|.5.|..3|
 |.2.|7.9|.5.|
 *-----------*


004659700000403000900070008410000075207000406560000013300060004000102000001834500
030109020400030009009000700800405001020000080900601007008000100200010003010803060
410000067800607004000020000030060010007502900080090040000040000200105009590000028
005403200000179000900000007780301095050000020190804036800000004000618000007905600
800000009002906300090801060051020930000308000028010740070104090004705600600000007
000000000037106290050090010090503020008060900040907030080030040061204580000000000

Code: Select all
 XY-chain (6)
 *-----------*
 |1..|2.3|..4|
 |..3|.7.|6..|
 |.4.|.1.|.9.|
 |---+---+---|
 |9..|...|..1|
 |.16|...|45.|
 |4..|...|..7|
 |---+---+---|
 |.2.|.5.|.3.|
 |..9|.8.|7..|
 |5..|9.2|..6|
 *-----------*


800762003074103890030000060280000036700000001140000059060000010021605970400391008
004090700000607000507000906010306080300000005020804090906000402000201000001060300
093000650200509003100000007080090060000201000020040010800000006300408005054000820
600809007004000600090602030203090106000307000809060703020906070001000200900205008

Code: Select all
 XY-chain (7)
 *-----------*
 |1..|6.3|..4|
 |.7.|2.8|.9.|
 |...|.4.|...|
 |---+---+---|
 |93.|...|.68|
 |..7|.8.|3..|
 |24.|...|.57|
 |---+---+---|
 |...|.6.|...|
 |.5.|4.2|.1.|
 |8..|9.5|..3|
 *-----------*


Code: Select all
 XY-chain (9)
 *-----------*
 |.8.|2.7|.5.|
 |4..|9.6|..2|
 |...|.5.|...|
 |---+---+---|
 |15.|...|.27|
 |..7|...|9..|
 |32.|...|.86|
 |---+---+---|
 |...|.4.|...|
 |2..|6.9|..8|
 |.9.|5.3|.1.|
 *-----------*


Code: Select all
 XY-chain (10)
 *-----------*
 |52.|.4.|.91|
 |17.|...|.54|
 |..4|...|2..|
 |---+---+---|
 |...|958|...|
 |6..|4.7|..2|
 |...|162|...|
 |---+---+---|
 |..8|...|4..|
 |45.|...|.38|
 |31.|.8.|.69|
 *-----------*


Code: Select all
 XY-chain (10)
 *-----------*
 |..5|...|3..|
 |.8.|.9.|.7.|
 |6..|.2.|..1|
 |---+---+---|
 |...|6.4|...|
 |.31|...|79.|
 |...|9.1|...|
 |---+---+---|
 |5..|.8.|..2|
 |.9.|.6.|.5.|
 |..3|...|6..|
 *-----------*
Last edited by Ocean on Thu Apr 13, 2006 8:00 am, edited 1 time in total.
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Postby ravel » Thu Apr 13, 2006 9:36 am

Nice thread again:)
IMHO unique rectangles of type 1, 2, and 4 should not be counted to the advanced techniques, e.g Oceans #1 is very easy. Compared to hidden triples they are eye-catching. (No one would solve Ruuds last superior puzzle with the hidden triple instead of the UR)
On the other hand multiple coloring often is very hard to spot, so i would prefer that all but 2 (maybe 3) strong links is advanced.
Also very easy to spot is the BUG+1 pattern (only 1 cell with 3 candidates).
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Postby RW » Thu Apr 13, 2006 4:36 pm

Ocean wrote:I also find that the puzzle listed as #1 under XY-chains (length 4) has an alternative (simpler?) solution strategy, as it almost falls in the "bivalue universal grave" (BUG).


At least I missed it, so it can't be that simple...:)

ravel wrote:IMHO unique rectangles of type 1, 2, and 4 should not be counted to the advanced techniques


I completely agree that they aren't "advanced" in the meaning of difficult, but they don't hurt anybody either, so I'll let them stay for now. However, I wouldn't let a puzzle that can be solved with an uniqueness rectangle on the list under any other technique. I plan to post some puzzles in the near future that require bigger uniqueness patterns that will probably be more challenging.

I'm sorry Ocean that I don't have the possibility to check your puzzles right now, I'll have to get back to them after easter holidays, but I will move them to the list as soon as possible.

Regards
RW
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Postby tarek » Thu Apr 13, 2006 9:22 pm

I'm not sure if you're after symmetry but here are 2 puzzles...

The first is not mine.....
Code: Select all
 . . 9 | . . . | 4 . . 
 . . . | . 7 . | . . . 
 7 . 4 | . . 2 | 6 . 1 
-------+-------+------
 . . 5 | 7 . 1 | . . . 
 . 8 . | 4 6 . | . 2 . 
 . . . | 5 . 8 | 3 . . 
-------+-------+------
 4 . 7 | 6 . . | 2 . 9 
 . . . | . 3 . | . . . 
 . . 6 | . . . | 1 . . 

*-----------------------------------------------*
| 8    12   9   | 13   5    6   | 4    37   237 |
|*12   6    3   | 19   7    4   | 8    59  ^25  |
| 7    5    4   | 39   8    2   | 6    39   1   |
|---------------+---------------+---------------|
| 3    4    5   | 7    2    1   | 9    6    8   |
| 9    8    1   | 4    6    3   |-57   2   ^57  |
| 6    7    2   | 5    9    8   | 3    1    4   |
|---------------+---------------+---------------|
| 4    3    7   | 6    1    5   | 2    8    9   |
|%15   19   8   | 2    3    79  |%57   4    6   |
| 25   29   6   | 8    4    79  | 1    357 -357 |
*-----------------------------------------------*
Eliminating 7 from r5c7(ALS-XY  A=12 in r2c1   B=257 in r5c9,r2c9   C=157 in r8c7,r8c1   x=2 y=1 z=7)
Eliminating 7 from r9c9(ALS-XY  A=12 in r2c1   B=257 in r5c9,r2c9   C=157 in r8c7,r8c1   x=2 y=1 z=7)


The second is one my own, it is not symmetrical,following a hidden pair...
Code: Select all
 . . . | . . 8 | . . . 
 . . 9 | . . . | . . . 
 5 2 . | . 4 . | 3 . . 
-------+-------+------
 . . 5 | . 6 . | . . 7 
 9 7 6 | 5 . 2 | 1 . . 
 1 . . | . . . | . . 9 
-------+-------+------
 . . 7 | . . 5 | . . . 
 2 . . | . 9 3 | . . 4 
 3 1 . | . . . | 6 . . 

*--------------------------------------------------------*
|-47    46    3    |*127  *257   8    | 9    *257   126  |
|^78   ^68    9    | 1237  2357 ^16   | 4     257   126  |
| 5     2     1    | 79    4     69   | 3     78    68   |
|------------------+------------------+------------------|
| 48    348   5    | 19    6     19   | 28    238   7    |
| 9     7     6    | 5     38    2    | 1     4     38   |
| 1     38    2    | 378   378   4    | 5     6     9    |
|------------------+------------------+------------------|
| 6     9     7    | 4     1     5    | 28    238   238  |
| 2     5     8    | 6     9     3    | 7     1     4    |
| 3     1     4    | 28    28    7    | 6     9     5    |
*--------------------------------------------------------*
Eliminating 7 from r1c1(ALS-XZ A=1257 in r1c5, r1c8, r1c4 B=1678 in r2c1, r2c2, r2c6  x=1 z=7)


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Postby ronk » Fri Apr 14, 2006 10:21 am

tarek wrote:Eliminating 7 from r5c7(ALS-XY A=12 in r2c1 B=257 in r5c9,r2c9 C=157 in r8c7,r8c1 x=2 y=1 z=7)
Eliminating 7 from r9c9(ALS-XY A=12 in r2c1 B=257 in r5c9,r2c9 C=157 in r8c7,r8c1 x=2 y=1 z=7)[/code]

Using the BUG principle ...
Code: Select all
 8   12  9   | 13  5   6   | 4   37   27+3
 12  6   3   | 19  7   4   | 8   59  -25
 7   5   4   | 39  8   2   | 6   39   1
-------------+-------------+--------------
 3   4   5   | 7   2   1   | 9   6    8
 9   8   1   | 4   6   3   | 57  2    57
 6   7   2   | 5   9   8   | 3   1    4
-------------+-------------+--------------
 4   3   7   | 6   1   5   | 2   8    9
 15  19  8   | 2   3   79  | 57  4    6
 25  29  6   | 8   4   79  | 1   57+3 37+5

 One or more of r1c9=3, r9c8=3, and r9c9=5 must be true.
 r1c9=3 -> r3c8=9 -> r2c8=5 -> r2c9<>5
 r9c8=3 -> r3c8=9 -> r2c8=5 -> r2c9<>5
 r9c9=5 -> r2c9<>5

 Therefore r2c9<>5, which solves the puzzle.
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Postby Ocean » Fri Apr 14, 2006 1:03 pm

tarek wrote:The first is not mine.....
Code: Select all
 . . 9 | . . . | 4 . . 
 . . . | . 7 . | . . . 
 7 . 4 | . . 2 | 6 . 1 
-------+-------+------
 . . 5 | 7 . 1 | . . . 
 . 8 . | 4 6 . | . 2 . 
 . . . | 5 . 8 | 3 . . 
-------+-------+------
 4 . 7 | 6 . . | 2 . 9 
 . . . | . 3 . | . . . 
 . . 6 | . . . | 1 . . 

*-----------------------------------------------*
| 8    12   9   | 13   5    6   | 4    37   237 |
|*12   6    3   | 19   7    4   | 8    59  ^25  |
| 7    5    4   | 39   8    2   | 6    39   1   |
|---------------+---------------+---------------|
| 3    4    5   | 7    2    1   | 9    6    8   |
| 9    8    1   | 4    6    3   |-57   2   ^57  |
| 6    7    2   | 5    9    8   | 3    1    4   |
|---------------+---------------+---------------|
| 4    3    7   | 6    1    5   | 2    8    9   |
|%15   19   8   | 2    3    79  |%57   4    6   |
| 25   29   6   | 8    4    79  | 1    357 -357 |
*-----------------------------------------------*
Eliminating 7 from r5c7(ALS-XY  A=12 in r2c1   B=257 in r5c9,r2c9   C=157 in r8c7,r8c1   x=2 y=1 z=7)
Eliminating 7 from r9c9(ALS-XY  A=12 in r2c1   B=257 in r5c9,r2c9   C=157 in r8c7,r8c1   x=2 y=1 z=7)


As alternative method, this one has also a short xy-chain (lenght 4, from r9c1 via r2c1/r2c4 to r2c8), which eliminates the '5' from r9c8. The rest is solved with single reductions only.
Last edited by Ocean on Mon Apr 17, 2006 1:51 am, edited 1 time in total.
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Postby Ruud » Fri Apr 14, 2006 1:23 pm

I will wait and see how this discussion develops, before I add it to my Benchmark list...

Ruud.
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Postby ronk » Fri Apr 14, 2006 2:52 pm

Ocean wrote:This one has an even shorter xy-chain (lenght 4, from r9c1 via r2c1/r2c4 to r2c8), which eliminates the '5' from r9c8.

I've learned to count the "discontinuity" as well, so your chain is length 5 to me, and it's length 5 whether counting cells or links.

It appears for "length" that you are counting only the bi-valued cells. Is that correct?
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Postby Ocean » Fri Apr 14, 2006 4:46 pm

ronk wrote:
Ocean wrote:This one has an even shorter xy-chain (lenght 4, from r9c1 via r2c1/r2c4 to r2c8), which eliminates the '5' from r9c8.

I've learned to count the "discontinuity" as well, so your chain is length 5 to me, and it's length 5 whether counting cells or links.

It appears for "length" that you are counting only the bi-valued cells. Is that correct?


True. I counted only the relevant part of the bivalue graph. The argument is: On that chain-stub, by simple logic, there has to be a '5' in at least one of the ends. Therefore all cells that 'see' both ends can eliminate candidate '5'.

Of course, if you also count 'discontinuities' (forming cycles), the length increases by 1, so length is a matter of definition (...maybe I should change my way of counting, or be more specific when reporting 'length'....).
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