marek stefanik wrote: what kind of magic would one have to use to prove this contradiction
- Code: Select all
123 . . | . . 123
. 123 . | . 123 .
. . 123 | 123 . .
––––––––––––––+––––––––––––––
. . 123 | 123 . .
. 123 . | . . 123
123 . . | . 123 .
|--------------------+------------------+
| 1 . . | . . 23 |
| . 2 . | . 13 . |
| . . 3 | 12 . . |
|---------------------------------------+
| . . 12 | a12+3 . . |
| . 13 . | . . b12-3 |
| 23 . . | . c12-3 . |
|--------------------+------------------+
|--------------------+-----------------+
| 1 . . | . . 23 |
| . 2 . | . 13 . |
| . . 3 | 12 . . |
|---------------------+----------------+
| . . 12 | 3 . . |
| . 13 . | . . b12 |
| 23 . . | . c12 . |
|--------------------+-----------------+
1..3......2..1......3..2...3.........1.........2.................................
1..3......2..1......3..2...2.........3.........1.................................
+---+---+---+ +---+---+---+
|1..|3..|...| |1..|3..|...|
|.2.|.1.|...| |.2.|.1.|...|
|..3|..2|...| |..3|..2|...|
+---+---+---+ +---+---+---+
|3..|...|...| |2..|...|...|
|.1.|...|...| |.3.|...|...|
|..2|...|...| |..1|...|...|
+---+---+---+ +---+---+---+
|...|...|...| |...|...|...|
|...|...|...| |...|...|...|
|...|...|...| |...|...|...|
+---+---+---+ +---+---+---+
1..3......2..1......3..2...3..1......1..2......2..3..............................
1..3......2..1......3..2...3..2......1..3......2..1..............................
1..3......2..1......3..2...3...2.....1...3.....21................................
1..3......2..1......3..2...3....1....1.2.......2.3...............................
1..3......2..1......3..2...2..1......3..2......1..3..............................
1..3......2..1......3..2...2....1....3.2.......1.3...............................
1..3......2..1......3..2...2....3....3.1.......1.2...............................
1..3......2..1......3..2...3..1......1..2......2..3..............................
1..3......2..1......3..2...3..2......1..3......2..1..............................
1..3......2..1......3..2...3...2.....1...3.....21................................
+---+---+---+ +---+---+---+ +---+---+---+
|1..|3..|...| |1..|3..|...| |1..|3..|...|
|.2.|.1.|...| |.2.|.1.|...| |.2.|.1.|...|
|..3|..2|...| |..3|..2|...| |..3|..2|...|
+---+---+---+ +---+---+---+ +---+---+---+
|3..|1..|...| |3..|2..|...| |3..|.2.|...|
|.1.|.2.|...| |.1.|.3.|...| |.1.|..3|...|
|..2|..3|...| |..2|..1|...| |..2|1..|...|
+---+---+---+ +---+---+---+ +---+---+---+
|...|...|...| |...|...|...| |...|...|...|
|...|...|...| |...|...|...| |...|...|...|
|...|...|...| |...|...|...| |...|...|...|
+---+---+---+ +---+---+---+ +---+---+---+
And hence this 6-template is fruitlessly invalid
+---+---+---+
|.45|.87|6.9|
|6.7|4.9|8.5|
|98.|56.|.74|
+---+---+---+
|.58|67.|94.|
|4.9|8.5|.67|
|76.|.94|.58|
+---+---+---+
|.76|95.|48.|
|5.4|..8|796|
|89.|746|5..|
+---+---+---+
+-------------------------------+-------------------------------+-------------------------------+
| 1 456789 456789 | 3 456789 456789 | 2456789 2456789 2456789 |
| 456789 2 456789 | 456789 1 456789 | 3456789 3456789 3456789 |
| 456789 456789 3 | 456789 456789 2 | 1456789 1456789 1456789 |
+-------------------------------+-------------------------------+-------------------------------+
| 3 456789 456789 | 456789 456789 456789 | 12456789 12456789 12456789 |
| 456789 1 456789 | 456789 2 3456789 | 3456789 3456789 3456789 |
| 456789 456789 2 | 1 3456789 3456789 | 3456789 3456789 3456789 |
+-------------------------------+-------------------------------+-------------------------------+
| 2456789 3456789 1456789 | 2456789 3456789 13456789 | 123456789 123456789 123456789 |
| 2456789 3456789 1456789 | 2456789 3456789 13456789 | 123456789 123456789 123456789 |
| 2456789 3456789 1456789 | 2456789 3456789 13456789 | 123456789 123456789 123456789 |
+-------------------------------+-------------------------------+-------------------------------+
The point is, that this pattern can be spotted quite easily manually.coloin wrote:So quite possibly there could be a new solving technique - based on invalid templates - but some already have employed valid templates as a technique
marek stefanik wrote:What I meant was that if you generate a puzzle from a known hard puzzle with JE, it will most likely contain a JE itself. Sometimes it can mutate into a Senior Exocet, SK loop or the half JE + SK loop (or even something new), but there will be some similarities.
This pattern seems completely different, so I'd be surprised if it came from a JE seed two clues at a time. If there are any families of difficult puzzles that do not have a known exotic pattern, it could be possible to discover some new ones.
Thanks for the insights into the creation process, especially the Expander sounds very cool.
see page 54 for fruit (any puzzle with 30+ clues except for the first one which has three guardians and no direct elimination).coloin wrote:
- Code: Select all
And hence this 6-template is fruitlessly invalid
+---+---+---+
|.45|.87|6.9|
|6.7|4.9|8.5|
|98.|56.|.74|
+---+---+---+
|.58|67.|94.|
|4.9|8.5|.67|
|76.|.94|.58|
+---+---+---+
|.76|95.|48.|
|5.4|..8|796|
|89.|746|5..|
+---+---+---+
eleven wrote:The point is, that this pattern can be spotted quite easily manually.coloin wrote:So quite possibly there could be a new solving technique - based on invalid templates - but some already have employed valid templates as a technique
....12.34
.134..2..
.423..1..
.21.34...
3..1...42
4..2...13
.34....21
1...234..
2...413..
....11.11
.111..1..
.111..1..
.11....11
1...111..
1...111..
.11.11...
1..1...11
1..1...11
+---+---+---+
|X..|X..|...|
|.X.|.X.|...|
|..X|..X|...|
+---+---+---+
|X..|...|...|
|.X.|...|...|
|..X|...|...|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
+---+---+---+ +---+---+---+ +---+---+---+
|1..|3..|...| |1..|3..|...| |1..|3..|...|
|.2.|.1.|...| |.2.|.1.|...| |.2.|.1.|...|
|..3|..2|...| |..3|..2|...| |..3|..2|...|
+---+---+---+ +---+---+---+ +---+---+---+
|3..|1..|...| |3..|.2.|...| |3..|..1|...|
|.1.|.2.|...| |.1.|..3|...| |.1.|2..|...|
|..2|..3|...| |..2|1..|...| |..2|.3.|...|
+---+---+---+ +---+---+---+ +---+---+---+
|...|...|...| |...|...|...| |...|...|...|
|...|...|...| |...|...|...| |...|...|...|
|...|...|...| |...|...|...| |...|...|...|
+---+---+---+ valid +---+---+---+ valid +---+---+---+ valid
+---+---+---+ +---+---+---+ +---+---+---+
|1..|3..|...| |1..|2..|...| |1..|2..|...|
|.2.|.1.|...| |.2.|.3.|...| |.2.|.3.|...|
|..3|..2|...| |..3|..1|...| |..3|..1|...|
+---+---+---+ +---+---+---+ +---+---+---+
|3..|1..|...| |2..|.1.|...| |2..|..3|...|
|.1.|..3|...| |.3.|X..|...| |.3.|.1.|...|
|..2|.X.|...| |..1|..2|...| |..1|X..|...|
+---+---+---+ +---+---+---+ +---+---+---+
|...|...|...| |...|...|...| |...|...|...|
|...|...|...| |...|...|...| |...|...|...|
|...|...|...| |...|...|...| |...|...|...|
+---+---+---+ invalid +---+---+---+ invalid +---+---+---+ invalid
+---+---+---+ +---+---+---+ +---+---+---+
|1..|3..|2..| |1..|3..|..2| |1..|2..|3..|
|.2.|.1.|.3.| |.2.|.1.|3..| |.2.|..3|.1.|
|..3|..2|..1| |..3|..2|.1.| |..3|.1.|..2|
+---+---+---+ +---+---+---+ +---+---+---
|3..|2..|1..| |3..|2..|1..| |3..|..1|2..|
|.1.|.3.|.2.| |.1.|.3.|.2.| |.1.|.2.|.3.|
|..2|..1|..3| |..2|..1|..3| |..2|3..|..1|
+---+---+---+ +---+---+---+ +---+---+---+
|2..|1..|3..| |.3.|1..|2..| |2..|.3.|1..|
|.3.|.2.|.1.| |..1|.2.|.3.| |.3.|1..|.2.|
|..1|..3|..2| |2..|..3|..1| |..1|..2|..3|
+---+---+---+ +---+---+---+ +---+---+---+
dobrichev wrote:Maybe close to this subject is this known invalid pattern from here.
- Code: Select all
....12.34
.134..2..
.423..1..
.21.34...
3..1...42
4..2...13
.34....21
1...234..
2...413..
+---------+---------+---------+
| XY . . | . 1 2 | . 3 4 |
| . 1 3 | 4 . . | 2 . . |
| . 4 2 | 3 . . | 1 . . |
+---------+---------+---------+
| . 2 1 | X 3 4 | . . . |
| 3 . . | 1 . . | . 4 2 |
| 4 . . | 2 . . | . 1 3 |
+---------+---------+---------+
| . 3 4 | . . . | Y 2 1 |
| 1 . . | . 2 3 | 4 . . |
| 2 . . | . 4 1 | 3 . . |
+---------+---------+---------+
+---------+---------+---------+
| * * * | * 1 2 | * 3 4 |
| * 1 3 | 4 . . | 2 . . |
| * 4 2 | 3 . . | 1 . . |
+---------+---------+---------+
| * 2 1 | * 3 4 | * * * |
| 3 . . | 1 . . | * 4 2 |
| 4 . . | 2 . . | * 1 3 |
+---------+---------+---------+
| * 3 4 | * * * | * 2 1 |
| 1 . . | * 2 3 | 4 . . |
| 2 . . | * 4 1 | 3 . . |
+---------+---------+---------+
+---------+---------+---------+
| X . . | X . . | . . . |
| . X . | . X . | . . . |
| . . X | . . X | . . . |
+---------+---------+---------+
| X . . | . . . | X . . |
| . X . | . . . | . X . |
| . . X | . . . | . . X |
+---------+---------+---------+
| . . . | X . . | . . . |
| . . . | . X . | . . . |
| . . . | . . X | . . . |
+---------+---------+---------+
+---------+---------+---------+
| . . . | . 3 4 | . 1 2 |
| . 1 3 | 2 . . | 4 . . |
| . 4 2 | 1 . . | 3 . . |
+---------+---------+---------+
| . 2 1 | . . . | . 3 4 |
| 3 . . | . 4 2 | 1 . . |
| 4 . . | . 1 3 | 2 . . |
+---------+---------+---------+
| . 3 4 | . 2 1 | . . . |
| 1 . . | 4 . . | . 2 3 |
| 2 . . | 3 . . | . 4 1 |
+---------+---------+---------+