The New Sudoku Players' Forum

[daj95376]

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Please forgive me if I've already posted a message similar to the following.

Consider the following three examples.

Code: Select all

 Unavoidable Set: 4-cell
 +-----------------------------------------------+
 |   .   7   .   |   .   .   .   |   .   8   .   |
 |   .   .   .   |   .   .   .   |   .   .   .   |
 |   .   8   .   |   .   .   .   |   .   7   .   |
 +-----------------------------------------------+


Code: Select all

 Deadly Pattern: 4-cell
 +-----------------------------------------------+
 |   .  78   .   |   .   .   .   |   .  78   .   |
 |   .   .   .   |   .   .   .   |   .   .   .   |
 |   .  78   .   |   .   .   .   |   .  78   .   |
 +-----------------------------------------------+


Code: Select all

 Unique Rectangle: 4-cell DP w/WXYZ where at least one of WXYZ is non-empty
 +-----------------------------------------------+
 |   .  78W  .   |   .   .   .   |   .  78X  .   |
 |   .   .   .   |   .   .   .   |   .   .   .   |
 |   .  78Y  .   |   .   .   .   |   .  78Z  .   |
 +-----------------------------------------------+


So, what are these called?

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 Z may be empty
 +-----------------------------------------------+
 |   .   7   .   |   .   .   .   |   .   8X  .   |
 |   .   .   .   |   .   .   .   |   .   .   .   |
 |   .   8Y  .   |   .   .   .   |   .  78Z  .   |
 +-----------------------------------------------+


Code: Select all

 one of X/Y may be empty
 +-----------------------------------------------+
 |   .   7   .   |   .   .   .   |   .   8X  .   |
 |   .   .   .   |   .   .   .   |   .   .   .   |
 |   .   8Y  .   |   .   .   .   |   .   7   .   |
 +-----------------------------------------------+


Code: Select all

 one of Y/Z may be empty
 +-----------------------------------------------+
 |   .   7   .   |   .   .   .   |   .   8   .   |
 |   .   .   .   |   .   .   .   |   .   .   .   |
 |   .   8Y  .   |   .   .   .   |   .   7Z  .   |
 +-----------------------------------------------+


I call them Unique Rectangles as well because of the non-empty XYZ.

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[JasonLion]

I have seen those called Avoidable Rectangles, which is my personal preference. I have also seen Almost Unavoidable Rectangles, though that is way less common.

[daj95376]

I have seen those called Avoidable Rectangles, which is my personal preference. I have also seen Almost Unavoidable Rectangles, though that is way less common.

Thanks Jason. I never took the time to learn Avoidable Rectangles. I'll study them further.

Please note, one of the patterns above was called a UR Type 1.1 by (I believe) Myth Jellies. ronk and I have used it on various occasions.

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[Leren]

Here are some puzzles which I got from the Hodoku site which are supposed to have Avoidable Rectangle moves in them.

Hidden Text: Show

#0607: Avoidable Rectangle Type 1
...195..2635..........3...88.........5.9..71.1..2....9..468..51......4.......7.2. # x ar1(1) s
..5...........268.7....14.....1.68.....3......87...1.38.12.43...3..6..2.26....... # x ar1(1) s
.86.4....2........1...76.9....4.7...8...9......9683.7....752..8.......457..3..1.. # x ar1(1) s
.6.....7....8456.2...73....83....2.52.6...9..57.2..................78.566...591.3 # x ar1(1) s
.5........6.5.42....8.71...4....36.8.........89.1..7..3...........2.7.1..72.3..9. # x ar1(1) s

#0607: Avoidable Rectangle Type 2
9.....6....1..6.387.6.8...........76..41......5.947.2.2.......5...25........9...1 # ssts ar2(3) s
..2....95.892...6.4...5......18...2.........9.9.621..8..8913...............4..38. # x ar2(2) s
.....78...169...7....1..56.8..........5..3...3...4.2...7...2......859..24...1..3. # x ar2(2) s
..4..8675.2.....3937..5..8.........75...16.9......5.....76........9....324.....1. # x ar2(2) s
1....2.5..2......3..46.8..72..........74..9.6.6..9.........6......1...8...5..32.4 # x ar2(3) ssts
7.1..8...695.......8.9..6.....4.6.........8.....5..26.........9.79..1.....625.1.4 # x ar2(1) ssts
.85....6......47...3....1.........5.6...43....7.82.3.....45967..........9.416...3 # x ar2(7) x
.......31.96...7.25..............8..7.94.........329.......8..5.32.5..1...1..9.87 # x ar2(6) x
......93...27....57.....8.......3....4..9...6..8..1374..5.8719....9......6....... # x ar2(5) x
...185....83.2.5..........726..5.7.3..9....6.73............6.59.4......2..79..... # x ar2(4) x
2...1.....17...5....6754.2....82..5.......6.4....71...6....3......2..79...968.... # x ar2(4) x
3.....7...4....2...79.3.46872...............9.91......1...52......7.138.4.2.6...1 # x ar2(2) x
........1.6.5...9.4..7..8....8.............45.31.64...853.....2..21....6.....3... # x ar2(2) x
32.5.........94..7.......3.....7..4.8431....9..68.......948..5.........4....12.8. # x ar2(2) x
1.9.......4......5...1....3..3.186.....9.7.3.5................8.....435..18.6..72 # x ar2(1) x
......132.6.5.3...8.....6.9..............184....938..12.5..4.....41......1..9...8 # x ar2(1) x

Whether or not the AR move shows up depends a lot on your solving order, so it's often a good idea to run them through Hodoku to see how they get to the AR move. Anyway - enjoy!

Leren

[daj95376]

Here are some puzzles which I got from the Hodoku site which are supposed to have Avoidable Rectangle moves in them.

...

Whether or not the AR move shows up depends a lot on your solving order, so it's often a good idea to run them through Hodoku to see how they get to the AR move. Anyway - enjoy!

Thanks Leren for the sample puzzles !!!

The Avoidable Rectangle Type 1 puzzles produced several UR Type 1.111m results from my solver. The Avoidable Rectangle Type 2 puzzles produced several UR Type 2.11nm results from my solver. In the last group, there were also a couple of UR 3.11nm results from my solver.

I'll update my documentation and do my best to remember the correlation. I'll also update my solver's output.


Note: the numbers after the decimal point are the ascending candidate counts for the four DP cells. A count of "1" means the cell is solved.

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