SudoCue Users

OK, here's a new (?) idea for the weekend: the combination of windoku and killer. I thought about posting it in the Maverick series but in my opinion it doesn't fit in there because it can't be finished without the additional constraints. Maverick should be reserved for "normal" killers.

About the puzzle:

The usual killer rules apply. But there are also 9 additional windows (45-cages) from windoku:
1. r159c159
2. r159c234
3. r159c678
4. r234c159
5. r678c159
6. r234c234
7. r234c678
8. r678c234
9. r678c678
These "windows" are 45-cages, so repetition of numbers is not allowed!

Visual aid with the corresponding numbers: OK, here's the puzzle:

3x3::k2560384228204103:41034618:4618:4618:4365:4365:4367:4367:4103:4370:4370:4370:4373:4365:4365:4365:4367:5402:4891:4373:4373:4373:4373:7968:7968:5402:5402:48912341:7968:7968:7968:4906:4906:4906:4891:5166:6447:6447:6447:6447:4915:4915:4906:4891:5166:5166:4409:6447:4411:4915:4915:5950:4159:4159:4409:4409:8003:4411:4411:5950:5950:4159:4159:8003:8003:8003:8003:8003:5950:5950:

Here's a picture where I tried to colour the additional windows. I hope you like it.

If you work with two solvers here's the layout code for the windoku part (without a picture):
3x3::k11521115211152511525115291153011529115341152911530115301153411534115291153011529115341152911521115211152511525115651156611565115701156511566115661157011570115651156611565115701156511521115211152511525

Rating: I really don't know. Can't be scored by SudokoSolver (puzzle not completed). I would estimate it as a hard 1.25, maybe a 1.5. Oh, one more thing one or the other might frown upon: you will need uniqueness to place the last numbers.

Have fun!

Cheers,
Nasenbaer

EDIT: Explanation added (in blue)

This was an interesting Killer variant, thanks Nasenbaer!

I had a bit of trouble adopting to the Windoku rules, so I had to start over again twice because of stupid mistakes. In my wt, I use the same numbers for the Windows (Win) as Nasenbaer suggested and noted if a placement effects other cells in the window.

I'm not a fan of uniqueness moves and this puzzle confirmed my opinion. I would accept them if otherwise there would be no solution but in this case without the UR there would be multiple solutions which are valid so I think they are also part of the final solution.

Windoku-Killer 1 Walkthrough:

1. R123
a) 9 locked in Outies N1 = 15(2) = {69} locked for C4+N2
b) 15(2) = {69} locked for R1 + Win2
c) Innies = 14(2) = [59] -> R3C4 = 5 (Win6), R3C9 = 9 (Win4)
d) 9 locked in 18(3) @ R2 -> 18(3) = 9{18/27/36} <> 4
e) 17(5) @ R3C4 = {12356} -> {1236} locked for R4
f) 4 locked in 17(3) @ N2 for Win6 -> 17(3) = {467} locked for R3+N1; R3C1 <> 4
g) R1C3 = 9, R1C4 = 6, R2C4 = 9
h) 18(3) = {189} -> {18} locked for R2+N1 + Win 6
i) Hidden Single: R3C8 = 8 @ R3 (Win 7)
j) 17(5) @ R2C5 = {12347} -> R2C56 = {47} locked for R2+N2

2. R123
a) 17(3) @ N3 = {368} -> {36} locked for R2+N3 + Win7
b) Outies R1 = 7(2) = {25} locked for Win4
b) 16(3) = {457} -> R2C9 = 5, {47} locked for N3
c) Hidden Single: R3C5 = 3 @ R3, R4C5 = 1 @ R4
d) Naked pair (12) locked in R13C7 for C7
e) 17(5) @ R3C4 = {12356} -> 6 locked for N4+Win6
f) Hidden Single: R3C1 = 6 @ N1, R2C1 = 2

3. C123
a) 19(4) = 1{378/459} because R1C1 = (35) blocks {3457} -> 1 locked for C1
b) Killer pair (35) locked in R1C1 + 19(4) for C1
c) Hidden Killer pair (89) locked in 16(4) for C1
-> 16(4) = 1{249/258/348} <> 6,7
-> 1 locked in 16(4) for C2+N7
d) 16(4) = 14{29/38} because R89C1 = (489) -> 4 locked C1+N7; R89C2 <> 4,8,9
e) 19(4) = {1378} locked for C1; 1 locked for N4
f) R1C1 = 5 (Win1), R1C2 = 3 (Win2), R2C2 = 8, R2C3 = 1
g) 16(4) = {1249} -> 2 locked for C2+N7
h) Hidden Single: R6C2 = 9 @ N4, R4C2 = 6
i) 20(3) = {569} because R7C2 = (57) -> R7C2 = 5 (Win8), R7C3 = 6
j) 9(2) = [45/72]

4. N47
a) 17(3) @ N7 = {278} -> 2 locked for C4+N8 + Win8
b) R8C2 = 1, R9C2 = 2 (Win2), R5C3 = 5 -> R5C2 = 4 (Win2), R3C2 = 7, R3C3 = 4
c) R4C4 = 3, R4C3 = 2
d) Hidden Single: R7C1 = 3 @ N7 (Win5), R6C3 = 3 @ N4, R6C4 = 4 @ C4, R9C4 = 1 @ C4
e) 25(5) = 347{29/56}

5. N5
a) 8 locked in 31(5) for R5 -> 31(5) = {25789} -> 2 locked for R5+N5, 5 locked for R4
b) 25(5) = {34567} -> R7C5 = 7 (Win5), {56} locked for R6+N5
c) R2C5 = 4 (Win4), R2C6 = 7 (Win7), R4C6 = 9, R4C8 = 4
d) R1C8 = 7 (Win3), R1C9 = 4 (Win1), R4C9 = 8, R4C1 = 7, R4C7 = 5
e) R5C1 = 1, R6C1 = 8 (Win5), R6C7 = 7, R9C1 = 9, R8C1 = 4

6. The Rest !
a) R8C5 = 9 @ N8, R9C9 = 7 @ C9, R9C3 = 8 (Win 2), R8C3 = 7, R5C4 = 7
b) R9C5 = 6 (Win 1), R5C9 = 3, R6C5 = 5, R6C6 = 6 (Win9)
c) 17(3) @ R6C6 = {458} -> R8C7 = 8, R7C6 = 4, R8C6 = 5, R9C6 = 3, R9C7 = 4
d) R8C4 = 2, R7C4 = 8, R9C8 = 5, R8C8 = 3, R7C7 = 9, R5C7 = 6, R5C8 = 9
e) R2C7 = 3, R2C8 = 6, R6C9 = 1, R6C8 = 2, R7C8 = 1, R7C9 = 2, R8C9 = 6
f) ! Unique Rectangle (28) on R15C56 -> R1C7 <> 1 (otherwise multiple solutions)
g) R1C7 = 2, R3C7 = 1, R3C6 = 2, R1C5 = 8, R1C6 = 1, R5C5 = 2, R5C6 = 8.

5 3 9 6 8 1 2 7 4
2 8 1 9 4 7 3 6 5
6 7 4 5 3 2 1 8 9
7 6 2 3 1 9 5 4 8
1 4 5 7 2 8 6 9 3
8 9 3 4 5 6 7 2 1
3 5 6 8 7 4 9 1 2
4 1 7 2 9 5 8 3 6
9 2 8 1 6 3 4 5 7

-----But------

Without Uniquess move R1C7 can be 1

Further solutions are:

5 3 9 6 8 2 1 7 4
2 8 1 9 4 7 3 6 5
6 7 4 5 3 1 2 8 9
7 6 2 3 1 9 5 4 8
1 4 5 7 2 8 6 9 3
8 9 3 4 5 6 7 2 1
3 5 6 8 7 4 9 1 2
4 1 7 2 9 5 8 3 6
9 2 8 1 6 3 4 5 7

5 3 9 6 2 8 1 7 4
2 8 1 9 4 7 3 6 5
6 7 4 5 3 1 2 8 9
7 6 2 3 1 9 5 4 8
1 4 5 7 8 2 6 9 3
8 9 3 4 5 6 7 2 1
3 5 6 8 7 4 9 1 2
4 1 7 2 9 5 8 3 6
9 2 8 1 6 3 4 5 7

So all in all there are 3 solutions.

Rating: (Hard) 1.0. The moves itself weren't difficult (apart from the UR) but I haven't solved a Windoku before so I made some false eliminations a couple of times.

Nasenbaer wrote:Oh, one more thing one or the other might frown upon: you will need uniqueness to place the last numbers.

Uniqueness can be used only for grids with a unique solution which is not the case for this grid since it has 3 solutions. i.e. this grid is invalid.

I really liked this puzzle until I got to the last 6 cells. There are 3 solutions as Afmob noted. I don't think that Uniqueness can be used to eliminate 2 of the solutions. I'd like to see another one of this type of puzzle.

OK OK, I get it. Uniqueness is BAD.

I'm no expert in creating killer puzzles, so I want to share with you how this one came into existence.

First there was the idea to create a windoku killer. I picked the last one posted by Ruud and solved it.

Then I started to create the killer, mainly with bigger cages because I thought that the additional constraints would help. I started solving it but didn't get too far.

Back to the drawing board. Now I concentrated on the layout of the cages, with some thoughts about the special windows. Another solving process revealed that it was still too hard, couldn't finish it.

After some tuning on the cages came the third solving process. I got very far until I realized that it didn't have a unique solution.

One more round of tuning gave me the puzzle you found here. I solved it up to the point where the uniqueness was required. I pressed F8 in SudokuSolver and the program suggested the uniqueness move, so I used it. Removing it would have meant that the puzzle would have been a lot easier.

At this point I had spent more than 4 hours on the design-solve-redesign process and had no second thought about the uniqueness. SudokuSolver gave me a move, so why bother, I thought. One mistake I hope I won't make again.

To sum it up: In the future I'll try to avoid uniqueness.

One more thing. Since this is not a regular killer (because of the additional constraints) it should have been posted in the puzzle section (thanks to Afmob who pointed that out to me). Sorry about that. The next one will be posted there (in the next couple minutes).

Cheers,
Nasenbaer