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PostPosted: Thu Dec 01, 2016 10:56 pm 
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Here's another take on an idea I came up with 9 years ago on the djape forums, a killer puzzle where cages are given as Nurikabe clues. Since there is very little cage coverage, the grid has to be very tightly constrained. The puzzle I made then consisted of a pair of grids that had the same solution.

This puzzle is made up of four overlapping 9x9 sudoku grids arranged in a butterfly pattern (1 in each corner), each with it's own set of main diagonals. The sum/size of all cages are given, but not their shapes. The shapes of cages must form islands in a valid Nurikabe solution. Givens are shaded, and thus cannot be part of a cage.

Here's the puzzle:

Hidden Text:
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PostPosted: Fri Dec 02, 2016 2:22 am 
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Not sure whether I'll try this puzzle. But one question anyway. Are the cages constrained to be completely within one of the four Sudoku grids? My guess is that they are.


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PostPosted: Fri Dec 02, 2016 3:24 am 
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There is no constraint about cages being completely within 1 of the four grids.

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PostPosted: Thu Dec 15, 2016 4:11 am 
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Whew. One of the hardest puzzles I've ever managed to complete. Took me days! First Nurikabe puzzle for me so maybe it would have been easier if I knew the techniques for them.

I'm not even going to attempt a WT. But here is my solution. White cells are the walls. Thanks h3lix! Happy Holidays to all.

Solution:
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PostPosted: Tue Mar 28, 2017 1:08 pm 
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wellbeback

How did you get started?

I've looked at the puzzle and your solution and other than r1c1 being {3/5/7/9} I cannot see how to start.

Maurice


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PostPosted: Thu Mar 30, 2017 5:18 pm 
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Hi Maurice

In the following I identify nonets by row and column. e.g., n13 contains 8 in cell 1.
I identify cells in a nonet with a capital 'C'.
e.g., We are given n13C1 = 8

Note that the cells that are given values in the puzzle are wall cells.

General rules.

1. For an edge nonet the cell values must match in the same row or column in the opposite edge nonet.
e.g.:
E.g., 8 in n13C1 -> 8 in n43 in the same column.
Given 8 in n42C9 and n43C4 is in a 9/3 cage -> n43C1 = 8.

2. Every cell is either a wall cell or a cage cell. Cages cannot be orthogonally adjacent.
-> Where known cells from different cages are separated by a single cell - that cell must be a wall cell.
E.g., n12C6 and n12C8 must be wall cells.

Similarly where known different cage cells are diagonally adjacent - the cells adjacent to both those cage cells must be wall cells.
E.g., n23C6, n24C7, and n33C3 must be wall cells.

3. All wall cells in the whole puzzle form a continuous chain.
-> E.g., n24C8 must be a wall cell.

4. Remember that there cannot be any block of wall cells larger than 2x2.
More:
In fact there are no wall blocks even of 2x2 in the solution, but I didn't assume that.

How I started...

Starting...:
I tried to identify which are wall cells and which are cage cells. Identifying cage cells often identifies wall cells and vice versa. I started on the largest and smallest cages.

E.g., 17/2 cage in n12.
Since n12C6 and n12C8 must be wall cells, implies the cage is n12C9 and either n13C7 or n22C3.
Either way -> n23C1 must be a wall cell.
Since neither n13C7 or n22C3 can be an 8 -> n12C9 = 8 and one of n13C7 and n22C3 = 9.
Using the diagonals, many of the 8s in the puzzle may be placed.

Another e.g., 10/4 n23 must be {1234} and it cannot include the given 2 in n23.
-> Must use the 2 in a different nonet.
Since n24C7 and n33C3 must be wall cells -> cage must be n23C789 (= {134}) + one of n22C9 or n33C1 (= 2)
-> n23C456 and n32C3 must be wall cells

Another e.g., 6/2 in n34 must be cells 1,2 or cells 1,4 in n34.
-> n34C5 is a wall cell.

Another technique I used...

42/8 in n44 can only use at most cells 6,8,9 in n43, and cells 6,8,9 in n34.
-> cannot use 8 in either n34 or n43
-> must use 8 in n44.
Since 42/8 cannot use cells 1, 2, 4 in n44, and 8 can only be in cells 1, 2, 4, or 5 in n44
-> n44C5 = 8 and the 42/8 cage must use it.
-> n44C24 are wall cells.

Trying to work out where the cage cells for the 42/8 and the 35/5 must go while still leaving connected wall cells leaves very restricted choices for where those cages can go.

Final technique,
Since cells 1,3,4,5,6 in n23 are all wall cells, n23C2 must be a cage cell.
Only cage that can reach it is 45/9 cage from n24 going through n14 and n13.
-> n13C8 must be a cage cell.
-> 17/2 cage must be n12C9 and n22C3 = [89]


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PostPosted: Mon Apr 03, 2017 11:26 am 
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Thanks wellbeback I'll go through it at the weekend


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