Nurikabe Sudoku


Rules:

This is a new Sudoku variation.   In addition to solving the Sudoku, one must determine how to place islands and "water" based on specially marked clues indicating island size.  The set of all numbers not in islands, the "water", should be orthogonally contiguous and there should be no 2x2 block of "water".  So, the island/water layout must be a valid Nurikabe solution as well.

Clues that are in bold and have a border around them double as Nurikabe clues and indicate that they are part of a island/polyomino of that size.  In these puzzles below, there are no invisible islands and each of these clues refer to a distinct island.

A special rule unique to this hybrid is that an island of size n must contain one block each of each number from 1 to n.  So, an island marked with a 3 clue contains two other pieces, marked 1 and 2 in some order.

The goal of the puzzle is to both solve the Sudoku grid in such that a way that one can solve the Nurikabe constraints as well.  Note: You may have to consider the placement of and values possible within the island(s) in order to resolve some Sudoku ambiguity.

Please PM if you think the explanation is unclear (especially after the walk-through).  I hope you enjoy these.  It was a fun challenge  to create them.

Sample Puzzle (4x4, Easy) and Walk-Through:


sample puzzle

Step 1 (Nurikabe)
: R3C2, the square at Row 3, Column 2, is an island of size 1.  Gray out R3C1, R3C3, R2C2 and R4C2.
 sample puzzle-step 2    

Step 2 (Nurikabe) : R2C4 must not be part of an island (specifically the island with the 3 clue at R3C4) otherwise R1C4 would be cutoff.  Gray it out.

sample puzzle-step 2

Step 3 (Nurikabe
) : The island containing a 3 at R3C4 can only grow downward, so it must include the 2 at R4C4.   
Step 4 (Nurikabe)
: The same island can only extend to the left to include R4C3. Note: This "3" island now contains numbers 1, 2 and 3.   
sample puzzle-step 1

Step 5 (Nurikabe)
: The "water" at R4C2 is trapped unless R4C1 is water as well. Gray it out.   
Step 6 (Sudoku
) : R4C2 must be a 3, R3C3 must be a 4 and so R3C1 must be a 2.   
Step 7 (Sudoku
) : R1C1 must be a 1 and so R2C1 must be a 3.

sample puzzle-step 1

Step 8 (Nurikabe
) : R2C1 and R2C3 must both be "water" otherwise, they will each cutoff a different region of water.   
Step 9 (Sudoku) : R1C4 must be a 4 and so R1C2 must be a 2.
  
sample puzzle-step 1

Step 10 (Nurikabe Sudoku)
: The 4 at R1C4 can't be a part of the island containing the 3 at R1C3 because 4 > 3.  Because it's orthogonal to that island, gray it out.  Now the Nurikabe portion is complete.
Step 11 (Sudoku) :  R2C2 must be 4.  R2C3 must be 2.  R2C4 must be 1.  Now we have our solution.  

sample puzzle-step 1

Note: For puzzles larger than this, my strategy generally would be try to do as much Sudoku solving as possible.  Once you have reached some sort of impasse, you could try determining where the islands are.  That said, if you see a case where there it could be only one way to extend an island with legal values, use that information.   

Don't forget that the two sides of the puzzle may rely on each other to determine a unique solution.
  
One other consideration: If it's not feasible to gray out the whole square with light pencil, try graying out a corner instead so you know it can't be part of an island.    

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On to the puzzles:
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Puzzle 1: (6x6, Easy to Medium) (Answer)

puzzle 1

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Puzzle 2: (8x8, Medium) (Answer

puzzle 2

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Puzzle 3: (9x9, Medium to Hard) (Answer)

puzzle 3

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Challenge

One more thing: I have a challenge for any puzzle writers out there.  Can anyone create a valid version of this puzzle with size 12x12 (broken up in 3x4 subgrids)?  Just the filled-in solution (grid of numbers and outlines of islands) would suffice.  Making a puzzle for someone else to solve would be an extra, simpler step.

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