Battleship Heyawake

As it sounds, this combination of the old favorite Battleships with the  more recent Nikoli puzzle Heyawake.  This idea was inspired by Thomas Snyder's great book:  Battleship Sudoku.

The solution must be a valid Heyawake solution while placing each of the ships specified so they do not touch each other, even diagonally. 

Unlike regular Battleship puzzles, in this variation, the ships are placed diagonally rather than vertically or horizontally.

Like Battleship, there are numeric clues outside the grid.  Because the ships are placed diagonally, the clues refer to the number of segments in the diagonals (which wraparound toroidially).  The arrows below indicate the two sets of diagonals for the same small sample (along with the segment counts outside the grid for each diagonal):
 
jut out

One more thing: due to the primitive tools at my disposal, you'll notice none of the "ships" have a head or tail.  So, none of the puzzles have ship segments placed in them as clues.


Sample Puzzle (6x6, Easy)                                                     and the answer:

sample puzzle                 sample answer

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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  (9x9, Easy to Medium):   (Answer)

 
puzzle 2

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Puzzle 3  (10x10, Medium):   (Answer)

 
puzzle 3

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