Sudoku Islands

Sudoku Islands takes regular 9 x 9 and adds in the Island twist.

Just like in a regular Sudoku puzzle, the digits 1 - 9 each appear exactly once in each row, column and 3 x 3 box. On top of each puzzle grid you’ll also see four “Islands” floating. Each Island also has 1 - 9 appearing uniquely in each of its nine grey squares.

1
A
8
6
2
4
B
C
9
7
8
5
6
3
2
1
9
5
D
2
4
6
5
2
3
5
2
7
7
1
6
2
8
3
2
5
9
4
Let's look at the gray island which overlaps the upper right hand corner. We've put the letters "A" - "D" in four of the spaces for illustration.
The island contains 1, 2, 5, 6 and 9 so it's missing 3, 4, 7 and 8.
To figure out where "3" goes, notice that neither "A" nor "C" can have a "3" since there's already one in that 3x3 box. It also can't go into "D" since there's already a "3" in that column, so it must go into space "B".
Likewise "4" can't go into space "D" since there's a "4" already in that 3x3 box and it can't go into space "C" because of the "4" in that row, so it must go into "A".
We can't put an "8" into "C" because of the "8" in that 3x3 box so "8" must go into "D".
The only place left to put a "7" is space "C".
1
4
8
6
2
4
3
7
9
7
8
5
6
3
2
1
9
5
8
2
4
6
5
2
3
5
2
7
7
1
6
2
8
3
2
5
9
4

Solving Hints
One simple rule to help solve Sudoku Islands is the "inside-out" rule.
Notice that any island which overlaps a box has exactly the same number of gray squares outside the box as there are white squares inside the box. The numbers that appear in the white squares are the same number that appear in the gray squares - in some order.
Going back to our sample above, notice the "5" that appears in the Island that intersects the upper right hand box. Without having done anything else, you know that you can fill in the white square on the right hand side of the box in the middle column in with a "5". In a regular Sudoku, the "5" could also appear in space "A", but since that would make there be two "5"s in the Island, you know that's not the case.
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