10
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This is a Sashigane puzzle, where you divide the grid into L shapes.

Rules taken from Nikoli:

  • Divide the grid into L shaped blocks - one block wide. All blocks must be L shaped.
  • Cells with open circles form the knee (bend) in a block.
  • The number in an open circle shows the number of cells in its block. Open circles without numbers may have any number of cells.
  • Cells with arrows form one end of its block, the arrow points towards the knee of this block.
  • The number of marks in a block (arrows or open circles) may be 0, 1, 2, or 3.

An example puzzle and its solution, taken from Nikoli:

example puzzle example solution

Now, solve this puzzle:

the real puzzle - see CSV file

Here is the puzzle in a playable form. The link leads to a puzz.link editor (which has a timer, if you care about that).

First answer with a fully-explained logical solution path gets the checkmark.

CSV version:

,,→,,,,
,,,,,,↓
,,←,,○,,
,,,6,,,
↓,,,,○,,
,,,,,,
,,,,,↑,
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9
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Solution

enter image description here

Explanation

Part 1

First notice the arrow in the bottom right hand corner. We cannot go up and right with this because it will leave a column on the right. Also, We cannot go up too far to interfere with either circle or with the arrow pointing down on the right. This means the only option is to develop this way.
enter image description here

Part 2

Now the empty circle just above this beginning must be in a corner which means the cell above it is connected to it and, since there is a circle above that, it cannot be connected to any other adjacent cell. The other empty circle and the circle with a six are also connected to adjacent cells proceeding out from this configuration but have one less restriction in their adjacency. This leads to the following deductions.
enter image description here

Part 3

Cells with arrows form one end of a block and point into knees so they may not extend perpendicularly or backwards. From that, we get the following
enter image description here

Part 4

The cell in the top right hand corner must extend into an L-shape. The only possibility here is to go down at the first opportunity, otherwise it interferes with other shapes in an illegal manner. Similarly, the L-shape coming from the arrow in the first row must also extend downward at the first opportunity. This puts us in the following position
enter image description here

Part 5

In the third column, second row, we find that the 3/4 box can be extended in just one way to prevent an illegal move and, following from this, the 3/4 box in the third row must wrap around this shape (otherwise we enclose a straight line region) as follows
enter image description here

Part 6

The next deduction uses the value "6". Notice that we do not have enough space to extend it up and left to get 6 cells. This means that it must extend down and must include at least two cells down and two cells to the left. In fact, we see immediately that it will also include a third cell to the left and only two down giving the following.
enter image description here

Part 7

From here, the bottom left can only be completed in one way (starting from the arrow, we quickly realise that one down and straight right causes issues and two down and more than one right also leads to problems).
Similarly, starting from the bottom right and moving up through this region, some easy deductions lead us to the following solution.
enter image description here

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