Draw a loop in the grid that goes through every cell. If the path makes a turn inside a cell it has to turn in the direction of the arrow. If a cell is empty, the path must not turn in that cell; if a cell contains a diamond, then the path may turn into any direction in that cell (including not turn at all).


In this example, the loop must enter and leave each corner cell in clockwise direction. Now consider the path going from the top left cell to the cell next to it. Here we have a choice: we could go down or continue to the right. However, going down would never lead to a complete solution, since the path would never be able to reach the right half of the diagram anymore. So, the path must continue to the right, and then obviously go right again.

Exactly the same reasoning applies to the bottom right corner, so also the bottom row must be traversed by a straight path. Now, if we would also make the left or right column straight, the middle four squares cannot be connected anymore, so that is not the case. Instead, the path in the bottom left corner goes up and then to the right, and the path in the top right corner goes down and then to the left. Finally, connecting these straight would result in two separate loops, so they have to bend back.

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