How to Solve the "Walls" Puzzle

Analysis of the puzzle https://en.grandgames.net/walls/id389670

1. Let's consider the cell with the number 5 in the top left corner (highlighted in red). Two blocks of cells adjoin it, where lines can be drawn (highlighted in blue). However, in order for the number of lines passing through this cell to be equal to 5, three cells from the vertical block must necessarily contain vertical lines (highlighted in green).

2. Reasoning similar to point 1 is applied to 4 cells with numbers (highlighted in red). Blocks of cells that need to be filled with corresponding lines are highlighted in green.

3. Let's consider the cell highlighted in blue. If it contains a vertical line, then the number of lines passing through the cells highlighted in red will not correspond to the numbers in these cells. Therefore, the sought-after cell must contain a horizontal line.

4. Let's consider 4 cells highlighted in red. For all of them, there remains only one option for filling the adjacent cells, which will allow the required number of lines to pass through these cells.

5. After completing step 4, 2 more cells have appeared, for which similar reasoning can be applied.

6. 2 more cells with fully determined neighbors have appeared.

7. The cell with the number 7 highlighted in red already has the required number of lines passing through it. Therefore, the cell highlighted in blue must contain a horizontal line.

8. For 3 cells with numbers, blocks with unambiguously determined positions have appeared (similarly to steps 1 and 4).

9. Now similar reasoning can be applied to 2 more cells.

10. The same reasoning as in step 7 is applied to two cells highlighted in blue. Thus, these cells must contain horizontal lines.

11. For the remaining 4 cells with numbers, there is only one possible option for filling the adjacent cells.

12. The puzzle is solved!