Editing Nonogram (section)

===Contradictions===
Some more difficult puzzles may also require advanced reasoning. When all simple methods above are exhausted, searching for [[reductio ad absurdum|contradictions]] may help. It is wise to use a pencil (or other color) for that to facilitate corrections. The procedure includes:
# Trying an empty cell to be a box (or then a space).
# Using all available methods to solve as much as possible.
# If an error is found, the tried cell will not be a box for sure. It will be a space (or a box, if space was tried).

[[File:Paint by numbers - Solving - Example9.png]]

In this example a box is tried in the first row, which leads to a space at the beginning of that row. The space then ''forces'' a box in the first column, which ''glues'' to a block of three boxes in the fourth row. However, that is wrong because the third column does not allow any boxes there, which leads to a conclusion that the tried cell must not be a box, so it must be a space.

The problem of this method is that there is no quick way to tell which empty cell to try first. Usually only a few cells lead to any progress, and the other cells lead to dead ends. Most worthy cells to start with may be:
* cells that have many non-empty neighbors;
* cells that are close to the borders or close to the blocks of spaces;
* cells that are within rows that consist of more non-empty cells.