# Hints for "Reveal labyrinth"

## Obvious hints

If the cell already has number of cells equal to this cell hint then the rest of unknown sides of this cell may be cleared. For example, 0-cell does not have any walls and all walls around it may be cleared.
 1 2 1 2 0 1 3 1 3
 1 2 1 2 0 1 3 1 3
1-cell located near the border of the labyrinth already has 1 wall known, and the other sides may be cleared. Similarly, 2-cell in the corner can be completely resolved: 1-cell does not have to be near the edge. Any time when a wall is put adjacent to 1-cell, the rest of this cell sides may be cleared. Same is true for 2-cell (when 2 walls are known the rest is clear) and 3-cell (when 3 walls are known, the remaining is clear).

On the other hand, 1-cell has 1 wall and 3 clear sides, so if 3 clear sides are known, the remaining must be the wall. Also, 2-cell has 2 walls and 2 clear sides, so when 2 sides are known to be clear, the rest are the walls. 3 cell that has one clear side known, has the walls in the rest:

## Hints, based on single-connectedness

There cannot be clear path between two 3-cells, for if it were, the 2x1 block would be surrounded completely by walls, which is impossible in a single-connected labyrinth.

Each corner (common point of 4 adjacent cells) must have at least one wall adjacent to it, for if it didn't have it, these for cells would form a cycle, which is a violation of conditions. So, if 3 pathes adjacent to a corner are known to be clear, the remaining is covered by a wall:

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