Fill-A-Pix

Fill-A-Pix is a puzzle with unfilled squares shown in gray. The goal of the puzzle is to color all squares white or black according to the rules, which should reveal an image.

The cycle of tiles is { Gray, Black, White }. Left clicking on the tile will advance the cycle by one color (Gray -> Black or Black -> White or White -> Gray) and right clicking on a tile will detract the cycle by one color (White -> Black or Black -> Gray or Gray -> White).

Rules

1. Each cell must be colored either white or black
2. Each clue cell (cell with a number) must touch that number of black cells. A cell touches itself and its eight neighbors

LEGUP Proof Rules

Case Rules

Black or White

When a cell can be colored either black or white based on the current state of the board, application of this rule will create a split in the tree, where one path has the cell as white and the other has the cell as black.

Satisfy Clue

Application of this rule will create different branches for each possible case to satisfy a clue. Satisfying a clue requires that the clue be touching the same number of black cells as the clue's value. This clue will only generate the branches if there are 5 or less cases, but can be used to manually create more.

Contradiction Rules

Too Few Black Squares

This rule comes directly from Rule #2. A clue (or numbered cell) must touch exactly that number of black cells, so if a clue is unable to touch that many, the board is in a state of contradiction.

Too Many Black Squares

This rule comes directly from Rule #2. A clue (or numbered cell) must touch exactly that number of black cells, so if a clue is touching more than that number of black cells, the board is in a state of contradiction.

Direct Rules

Finish with Black

If the number of unknown cells touching a clue plus the number of black cells touching the same clue is equal to the value of the clue, then the unknown cells must all be black in order to satisfy the clue.

Finish with White

If the number of black cells touching a clue is equal to the value of the clue, then the clue is satisfied and all unknown cells touching the clue must be white.

Mirror

When two adjacent clues have the same value, the number of black cells in their unshared regions (i.e. the neighbors of clue 1 that are not neighbors of clue 2) must be equal. Importantly, this rule does not say anything about the location of the black cells in those regions.

Touching Sides

Similar to the Mirror rule, when two clues are adjacent, the difference between the number of black cells in the unshared regions is equal to the difference in the values of the clues.

Touching Corners

Similar to the Touching Sides rule, when two clues are diagonally adjacent, the difference between the number of black cells in the unshared regions is equal to the difference in the values of the clues.

Untouching Shared

Similar to the Touching Corners rule, when two clues are not touching, but share neighboring cells, the difference between the number of black cells in the unshared regions is equal to the difference in the values of the clues.