Thermometers

Thermometers is a game that combines the fun of grid puzzles with the thrill of the neurotoxin mercury! The puzzle is made up of empty thermometers and the goal is to fill each thermometer according to the rules of the game.

Controls

• Left clicking on a tile fills/empties it
• Right clicking on a tile blocks/unblocks it from being filled

Rules

1. Each blank space in the thermometer must be either filled or blocked
2. The numbers outside the grid indicate how many cells in each row and column are filled
3. Thermometers must start filling from the head (circular part) and fill towards the tip without any gaps

Proof Rules

Case Rules

Mercury or blocked

Derived from rule 1

Each empty tile must be filled with mercury or blocked.

Satisfy mercury

Derived from rule 2

There are multiple ways to fill with mercury in order to satisfy the target number for a row/column.

Contradiction Rules

Too many mercury tiles

Derived from rule 2

Cannot have the filled tiles in one row or column exceed the assigned number outside the grid.

Too few mercury tiles

Derived from rule 2

Cannot have less filled tiles in one row or column than the assigned number outside the grid.

Discontinuous mercury

Derived from rule 3

The thermometer cannot have mercury in a body tile while a previous tile is blocked.

Direct Rules

Rest is empty

Derived from rule 3

If a segment of a thermometer is blocked all empty tiles of the thermometer after that must also be blocked.

Prior is filled

Derived from rule 3

If a tile in the body of a thermometer is filled, all previous empty spaces must also be filled

Finish with blocked

Derived from rules 1 and 2

If a row or column has the needed number of mercury tiles, the remaining empty tiles must be blocked.

Finish with mercury

Derived from rules 1 and 2

If in one row or column the remaining empty tiles and filled tiles match the number of the mercury tiles assigned outside of the grid, then all the remaining empty tiles need to be filled.

Minimum fill

Derived from rules 2 and 3

If every other tile in a row or column besides the tiles of one thermometer being filled would not meet or exceed a row or column's number then the remaining thermometer must be filled at least the remaining amount.

Thermometer too large

Derived from rule 2

If a thermometer has more unassigned tiles than needed to satisfy a row or column the additional tiles must be blocked off.