Thermometers [WIP]

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
• Empty unblocked tiles are considered unassigned.

Rules

1. Each blank space in the thermometer must be either mercury 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 unassigned 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 tiles of mercury in one row or column exceed the assigned number outside the grid.

Not enough mercury

_Derived from rule #2. _ Cannot have less tiles of mercury in one row or column than the assigned number outside the grid.

Mercury in body

_Derived from rule #3. _ The thermometer cannot have mercury in its body part while its previous part has no mercury.

Direct Rules

Rest is empty

_Derived from rule #3. _ If an earlier segment of a thermometer is blocked all segments of the thermometer after that must also be blocked.

Finish with empty

Derived from rule #1 + #2. If a row or column has the needed number of mercury tiles, the other remaining space must be blocked.

Finish with mercury

_Derived from rule #1 + #2. _ If in one row or column, all the other tiles are blocked, and if the remaining unassigned tiles matches the number of the mercury tiles assigned outside of the grid, then all the remaining unassigned tiles need to be filled out with mercury.

Finalize column or row

_Derived from rule #2 + #3: _ If there is only one remaining thermometer in a row/column that can be filled out and the row/column needs more mercury tiles, then the head of that thermometer must be filled out.