Thermometers

Thermometers is a logic puzzle played on a grid containing thermometer shapes. Each thermometer has a bulb (base) and extends in one direction. The player must fill in portions of each thermometer, always starting from the bulb — just like mercury rising. Clues along the edges of the grid indicate how many filled cells are in each row and column. The challenge is to determine exactly how much to fill each thermometer while satisfying all the row and column counts.

Rules

1. The grid contains thermometer shapes, each with a bulb (round end) at one end and a flat end at the other. Thermometers can be horizontal or vertical.
2. Each thermometer is filled continuously from its bulb upward/outward. You cannot skip cells — if a cell is filled, all cells between it and the bulb must also be filled.
3. A thermometer may be completely empty, partially filled, or completely filled.
4. Numbers along the left side and top of the grid indicate how many cells in that row or column must be filled.
5. All row and column counts must be satisfied simultaneously.

Strategies

• Zero Rows/Columns: If a row or column count is 0, all thermometer cells in that line must be empty. This means any thermometer passing through that line stops before reaching it (or is entirely empty if its bulb is in that line).
• Full Rows/Columns: If a row or column count equals the number of thermometer cells in that line, all of them must be filled.
• Bulb Forcing: If a thermometer's tip (far end from bulb) must be filled (based on row/column counts), then the entire thermometer must be filled.
• Empty Tip Propagation: If a cell in a thermometer is determined to be empty, all cells farther from the bulb in that same thermometer must also be empty (mercury cannot jump over gaps).
• Counting Constraints: Compare the row/column count with the thermometers passing through it. If only certain combinations of fill levels produce the correct count, those are forced.
• Cross-referencing: A thermometer cell belongs to both a row and a column. Use the constraints from both directions to narrow down which cells must be filled or empty.

Thermometers is a relatively modern logic puzzle that gained popularity through online puzzle communities and puzzle magazines in the 2000s. The puzzle's exact origin is difficult to pinpoint, but it emerged from the rich tradition of grid-based logic puzzles that flourished in Japan and Europe during the late 20th century.

The thermometer metaphor — mercury rising from a bulb — provides an intuitive physical model that makes the rules immediately understandable. This "continuous fill from one end" constraint gives the puzzle a unique character among grid puzzles, as it introduces a directional, ordered element that most cell-based puzzles lack.

Thermometers has been featured in the World Puzzle Championship and various national puzzle competitions. It is valued in competitions for its quick-to-learn rules and scalable difficulty. Small grids with many clues can be solved in under a minute, while large grids with sparse clues can challenge experienced solvers.

The puzzle appears in numerous puzzle books and apps, and is a popular choice on puzzle websites like puzzle-thermometers.com. Its visual clarity — you can see the thermometer shapes and the filling level at a glance — makes it particularly well-suited to digital formats where filled cells can be animated to "rise" from the bulb. Educators have also adopted the puzzle as a tool for teaching logical reasoning and combinatorial thinking in an accessible, visually appealing format.