Thermometer Sudoku introduces an elegant sequential constraint to the classic puzzle. Thermometer shapes are drawn across the grid, and digits along each thermometer must strictly increase from the bulb to the tip. This simple rule creates rich logical deductions that reward careful analysis and make every solve deeply satisfying.
Thermometer Sudoku uses the standard 9x9 grid with all the usual Sudoku rules - each row, column, and 3x3 box must contain the digits 1 through 9 exactly once. What sets it apart are the thermometer shapes overlaid on the grid. Each thermometer consists of a rounded bulb at one end and a pointed or flat tip at the other, with a line of cells connecting them.
The key constraint is straightforward: digits must strictly increase along the thermometer from bulb to tip. The bulb holds the smallest digit on that thermometer, and each subsequent cell along the thermometer must contain a larger digit. This means digits on a thermometer are never equal and always grow as you move toward the tip.
Thermometers can be straight or curved, short or long, and they can cross row, column, and box boundaries. A single puzzle might contain anywhere from a few thermometers to a dozen or more, each interacting with the others and with the standard Sudoku constraints to create a complex web of deductions. The variant has become a staple in competitive puzzle solving and is widely featured in online puzzle platforms.
Thermometer Sudoku follows all standard Sudoku rules, plus one additional constraint: digits along each thermometer must strictly increase from the bulb (rounded end) to the tip. The bulb always contains the smallest digit on that thermometer. No two cells on the same thermometer can contain the same digit. Thermometers can cross box boundaries - the increasing rule applies regardless.
For example, a thermometer with four cells might contain the sequence 2, 4, 7, 9 - each digit is larger than the previous one. A sequence like 3, 5, 5, 8 would be invalid because 5 does not strictly increase to 5. Every puzzle has exactly one valid solution achievable through pure logic.
Thermometer Sudoku is rated intermediate to hard. While the increasing constraint is simple to understand, exploiting it effectively requires practice. The interactions between multiple thermometers and standard Sudoku logic can create subtle deductions that challenge even experienced solvers.
This variant is perfect for players who have a solid foundation in basic Sudoku and enjoy thinking about ordering and sequences. If you appreciate puzzles that reward careful logical reasoning rather than pure arithmetic, Thermometer Sudoku is an excellent choice. It is also a great introduction to constraint-based variants for solvers who find Killer Sudoku's arithmetic intimidating.
Focus on long thermometers first. A thermometer with five cells must contain five strictly increasing digits chosen from 1 to 9. The bulb can be at most 5 (since you need four digits larger than it), and the tip must be at least 5 (since you need four digits smaller than it). A six-cell thermometer is even more constrained: the bulb can be at most 4 and the tip must be at least 6.
Pay attention to where thermometer bulbs and tips land in the grid. If a bulb is in a row that already has low digits placed, you can narrow down the bulb's value quickly. Similarly, if a tip is in a column with high digits already filled, the tip's value becomes highly constrained.
Use pencil marks to track possible values along each thermometer. Mark the minimum and maximum possible digits for each cell based on the thermometer's length and position. Then apply standard Sudoku strategies like naked singles and hidden singles to further refine candidates. The interplay between thermometer constraints and standard elimination is where the most satisfying deductions emerge.
Thermometer Sudoku originated in the creative puzzle design community and gained widespread attention through puzzle competitions and online platforms. The variant's visual appeal - thermometer shapes are intuitive and easy to understand at a glance - helped it become one of the most popular constraint-based Sudoku variants.
The puzzle type has been featured in the World Puzzle Federation's competitions and is a regular fixture on platforms like Logic Masters India and Cracking the Cryptic. Its combination of visual elegance and logical depth makes it a favorite among both casual solvers and competitive puzzlers. Thermometer Sudoku continues to evolve, with puzzle designers creating increasingly creative thermometer arrangements that push the boundaries of what this variant can offer.
Thermometer Sudoku is a variant of classic Sudoku that features thermometer-shaped lines drawn across the grid. Digits along each thermometer must strictly increase from the bulb (rounded end) toward the tip. This ordering constraint works alongside standard Sudoku rules to create a uniquely challenging puzzle.
No. The digits must increase from bulb to tip, but they do not need to be consecutive. For example, a three-cell thermometer could contain 2, 5, 8 - as long as each digit is larger than the one before it moving from bulb to tip.
Yes. Thermometers can span multiple rows, columns, and 3x3 boxes. The increasing constraint applies along the entire thermometer regardless of which boxes the cells belong to. This cross-boundary nature is what makes thermometers such powerful solving tools.
Thermometer Sudoku is generally rated intermediate to hard. The thermometer constraints add a sequential ordering element that can be tricky to manage alongside standard Sudoku logic. However, thermometers also provide strong constraints that can actually help eliminate candidates, so some puzzles solve more smoothly than their difficulty rating suggests.
Start by analyzing long thermometers first, as they are the most constrained. A thermometer spanning 5 or more cells severely limits which digits can appear at each position. The bulb of a long thermometer must contain a very low digit, while the tip must contain a high digit. Use these constraints to place or eliminate candidates, then apply standard Sudoku techniques to complete the puzzle.
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