Thermo Sudoku: rules, strategy and how to start
A thermometer looks like decoration until you realise it is a chain of inequalities. The bulb is the smallest digit on the line, the tip the largest, and everything between is trapped.
Why the rule changes everything
The thermometer is the only common variant where every cell of the line is ordered. That means each cell carries two bounds at once — bigger than everything behind it, smaller than everything ahead.
A three-cell thermometer with a 1 in the bulb forces the next cell to be at least 2 and the tip to be at least 3. A bulb of 7 kills the line entirely, which is exactly why a bulb can never be 8 or 9.
How to start a board
- Find every digit 1 you can: a bulb cell that sees a 1 in its row, column or box can be eliminated, and a tip that sees a 9 is dead.
- Work short thermometers first — two or three cells. They constrain hard and they resolve early.
- Mark the ends: the bulb can only be 1–7, the tip only 3–9. Write those bounds as pencil marks before placing anything.
Common mistakes
- Treating a thermometer as a set rather than an order. 3-5-4 is illegal on a thermo even though the digits are the same as 3-4-5.
- Forgetting that thermometers ignore box boundaries — the line does not reset when it crosses into a new box.
- Placing a middle digit without checking both neighbours. The middle cell is the most constrained cell on the board.
Frequently asked questions
Can a thermometer repeat a digit?
No. Repeats are forbidden by the strict ordering, and also by sudoku if the cells share a unit.
What if a thermometer is only two cells?
Then it is a simple inequality: the bulb is smaller than the tip. It is the easiest form and the best place to start.
Every board on this site is generated with a uniqueness check, so the puzzle in front of you has exactly one solution and every digit can be proved rather than guessed.
Play Thermo Sudoku ↗