Medium Thermo Sudoku

Digits must increase from the bulb end to the tip along each thermometer. Temperature direction constrains every placement.

Easy Medium Hard Expert

Thermo Sudoku at medium difficulty. Thermometer bounds interact with rows, columns, and boxes — you'll need both bound logic and standard Sudoku technique.

9
1
5
4
8
3
1
6
2
1
7
5
9
2
5
1
7
8
3
4
3
3
2
6
4
9
5
6
2
7
6
3
Mistakes
0/3
Score
-
Time
00:00
Try Hard →
Progress0%

What is Thermo Sudoku?

Difficulty
★★★★☆
4/5
Constraint Type
Line Constraints
Typical Givens
20–28
Avg. Solve (Medium)
22 min

Solving Techniques for Medium Level

Technique Description Level
Range Restriction from Length A thermometer with N cells must use N strictly increasing distinct values. The bulb is at least 1 and the tip is at most 9, giving a calculable valid range for each cell. Beginner
Minimum/Maximum Bounding The bulb value is ≤ 9 − (N − 1). The tip value is ≥ N. Apply these bounds immediately to prune all thermometer candidates. Beginner
Overlapping Thermometer Deduction Two thermometers sharing a cell give tighter combined bounds than either alone. Intermediate
Short vs. Long Thermometers A 2-cell thermometer is simply a greater-than relationship. A 9-cell thermometer forces exactly 1–9 in order. Intermediate

Master these, then take on Hard Thermo Sudoku to learn Advanced techniques.

Average Solve Time by Difficulty

Easy
10 min
Medium
22 min
Hard
45 min
Expert
75 min
Want a full walkthrough of rules, strategies, and solving steps? How to Play Thermo Sudoku →

Frequently Asked Questions — Medium Thermo Sudoku

What techniques do I need for medium Thermo Sudoku?
Medium puzzles require combining thermometer bounds with standard Sudoku techniques. Calculate the minimum value at each position (bulb value plus positions from bulb) and maximum value (tip value minus positions from tip), then cross-reference with row, column, and box constraints. Hidden singles and naked pairs become necessary once obvious thermos are resolved.
How do I calculate the minimum and maximum for a thermometer cell?
For a cell k positions from the bulb on an n-cell thermometer: the minimum value is k+1 (at least 1 more than the cell before it, starting from 1 at the bulb). The maximum value is 9 minus (n minus k minus 1) — enough room for all remaining cells to fit below 9. Any digit outside this range can be eliminated immediately.
Can thermometers interact with each other in medium Thermo Sudoku?
Yes. Two thermometers that pass through the same row or column restrict each other indirectly through standard Sudoku uniqueness. A digit resolved on one thermometer removes it as a candidate from cells in the same row and column that belong to a different thermometer. This cross-thermo interaction is the main source of medium-level deductions.
How long does a medium Thermo Sudoku take?
Most players finish a medium Thermo Sudoku in 15 to 30 minutes. If you methodically calculate bounds first and then apply row/column/box elimination, progress is steady. Getting stuck usually means a bound calculation has been missed on a shorter thermometer.
What does it mean when a thermometer has only one valid combination?
If the calculated minimum and maximum for every cell on a thermometer are equal, the entire thermometer is fully determined — you can fill in all its cells immediately. Even when not fully determined, a thermometer with only one or two valid sequences provides very tight constraints on all surrounding cells.

More questions? See the full Thermo Sudoku guide.