Hard Thermo Sudoku

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

Easy Medium Hard Expert

Hard Thermo Sudoku. Fewer givens, overlapping thermos — expect multi-step bound deductions and extensive pencil-mark work.

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

What is Thermo Sudoku?

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

Solving Techniques for Hard 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
Forcing Chains via Thermometers When a value is forced into a thermometer cell, all cells closer to the bulb must be smaller and all closer to the tip must be larger. Advanced
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

Ready for the ultimate test? Try Expert Thermo Sudoku — the hardest puzzles on Sudoku.by.

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 — Hard Thermo Sudoku

What makes hard Thermo Sudoku puzzles difficult?
Hard puzzles have many overlapping thermometers and fewer given digits, meaning your initial bounds calculations leave a wide range of possibilities. Progress requires multi-step deduction chains where resolving one thermometer position propagates through several rows and columns before unlocking the next placement.
Should I use pencil marks for hard Thermo Sudoku?
Yes. For hard puzzles you need to track the range of possible values for each thermometer cell alongside standard Sudoku candidates. Write the minimum and maximum possible digit for each cell as a quick reference, then update both the thermo bounds and the row/column/box marks together every time you place a digit.
How do I handle thermometers with many valid sequences at hard level?
Focus on the endpoints first. The bulb and tip positions always have the tightest constraints. Once you fix a value near one end, the valid sequences for the remaining positions shrink dramatically. Work inward from both ends simultaneously rather than trying to enumerate all sequences for the whole thermometer.
What is thermometer forcing in hard Thermo Sudoku?
Thermometer forcing means assuming a value for one cell and tracing its consequences through bounds and Sudoku rules until you either solve the puzzle or reach a contradiction. Unlike trial-and-error, forcing is logical — you are proving that only one value avoids a chain of impossibilities. It is used sparingly but is sometimes the only path forward on hard puzzles.
How long does a hard Thermo Sudoku take to solve?
Expect 30 to 60 minutes on hard puzzles. If you are stalled, check whether any thermometer has a cell where minimum equals maximum — that cell is fully determined. Also verify that every row and column containing a multi-thermo intersection is fully updated with the latest bound eliminations.

More questions? See the full Thermo Sudoku guide.