Sudoku Made and maintained by Brian Hamilton and Karan Hamilton.
Brian builds the playable puzzle tools, while Karan helps test clarity, difficulty feel, and the player experience.
Playable puzzles and controls are tested in the browser for rule accuracy, usability, and a clear solving experience. See how we make and test puzzles, our editorial standards, or report a problem.
What is Thermo Sudoku?
Thermo Sudoku, also called Thermometer Sudoku, is ordinary sudoku with grey thermometers drawn over the grid. Fill it so that:
- every row, column and 3×3 box holds 1 to 9 exactly once;
- and along each thermometer the digits strictly increase from the round bulb to the tip.
Strictly means no repeats: 2, 5, 5, 8 along a thermometer breaks the rule as surely as 5, 2, 8 does. A thermometer runs through cells that touch side to side, two never share a cell, and on this page they are three to six cells long. Nothing else changes — no arithmetic, no extra regions, just an order.
Sudoku logic works on houses: nine cells that must hold 1 to 9 once each. A thermometer is a different kind of constraint. A four-cell one holds four different digits, but which four is open, and it says nothing about the cells beside it. What it gives you is an order, and an order pins values in a way a house never can: the bulb of a five-cell thermometer can only be 1 to 5 before you have looked at a single given.
What does a thermometer tell you before you place anything?
Read the thermometers first. Every cell on one has a floor and a ceiling from its position alone — the bulb of an L-cell thermometer is at most 10 − L, the tip at least L — and every digit already on the line cuts it in two: everything before it is smaller, everything after it is larger. Write the survivors in as pencil marks and half the work of the variant is done.
| Cells | Bulb | 2nd | 3rd | 4th | 5th | 6th |
|---|---|---|---|---|---|---|
| 3 | 1–7 | 2–8 | 3–9 | — | — | — |
| 4 | 1–6 | 2–7 | 3–8 | 4–9 | — | — |
| 5 | 1–5 | 2–6 | 3–7 | 4–8 | 5–9 | — |
| 6 | 1–4 | 2–5 | 3–6 | 4–7 | 5–8 | 6–9 |
From the rule alone, before any given is read: the k-th cell of an L-cell thermometer can hold k to 9 − L + k, and the last filled column in each row is the tip. This page deals thermometers of 3 to 6 cells; the 7-cell ones in puzzle books run 1–3 at the bulb to 7–9 at the tip. A digit already on the line tightens everything on both sides of it.
That first read does more than it looks. Across 40 boards per level it strikes a median of 15 pencil marks on Easy and 53 on Expert before any digit is placed, and settles four to seven cells outright. Cells on a thermometer start no tighter than the rest of the grid — 3.3 candidates each on Easy against 3.2 elsewhere — and finish the read at 1.8 to 2.4, about half.
Do the thermometers actually do any work?
Every board this page deals is built so that the answer depends on them: the generator removes digits until the puzzle has one answer under thermo rules, then checks the same givens under plain sudoku rules and keeps digging until they no longer have one. On the board above:
We checked 160 fresh boards, 40 per level: every one has a single answer with its thermometers and more than one without them. Without them, Easy givens have a median of six answers and up to 40, Medium a median of 30, and Hard and Expert more than 200 on every board we tried. A solver that ignores the thermometers stalls on every board at every level.
How do the four levels differ?
We ran 40 fresh boards per level through a solver that knows one technique at a time, then took techniques away to see which boards stopped:
| Level | Given digits | Thermometers | Cells on a thermometer | Marks the first read strikes | Reading and singles finish it | Beyond our solver |
|---|---|---|---|---|---|---|
| Easy | 29–32 | 4–6 of 3–5 cells | 18 | 15 | 95% | 3% |
| Medium | 27–28 | 4–6 of 3–5 cells | 18 | 19 | 90% | 8% |
| Hard | 25 | 5–7 of 4–6 cells | 26 | 42 | 90% | 10% |
| Expert | 21 | 6–8 of 4–6 cells | 30 | 53 | 93% | 5% |
40 boards per level from this page’s generator, fixed seed; medians, and shares rounded. The solver reads every thermometer to a fixed point, then knows naked and hidden singles, locked candidates, naked pairs and triples, and the X-Wing; the boards it does not finish needed locked candidates (2–3% per level) or something it does not know, and every one of them still has exactly one answer. Easy and Medium come up to four givens short of their target when that is what it takes to make the thermometers load-bearing.
The levels differ in how much you are told, not in which techniques you need. Thermometer reading plus naked and hidden singles finish about nine boards in ten at every level, and locked candidates cover most of the rest. What grows is the reading: an Expert board has 21 givens and around seven thermometers over 30 of its 81 cells, and its first read strikes 53 marks. This page used to say Hard and Expert demand advanced techniques and deep chains; we measured, and they do not.
The generator takes a finished grid, draws the thermometers along it, and removes digits one at a time, keeping a removal only while the puzzle still has exactly one answer under thermo rules; a search it cannot finish answers “not proven” and the clue stays. We re-solved 160 fresh boards with a separate counter written for the purpose: every one had exactly one answer, at its level’s clue target. A board takes 2 to 5 milliseconds to build, 24 at worst.
Which level should you play?
Medium is where this variant is at its best. Twenty-seven or 28 givens and four to six short thermometers: the reading does real work on every board without being the whole game. Easy is the same thermometers with four more givens, and the right place to learn to read a line.
Hard and Expert are a different feel rather than a different skill: longer thermometers, more of them, and on Expert more than a third of the grid under them with 21 givens beside, so most of the solve is re-reading lines as digits land. A board that feels impossible rather than hard is one of the one in ten that needs more than singles and locked candidates; it still has exactly one answer.
What goes wrong on a Thermo Sudoku
- Reading the tip as the bulb. The round end is the small end; the digits grow towards the tip.
- Allowing a repeat. Increase means strictly increase: two 5s on one line is a mistake.
- Reading a line once. A digit placed on a thermometer, or beside one of its cells, tightens both sides again. Re-read the line every time; the second read is where most placements come from.
- Treating the thermometer as its own world. It orders its cells, but each is still in a row, a column and a box. Placements come from the two together: the houses leave three or four digits, the order leaves one.
- Leaving the thermometers for later. Ignore them and every board here has several answers, so a solve that contradicts itself late usually went past a thermometer unread.
Where does Thermo Sudoku come from?
The name comes from Mutant Sudoku (2009), the variant collection by Thomas Snyder and Wei-Hwa Huang, where the thermometer was introduced as a friendlier way of drawing the greater-than and less-than puzzles before it — Greater Than Sudoku on this site is that older form, with inequality signs between neighbouring cells. Competition setters and the YouTube channel Cracking the Cryptic have kept thermometers in front of solvers since. Thermometer Sudoku is the same puzzle under its longer name.
What do the buttons do?
Select a cell, then a digit from 1 to 9; the page opens on Medium. Selecting a cell on a thermometer highlights the rest of that thermometer as well as its row, column and box. Under the grid:
- Notes turns pencil marks on and off. A correct digit clears itself from the notes of its row, its column and its box; a wrong one leaves your notes alone, and the thermometers are yours to re-read.
- Erase clears the selected cell, and pressing the same digit twice does the same.
- Undo takes back the last change to a cell, though not the notes a correct digit cleared elsewhere, and not the Mistakes count.
- Hint fills one cell with its answer, picked at random rather than the cell you could work out next.
- Solve asks first, then fills the grid and stops the timer.
- New Game deals another board at the level you are on; the level buttons deal one at theirs.
Digits 1–9, the arrow keys, Backspace or Delete and Ctrl+Z all work from a keyboard. The board is saved in this browser after every move, thermometers and timer included, so it is waiting when you come back.
Where to go next
Thermo Sudoku is the gentlest of the “lines on the grid” variants, because an order is the easiest line to read. Arrow Sudoku draws lines whose digits must add up to the digit in the circle, so the reading becomes arithmetic, and Killer Sudoku replaces the givens with cage sums altogether. Consecutive Sudoku marks neighbours that differ by exactly one, a cousin of the thermometer’s order, and X-Sudoku is the place to go if you would rather add a region than a line.