Thermometers rules
The grid is covered by thermometers. Each one starts at a round bulb and runs through one or more cells to a rounded tip, straight or with bends. Your job is to decide how far the mercury rises in every thermometer, so that each row and each column has exactly as many filled cells as the number beside it.
The puzzle is also called the thermometer puzzle or the Thermometers logic puzzle. Some collections split it into straight and curved thermometers; the boards here mix both.
- Mercury starts at the bulb and rises toward the tip without gaps: a filled cell means every cell between it and the bulb is filled too.
- So an empty cell means every cell after it, toward the tip, is empty too.
- A thermometer can be empty, partly filled or full.
- The number beside a row, or above a column, is the exact number of filled cells in that line.
- Every puzzle here has exactly one answer.
A 6×6 Thermometers puzzle and its answer
Here is a real Easy puzzle from our generator, and its one answer. Row E needs 6, and columns 1 and 2 need 6 as well, so those three lines fill completely. The thermometer from E1 runs up to C2 and fills all 4 of its cells, and the long one from D2 fills all 5. The thermometer from A3 stays empty, and the ones from B3 and D5 hold only their bulbs.
How to play Thermometers on this page
Tap a cell to set the mercury there: that cell and everything back to the bulb fill. Tap the top filled cell again to lower the mercury by one. To mark cells empty, use a long press, a right click or the Empty mode: that cell and the rest of its thermometer to the tip get a cross. Drag along a thermometer to slide its mercury up or down. On a keyboard, the arrow keys move, Space or Enter fills, X marks empty and Delete clears.
A count turns green when its line is complete and red when it has too many. Check marks any mistake, a switch under the board compares every mark with the answer as you play, and Hint explains the next step in words and shows the cells and counts it uses. Undo, Redo, Pause and Reset are under the board.
Pick a board from 6×6 to 15×15 and one of four levels. The 12×12 and 15×15 boards add Focus mode and a size dial, so the cells stay big enough to tap.
Count a line, and let the mercury flow
Two quick rules do a lot of the work. A filled cell fills everything back to its bulb, and a cell marked empty empties everything on toward the tip. Then count: when a line already has its number of filled cells, the rest of it is empty; when it needs every cell it can still fill, they all fill. A count of 0 empties its whole line at once.
In the board below, row B needs 2. B1 to B4 are already empty, so only B5 and B6 are left, and both must fill. B6 belongs to the thermometer that starts at D6, so the mercury reaches back to its bulb: C6 and D6 fill too. Every Easy board can be solved with these steps alone.
Room in a line
On harder boards, look at one line and ask how many of its cells each thermometer crossing it can still give. A thermometer gives its cells in order from the bulb, so one that only reaches a row with its tip can give that row 1 cell at most, and only if it fills completely.
In the board below, nothing is marked yet and row A needs 5. Four thermometers cross row A. The ones from A1 and A2 give it at most their bulbs, 1 cell each, and the long one from E3 reaches row A only with its tip, A3: 1 more. That is 3 at most, so the thermometer from A4, which lies along the row, must give at least 2: A4 and A5 fill. The same count works the other way: if the other thermometers must give a line most of its number, a thermometer can be capped below its full length.
Two lines together
When one line on its own says nothing new, take two lines that share thermometers: a row and a column, or two neighbouring rows or columns. Whatever a shared thermometer gives one line, it gives the other too, so the two counts limit each other. List the ways the thermometers on both lines can fill and keep only those that meet both counts.
In the board below, row B needs 4 and column 1 needs 3, and the thermometers from A1 and D1 cross both. Of all the ways the thermometers on these two lines can fill, every one that gives row B its 4 and column 1 its 3 puts mercury in the thermometer from B4. So B4 fills. Hard boards always need this step at least once.
What if…?
Expert boards sometimes need a short test. Suppose a cell is filled, so its thermometer fills back to the bulb, then follow the counts line by line. If a line ends up with too many filled cells, or can no longer reach its number, the supposition was wrong and the cell is empty. The same works the other way round, supposing a cell is empty.
In the board below, suppose B3 were filled, and with it the bulb in C3. Then row C would have its 3, so the rest of row C would be empty; column 2 would need all its open cells; row D would then have its 3; and column 3 would end up with more than 2 filled. So B3 is empty. On our 8×8 Expert boards a what-if is needed at least once, usually just once and never more than 8 times, and each chain is a few count steps, never a long search.
What the four levels mean
Each level is set by the hardest step a puzzle needs, not by the size of the board, so an Easy 15×15 is long but never tricky. We solve every board with the same steps the Hint button explains, and the table shows what that took on 1,950 verified 8×8 boards (the page's first board size).
An 8×8 board usually has 16 thermometers, 4.1 cells long on average and up to 9 cells, with about 2 that are a single cell.
| Level | Hardest step | Hint presses (median) | Boards with a what-if |
|---|---|---|---|
| Easy | Line count | 14 | 0% |
| Medium | Room in a line | 18 | 0% |
| Hard | Two lines together | 26 | 0% |
| Expert | What if | 28 | 100% |
A Hint press can fill or empty several cells at once. Medium boards always need Room in a line, Hard boards always need Two lines together, and every Expert board needs a what-if (56% of them need two lines together as well).
How we make each puzzle
The generator lays random thermometers over the grid, straight and bent, and picks a fill level for each. Then it changes the levels one thermometer at a time until our solver finishes the board using exactly the steps of the chosen level. That solver only finishes a board that has one answer, so every puzzle you get has exactly one.
Small boards are made in your browser in a second or two. The slowest sets (12×12 Hard and Expert, 15×15 Easy, Hard and Expert) come from 1,000 boards we made in advance. Daily, starter, banked and printed boards are also checked by a second, independent counter that knows nothing about the solving steps.
Daily puzzle, sharing, printing and stats
The Daily puzzle is one 8×8 board a day, the same for everyone: Easy on Mondays, Medium on Tuesdays, Wednesdays and Sundays, Hard on Thursdays and Fridays, Expert on Saturdays. The calendar runs to 31 August 2031.
Share copies a link that opens exactly your board, with its puzzle number. Print gives you the board you are playing with an answer page, or a pack of up to 50 new puzzles, 1, 2 or 4 to a page. Your stats (solved puzzles, best and average times, days in a row) stay in this browser only.
Puzzles like Thermometers
Thermometers and Nonograms look like cousins: both are grids solved with number clues around the edges. A Nonogram clue gives the lengths of separate blocks in a line, while a Thermometers count only says how many cells are filled, and the thermometer shape makes a filled cell pull its neighbours back toward the bulb.
Two more puzzles fill cells to meet row and column counts: in Aquarium water settles to a flat level in each tank, and in Kakurasu each shaded cell counts its position in the row and column.