What is a Thermometers puzzle?

It is a logic puzzle on a grid tiled with thermometers, each a straight run of squares with a round bulb at one end. Mercury fills a thermometer from its bulb and never skips a square, so each one is either empty, full, or filled to some point in between. The numbers beside each row and column say how many squares in that line hold mercury.

Is this Thermometers generator free?

Yes. Pick a grade, generate a puzzle and print it with its answer, with no sign-up and no watermark. It is free for classroom, home and personal use.

How do I start solving one?

Start with the lines whose number is 0 or equals the length of the line, since those decide every square in them at once. Then work on each thermometer from both ends: a square you know is empty makes every square above it empty too, and a square you know is filled makes every square below it, down to the bulb, filled.

Why do harder grades use longer thermometers?

Because a thermometer has only as many states as it has squares, and the row and column numbers have to pin all of them down. On a 10 by 10 board of thermometers at most three squares long, almost no board we generated had a single answer; with eight-square thermometers about a third did. Longer thermometers are what make a bigger board work at all.

Is it like a nonogram?

They both count filled squares along rows and columns, but a nonogram tells you the runs within a line and leaves you to place them anywhere in it. Here the runs are drawn on the board and the only thing you choose is how far up each one the mercury rises, which makes the solving feel much more like arithmetic and much less like pattern matching.

Does every puzzle have one solution?

Yes. Filling a tiling of thermometers to random levels always gives a legal board, but it rarely gives one that its own numbers pin down, so every puzzle here is checked by the same solver our Publisher Studio uses before it prints.

What size are the pages?

The free tool prints at 8.25 by 11 inches, a popular large-print size. Our Publisher Studio will export the same book at any KDP trim, from 5.06 by 7.81 up to 8.27 by 11.69, as a print-ready 300 DPI interior.

Free tool

Free Thermometers generator, with the answer

Pick a board and generate a Thermometers puzzle, then print it with its filled answer. Every puzzle fills exactly one way, with no sign-up and no watermark. It runs on the same engine as our KDP Publisher Studio.

Difficulty

A bigger board is harder. Longer thermometers sound easier and are what make a big board solvable at all: each one has only as many states as it has cells, so a grid of short ones leaves the counts with too little to pin down.

10×10 board, 19 thermometers. Mercury fills each thermometer from its bulb and never skips, and the numbers beside each row and column count the filled squares in that line.

Two pages: the puzzle and its answer. Every puzzle is proved to have exactly one answer by the same engine as our KDP studio.

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This makes one puzzle. Sign up to turn it into a full Thermometers book for Amazon KDP: hundreds of graded puzzles at any trim, as print-ready PDFs.

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The puzzle and its answer, as they print.

Thermometers Hard

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Thermometers Hard · Solution

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How to make a Thermometers puzzle

1Pick a difficulty. Choose a board. Harder grades use a bigger grid tiled with longer thermometers.
2Generate the puzzle. Press Generate puzzle. You get a fresh board, proved to fill exactly one way.
3Print the two pages. Press Print / save PDF. You get two pages: the puzzle on page one and its filled answer on page two.

How to solve a thermometers puzzle

The grid is tiled with thermometers, each a straight run of squares with a round bulb at one end. Fill each one from its bulb, never skipping a square, so that the numbers beside each row and column count the filled squares in that line.

The method

1Start with the lines that have no choice. A row or column numbered 0 is entirely empty, and one numbered the full width of the board is entirely filled. Both decide every square in the line at once, and both usually decide parts of several thermometers that run across it.
2Work each thermometer from both ends. A square you know is empty makes every square further from the bulb empty too, and a square you know is filled makes every square back down to the bulb filled. One deduction anywhere on a thermometer travels the whole length of it.
3Count what a line still needs, not what it has. Subtract the squares you have already filled from the line number. What is left has to come from the thermometers still undecided in that line, and often only one way of splitting it fits.
4Use the most a thermometer could give. If a line needs four and the thermometers crossing it could supply at most four between them, every one of them is filled as far as that line. The same argument upside down empties them when a line has nothing left to give.

The one rule people get wrong: Mercury rises from the BULB, not from the top of the page. A thermometer drawn pointing left fills from its right-hand end, and the bulb is the only thing on the board that says which end that is, which is why it is drawn so much wider than the tube.
What the answer page shows: The same board with the mercury drawn in, so each thermometer shows at a glance how far up it was filled.
How the grades differ: A bigger board, tiled with longer thermometers. The longer ones sound easier and are what make a big board work at all: a thermometer has only as many states as it has squares, so a large grid of short ones leaves the numbers with far too little to pin down.
Is it the same as a nonogram?: No. Both count filled squares along the rows and columns, but a nonogram tells you the runs in a line and leaves you to place them, while here the runs are printed on the board and the only question is how far along each one the mercury reaches.
Good for: Anyone who likes a puzzle that is mostly careful arithmetic.

Publishing a whole book?

This tool makes one puzzle for home or the classroom. To make a Thermometers book you can sell on Amazon KDP, Publisher Studio generates hundreds of graded puzzles across a difficulty curve, at any KDP trim, as a print-ready interior and solutions PDF.

See the KDP Thermometers maker

Questions

What is a Thermometers puzzle?: It is a logic puzzle on a grid tiled with thermometers, each a straight run of squares with a round bulb at one end. Mercury fills a thermometer from its bulb and never skips a square, so each one is either empty, full, or filled to some point in between. The numbers beside each row and column say how many squares in that line hold mercury.
Is this Thermometers generator free?: Yes. Pick a grade, generate a puzzle and print it with its answer, with no sign-up and no watermark. It is free for classroom, home and personal use.
How do I start solving one?: Start with the lines whose number is 0 or equals the length of the line, since those decide every square in them at once. Then work on each thermometer from both ends: a square you know is empty makes every square above it empty too, and a square you know is filled makes every square below it, down to the bulb, filled.
Why do harder grades use longer thermometers?: Because a thermometer has only as many states as it has squares, and the row and column numbers have to pin all of them down. On a 10 by 10 board of thermometers at most three squares long, almost no board we generated had a single answer; with eight-square thermometers about a third did. Longer thermometers are what make a bigger board work at all.
Is it like a nonogram?: They both count filled squares along rows and columns, but a nonogram tells you the runs within a line and leaves you to place them anywhere in it. Here the runs are drawn on the board and the only thing you choose is how far up each one the mercury rises, which makes the solving feel much more like arithmetic and much less like pattern matching.
Does every puzzle have one solution?: Yes. Filling a tiling of thermometers to random levels always gives a legal board, but it rarely gives one that its own numbers pin down, so every puzzle here is checked by the same solver our Publisher Studio uses before it prints.
What size are the pages?: The free tool prints at 8.25 by 11 inches, a popular large-print size. Our Publisher Studio will export the same book at any KDP trim, from 5.06 by 7.81 up to 8.27 by 11.69, as a print-ready 300 DPI interior.

Short of ideas? Browse our ready-made printables for this puzzle and print one today.