Thermo Sudoku

Thermo Sudoku, with the thermometers guaranteed consistent

An ordinary 9×9 sudoku with shapes laid over it. Each shape is a thermometer — a round bulb with a line running out of it — and the digits along that line have to climb, strictly, from the bulb outward to the tip.

Every grid here carries up to four thermometers, each three cells long, running either along a row or down a column. They never overlap, so no cell belongs to two of them.

An honest note on how the puzzles are built

The grid is generated as a standard sudoku first, with between 28 and 34 givens, and the clues are carved so that it has exactly one solution under the ordinary rules alone. The thermometers are then drawn onto triples that already increase in that solution.

What that means in practice: the thermometers are always true, and they will often save you time, but you never need them. You cannot get stuck in a position where only thermometer logic can rescue you, because the grid was already solvable without it.

That is a deliberately conservative construction. A thermo puzzle carved to depend on its thermometers is a harder and better puzzle, and it is also one where a printing or reading error in a single overlay makes the grid unsolvable. These sheets are safe to hand to a room of people.

What the thermometers give you

A three-cell thermometer is worth more than it looks. The bulb can hold at most 7. The tip must be at least 3. Three cells lose candidates at a stroke.

Better still is where a thermometer crosses a row or box you have partly filled: the increase forces an order on cells that plain sudoku logic would leave interchangeable, and that is usually where the puzzle opens up. Beginners tend to solve around the thermometers and use them only for confirmation. Solving through them is faster.

What the form offers

Puzzles per page, from 1 to 4, and whether to print the solutions page. Two to a page is the default and keeps the overlays crisp; four is readable but tight, since a thermometer bulb has to stay clearly a bulb.

The seed reproduces an exact set of puzzles, which is what you want if a club or a class is racing the same sheet.

Coming to it from ordinary sudoku

The rules you already know are unchanged. Rows work the same way, so do columns, so do boxes, and no digit has acquired a new meaning. All that is added is a direction on a handful of triples.

Give a first-timer the sheet without explaining, and most people work out the thermometer rule from the shape alone within a minute, which is a fair sign that the notation was well chosen by whoever invented it.

Print at 100% on A4 or US Letter.