What is Thermo Sudoku?

Thermo sudoku is a sudoku variant where ‘thermometers’ are overlaid on the grid. 

All the numbers placed in cells overlaid by a thermometer must increase in value from the circle bulb of the thermometer to the other end. 

For example, as the thermometer in the thermo sudoku below has a length of nine, we know that the circular bulb must be 1 and all the other cells go up in order until we reach 9 at the other end. 

This is obviously an incredibly simple example as the values of all the cells covered by the thermometer are forced. 

You will rarely see a nine-cell thermometer in actual thermo sudokus. Instead, they will be of varying lengths including very short ones consisting of only two cells. 

Thermo sudokus can have multiple branches and bulbs

More complex thermo sudokus can have multiple thermometer ‘branches’ from the bulb and even multiple bulbs like in the example below from puzzlemaster John Bulten. 

In this example you will notice that the thermometer in the top left has two branches and the other three thermometers on the sides have two bulbs each. 

The exact same regular thermo sudoku rules apply here: every number in each thermometer must increase in value as you move away from the bulb. 

You can view the solution to the puzzle above here.

Can the same number appear in the same thermometer? 

Yes! When thermometers contain multiple branches or bulbs, it’s possible for the same thermometer to contain the same number more than once. Obviously provided that all the regular sudoku rules are followed. 

For example, in the thermo sudoku below, it’s possible that the two ends of the thermometer could both be 9s.  

They could also be both 8s or both 7s. However, they cannot be both 6s as there aren’t enough cells from the bulb to get to the end of the longer branch without repeating a number along the way. 

Likewise, if this example had two bulbs like below, then it’s also possible that both contain 2s. 1s and 3s also work in this example.

Thermo sudoku with no given digits 

Because of the additional constraints thermometers present, it’s possible to have thermo sudokus with no given digits. Like in the example below from World of Sudoku.

In addition to there being no given digits, the other beautiful aspect about this particular puzzle is how the thermometers from the year “2020”. 

Often thermometers will be arranged to form some kind of particular pattern or form like in this case. 

Thermo sudoku tips 

A few tips for solving thermo sudokus include:

• Start with longer thermometers. The longer the thermometer, the less flexibility there is with what values they can contain. A 2-cell long thermometer can contain any set of two digits from 1 and 2 all the way to 8 and 9, whereas if you have a 9-cell thermometer you automatically know what each value is as it must increase from 1 to 9 in order. 
• Don’t forget about the regular sudoku rules. Use the thermometers to help reduce the possible digits for certain cells where regular sudoku rules have left you with multiple possibilities. 
• Once you know one value of any cell along a thermometer, you know all the other cells towards the bulb must be a digit of lower value and all the other cells higher up the thermometer must be digits of higher values. 

Want to learn about more sudoku variants?

There are plenty of other sudoku variants you might be interested in, including: 

• Chess sudoku
• Samurai sudoku