Thermo Sudoku Rules and Solving Tips for Beginners

By Andrew Boyko, developer of CageDoku · Updated October 23, 2026

Thermo Sudoku is classic Sudoku with one extra rule. Some cells are connected by a thermometer: a path that starts at a round bulb and ends at a tip. Digits must strictly increase from the bulb to the tip, so a thermometer never repeats a digit. The visual rule makes it one of the friendliest Sudoku variants for beginners.

The rules

1. Every row, column and 3×3 box contains 1 to 9 once.
2. On every thermometer, digits strictly increase from the bulb (round end) to the tip.

The range trick

For a thermometer of length n, the cell in position i (the bulb is position 1) can only hold digits from i up to 9 − (n − i). Example: on a 4-cell thermometer the cells can hold 1-6, 2-7, 3-8 and 4-9. The bulb can never be 7, because three larger digits would not fit. Writing these ranges as candidates first removes a surprising amount of clutter.

Tip 1: long thermometers are almost solved

A 9-cell thermometer is simply 1 to 9. An 8-cell thermometer has a bulb of 1 or 2 and a tip of 8 or 9. The longer the thermometer, the less freedom it has.

Tip 2: known digits split the range

If the middle cell of a 3-cell thermometer is 5, the bulb is 1-4 and the tip is 6-9. Every digit you place on a thermometer shrinks the ranges of the cells before and after it.

Tip 3: ones and nines

Any 1 on a thermometer must be its bulb, and any 9 must be its tip. Use this to decide where the 1s and 9s of a box can go.

Tip 4: combine with rows, columns and boxes

Thermometer cells that share a row, column or box cannot repeat digits anyway. When a thermometer cell sees a digit already placed in its row, column or box, remove it from that cell and check whether the range collapses.

Practice

CageDoku includes a short Thermo tutorial and hints that name the technique and highlight the cells. Try a Thermo puzzle free in your browser, or get the app for Android.

Frequently asked questions

Can digits repeat on a thermometer?

No. They strictly increase from the bulb to the tip.

Is the bulb always the lowest digit?

Yes, the digit in the bulb is the smallest on its thermometer.

Where should a beginner start?

With short thermometers, where the range trick gives quick eliminations.

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