All Sudoku Variants
9×9 · Constraint

Thermo Sudoku

Also known as Thermometer Sudoku

Digits along a thermometer must strictly increase from the bulb to the tip.

3 62479

An example Thermo puzzle: digits increase from the bulb (darker) along the thermometer — 2, 4, 7, 9.

Thermometer Sudoku — usually shortened to Thermo — draws grey thermometers across the grid. Each one starts at a rounded bulb and runs along a thin stem to its tip. The single rule is beautifully simple: the digits must increase as you move away from the bulb. That one idea, applied along every thermometer, turns a nearly empty grid into a puzzle you can solve by pure logic.

The rule: always uphill from the bulb

Read a thermometer from its bulb to its tip and the numbers must go strictly up — each cell holds a larger digit than the one before it. There is never a plateau and never a dip: on a standard thermometer, equal or falling values are both forbidden. Everything else is ordinary Sudoku, so each thermometer cell still has to obey its row, column and box.

●24579

The bulb is on the left. Values rise strictly along the stem: 2 < 4 < 5 < 7 < 9.

Reading a thermometer: how length pins the ends

The real power of a thermometer is that its length squeezes both ends of the number range at once. Because every step must go up by at least one, a thermometer of five cells cannot start too high or finish too low. The bulb needs at least four larger digits above it, so it can be at most 5; the tip needs at least four smaller digits below it, so it must be at least 5. Work inward and every cell gets its own window.

●1–52–63–74–85–9

A five-cell thermometer forces a window on every cell — the bulb can be at most 5, the tip at least 5, before any other clue is used.

Those windows are candidates you can pencil in immediately, and they interact with the rest of the grid at once. If a row already contains the 5, the bulb above drops to 1–4; if a box rules out 9, the tip falls to 5–8. A long thermometer is one of the most constraining features in all of Sudoku — an eight- or nine-cell thermometer can fix most of its cells before you place a single ordinary digit.

Solving strategy

  • Start with the longest thermometers. The more cells a thermometer has, the tighter its windows — a nine-cell thermometer spells out 1-2-3-4-5-6-7-8-9 exactly.
  • Push from both ends. Set the smallest window at the bulb and the largest at the tip, then meet in the middle.
  • Feed the ordinary grid. Every value a thermometer forces behaves like a given for its row, column and box — chase the singles it creates before returning to the thermometers.
  • Watch shared cells. Where two thermometers cross or a bulb sits in a busy box, the two constraints together often nail a single digit.

A worked example, step by step

Let's solve a real one. Here is a row whose left five cells form a thermometer (bulb on the left), and whose right four cells are already filled with 2, 4, 6 and 8.

2 4 6 8●

Step 0. The setup: a five-cell thermometer and the givens 2, 4, 6, 8.

Step 1 — find the remaining digits. The row already uses 2, 4, 6 and 8, so the thermometer must contain the five that are left: 1, 3, 5, 7 and 9. Because the thermometer must climb from bulb to tip, the smallest of those (1) is forced into the bulb and the largest (9) into the tip.

2 4 6 8●19

Step 1. Smallest remaining (1) fills the bulb, largest (9) the tip.

Step 2 — fill the middle in order. Three digits are left for the three middle cells: 3, 5 and 7. There is only one way to place them and still keep climbing — 3, then 5, then 7 — so the thermometer completes itself.

2 4 6 8●13579

Step 2. The middle falls into place: 1-3-5-7-9, and the whole row is solved.

That is the Thermo rhythm in miniature: the length of the thermometer and a few givens decide which digits are available, and the "always climbing" rule then forces their order. On a full grid the same reasoning ripples outward — every digit the thermometer fixes acts as a fresh given for its column and box.

Common mistakes

  • Allowing equal values. A standard thermometer is strictly increasing — never repeat a value along it. (The gentler "slow thermometer" variant does allow equal steps, but the plain version does not.)
  • Reading it from the wrong end. Values increase away from the bulb; if you start at the tip you will invert every deduction.
  • Ignoring the length limit. The number of cells caps the ends before any digit is placed — solvers who skip that miss the easiest deductions in the puzzle.
  • Forgetting normal Sudoku. A thermometer cell still cannot repeat a digit in its row, column or box; the thermometer rule is an extra constraint, not a replacement.

Can I play it here?

Not yet — Thermo Sudoku isn't one of the puzzle types SudokuStreak generates for now. But you can learn its rules above, and there's plenty here to sink your teeth into meanwhile: