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9×9 · Constraint

Slow Thermometer Sudoku

Also known as Slow Thermo Sudoku

A thermometer whose digits must never decrease from bulb to tip — they only need to stay level or rise.

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An example Slow Thermometer puzzle: digits never decrease from the bulb — they may repeat, here 3, 3, 6, 8.

Slow Thermometer Sudoku is a gentler thermometer. On a normal thermometer the digits must strictly increase from bulb to tip; on a slow thermometer they only have to be non-decreasing — each cell is greater than or equal to the one before it. The values may hold steady, so long as the ordinary Sudoku rules still allow it.

The rule: never go down (but you may stay level)

Read a slow thermometer from bulb to tip: every step is "≥" rather than ">". A strict thermometer must climb (2 < 4 < 5); a slow one may repeat a value where the thermometer bends into a different row, column or box, so a step like 4 ≤ 4 is legal.

●≤≤≤

Every step is ≤: the values rise or stay level from the bulb (left) to the tip.

A worked example, step by step

Where a slow thermometer runs inside one row (so no repeats are possible there), it still climbs strictly — but its cells can reach a touch further than a strict one. Take a four-cell slow thermometer whose bulb sits in a row that already contains a 1.

Step 1 — the bulb loses its smallest option. On a strict four-cell thermometer the bulb's window is 1–6. Here the row's 1 is taken, so the bulb climbs to 2–6.

●2–6≥ bulb≥

Step 1. With the 1 gone from the row, the bulb is 2–6; each later cell is ≥ the one before.

Step 2 — read up the tube. Each cell is at least as large as the last, so the tip carries the biggest value. Because equal steps are allowed only across a box or line border, a slow thermometer that stays inside one unit behaves like a strict one — the "slow" freedom pays off exactly where the thermometer bends.

Where the slow rule matters

The difference between slow and strict shows up whenever a thermometer crosses from one box (or line) into another. There, two touching cells may hold the same digit, because they no longer share a unit — something a strict thermometer forbids everywhere. That extra option makes long slow thermometers a little roomier than their strict cousins, but the "never decrease" backbone still drives every deduction.

Solving strategy

  • Still push from both ends. The bulb takes the smallest value, the tip the largest — just as with a strict thermometer.
  • Allow equals across borders. Where the tube crosses a box or line, neighbouring cells may match.
  • Inside one unit, treat it as strict. Cells sharing a row, column or box can't repeat, so there it climbs step by step.
  • Feed the grid. Each digit a thermometer fixes behaves like a given for its row, column and box.

Common mistakes

  • Allowing a decrease. Slow means non-decreasing — values may stay level but never fall.
  • Repeating inside one unit. Equal steps are only legal where the thermometer crosses into a different row, column or box.
  • Treating it exactly like a strict thermometer. The extra "equal" option loosens long tubes that bend between boxes.
  • Forgetting ordinary Sudoku. Thermometer cells still obey their rows, columns and boxes.

Can I play it here?

Not yet — Slow Thermometer 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: