How to solve curved thermometer puzzles
Curved thermometers follow the same rules as straight ones, but because they bend, one tube can sit in several rows and columns at once. That changes how you count and how far each deduction spreads.
Part of the complete guide to solving thermometer puzzles · lesson 6 of 10
Step 1: Trace from the bulb
On a straight puzzle you can read a thermometer at a glance. On a curved one, start at the round bulb and follow the tube to its flat tip. Number the cells 1, 2, 3… along the way, at least in your head. That numbering is the fill order, and it is all that matters for the rules: the first k cells are mercury and the rest are air.
Step 2: Count line by line, not tube by tube
Clues count cells per row and column, so you need to know how many cells a thermometer puts into each line at each fill level. Take this U-shaped thermometer, which starts at the bottom of column 1, climbs, turns, and comes back down column 2:
| Fill level | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Cells in row 4 | 0 | 1 | 1 | 1 | 1 | 1 | 2 |
| Cells in row 3 | 0 | 0 | 1 | 1 | 1 | 2 | 2 |
| Cells in row 2 | 0 | 0 | 0 | 1 | 2 | 2 | 2 |
Notice that its share of row 4 jumps from 1 to 2 only at full fill, because the second cell in row 4 is the tip. So if row 4 needs this thermometer to supply 2 cells, the whole thermometer must be full. If row 4 can only take 1 from it, the tip is air but nothing else is decided. This table is all the squeeze and ceiling need. The rule from that lesson gives a required range of cells, and the table converts it into a range of fill levels.
Step 3: Let flow carry deductions around corners
The flow rules (mercury back to the bulb, air forward to the tip) follow the tube, so on curved puzzles they cross lines. Here column 3 needs 3, the whole column:
The top-right cell is the tip of the L-shaped thermometer, so filling it fills all five of its cells: along row 1 and down column 1 to the bulb at the bottom. A single column clue has decided cells in all three rows and all three columns.
Habits that help on curved puzzles
- Look for tips in tight lines. If a line needs a cell that is the tip of a long curved tube, the whole tube is mercury. That is often the biggest single deduction on the board.
- Look for bulbs in empty lines. If a bulb sits in a line that must be all air, the whole thermometer is empty, wherever it goes.
- Watch for double visits. When a tube enters the same line twice, write down both positions. Mixing them up is the most common curved-puzzle mistake.
- Use hover highlighting. In our game, hovering over a cell highlights its row and column, which makes it easier to see which of a curved tube's cells fall in a line.
See it on a full puzzle
The curved 8×8 walkthrough applies all of this to a real puzzle. Look at how many steps decide cells outside the line being examined. That's flow working around corners.
Questions
Can a curved thermometer cross the same line twice?
Are the overlap and ceiling rules still valid?
Is there a difference in how the game handles curved puzzles?
Try a curved puzzle
Start with 6×6 curved and work up.