Thermometer prefix grid
Fill only continuous prefixes from each thermometer bulb to satisfy every row and column total.
Logic & rule checking · Shape & spatial thinking
- Players
- 1–4 cooperative
- Time
- 12–20 minutes
- Materials and quantities
- One 4×4 grid with four labelled thermometer paths and row/column totals; pencil.
1–4 cooperative
Prepare
Rows count bottom-up. Four disjoint paths cover the board: A1→B1→B2→A2; C1→D1→D2→C2; A3→A4→B4→B3; C3→D3→D4→C4. The first cell in each path is the bulb, regardless of how its curve looks.
Play
For each path choose a fill length from 0 to 4. Length 0 fills nothing; length 2 fills its first two cells. You may never fill a later cell while skipping an earlier one. Row totals from row 1 to 4 are 4,1,3,2; column totals A–D are 2,2,3,3.
Example
Length 3 on path A1→B1→B2→A2 fills A1,B1,B2 but leaves A2 white. Filling A2 alone is invalid. Row 1’s total 4 forces all its four cells to fill; use each path’s order to reason about later rows.
Finish
Record all four prefix lengths and count every row and column independently. The key supplies one checked length vector; no unique-solution claim is made. A fill that reaches the totals but contains a gap inside a thermometer is not valid.
Adapt
Place large removable markers following a written path before looking at all totals. Keep the coordinate list visible. This is a logic puzzle, not a temperature reading or a device for measuring children.
Aim: Fill only continuous prefixes from each thermometer bulb to satisfy every row and column total.
Practice within this activity: Fill only continuous prefixes from each thermometer bulb to satisfy every row and column total.
Adult observation: Ask the participant to explain one legal choice. Accept passing and a partner writing; do not infer a lasting ability from a single round.
Mechanism and adaptation: A separately written PartyPageKit version of the mechanism described below, with original examples and materials. The earliest inventor is not established here.
Goals describe observable activity choices, not measured long-term gains or institutional endorsement.
Free alternatives: Copy the four coordinate paths and totals onto a hand-drawn grid; a circled first cell marks the bulb.
Buying recommendations reserved; no purchase required.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Player thermometer paths
Bulb = first coordinate. Row totals 1→4: 4,1,3,2; columns A→D: 2,2,3,3. Fill only a continuous prefix from each bulb.
Player ordered path list and lengths
| Path order | Fill length 0–4 |
|---|---|
| A1 → B1 → B2 → A2 | ________ |
| C1 → D1 → D2 → C2 | ________ |
| A3 → A4 → B4 → B3 | ________ |
| C3 → D3 → D4 → C4 | ________ |
Teacher instructions and checked example · separate
1–4 cooperative
One 4×4 grid with four labelled thermometer paths and row/column totals; pencil.
Copy the four coordinate paths and totals onto a hand-drawn grid; a circled first cell marks the bulb.
Print only the relevant player pages; keep this teacher page separate. Read the full web rules before leading. A helper may write or move pieces, and anyone may pause or pass. No classroom or physical-printer trial is claimed.
One valid length vector is 3,2,1,4. It gives row counts 4,1,3,2 and column counts 2,2,3,3. Inspect path order as well as totals.