Area-clue rectangles
Partition the whole grid into rectangles certified by one area clue each.
Logic & rule checking
- Players
- 1–3
- Time
- 15–25 minutes
- Materials
- Printed puzzle, pencil and separate host key
Prepare
Use the 4×4 grid with A1=6,D1=2,A3=4,D4=4. Numbers occupy fixed cells; blank cells carry no clue. A rectangle consists of consecutive rows and columns and may be one cell wide.
Follow the rule
Draw boundaries along grid edges. Every cell must lie in exactly one rectangle. Each rectangle must contain exactly one numbered cell, and its area in cells must equal that number.
Check each step
A clue 6 permits 1×6,2×3,3×2 or 6×1 in principle, but the 4×4 board excludes the six-long choices. A shape with six cells but an L-shaped outline is not a rectangle.
Worked example
One solution takes A1:C2 as the six-cell rectangle, D1:D2 as the two-cell rectangle, A3:B4 and C3:D4 as four-cell rectangles. The four areas total 16 and each contains exactly one clue.
Finish and adapt
Check straight rectangular boundaries, area, one clue and full coverage separately. Do not accept merely because areas total 16: overlap can conceal a gap. Any valid partition is accepted; this page does not establish unique solvability.
Purpose, observation and provenance
Within this activity: Partition the whole grid into rectangles certified by one area clue each.
Check each constraint independently rather than compare only with the sample answer.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
Official mechanism reference / 官方机制规则 — Background rules only; all small boards, examples and explanatory text are prepared for this kit. No publisher artwork is reproduced.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
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.
Area-clue rectangles · Player sheet
Before you begin
- Use the 4×4 grid with A1=6,D1=2,A3=4,D4=4. Numbers occupy fixed cells; blank cells carry no clue. A rectangle consists of consecutive rows and columns and may be one cell wide.
- Draw boundaries along grid edges. Every cell must lie in exactly one rectangle. Each rectangle must contain exactly one numbered cell, and its area in cells must equal that number.
- A clue 6 permits 1×6,2×3,3×2 or 6×1 in principle, but the 4×4 board excludes the six-long choices. A shape with six cells but an L-shaped outline is not a rectangle.
| Proposed cells / boundaries | Constraint checked |
|---|---|
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |
Area-clue rectangles · Host key — keep separate
Rectangles A1:C2,D1:D2,A3:B4,C3:D4 have areas 6,2,4,4.
Read the rules as well as this example. Other valid solutions may exist for the puzzle boards. This key is not a claim of uniqueness or measured learning gains.
| Constraint / action | Evidence / correction |
|---|---|
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |
Related activities
Activity library · Rectangle packing puzzle — Printable Materials & Rules