Domino pair cover
Cover a numeric rectangle with the complete double-two pair inventory.
Logic & rule checking
- Players
- 1–3
- Time
- 15–25 minutes
- Materials
- Printed puzzle, pencil and separate host key
Prepare
The player sheet has 3 rows of 4 cells. Its rows from bottom to top are 0,0,0,1 / 0,2,1,1 / 1,2,2,2. Required unordered pairs are 00,01,02,11,12,22, one of each. This is a reduced double-two set.
Follow the rule
Draw boundaries so each tile covers exactly two orthogonally adjacent cells. Every cell must belong to one tile. The two printed digits determine that tile’s pair; 01 and 10 are the same pair.
Check each step
Use every required pair once. Two neighbouring zeros elsewhere do not entitle you to use a second 00. Cross out a pair on the inventory only after recording its two coordinates.
Worked example
One solution pairs the first two and last two cells in every row. It produces 00,01 in row 1; 02,11 in row 2; 12,22 in row 3. Count six tiles and twelve covered cells.
Finish and adapt
Finish when coverage and pair inventory both agree. Another covering is accepted if it satisfies both; no uniqueness claim is made. Use pencil outlines or paper rectangles instead of commercial dominoes. Keep the answer page separate during solving.
Purpose, observation and provenance
Within this activity: Cover a numeric rectangle with the complete double-two pair inventory.
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.
Domino pair cover · Player sheet
Before you begin
- The player sheet has 3 rows of 4 cells. Its rows from bottom to top are 0,0,0,1 / 0,2,1,1 / 1,2,2,2. Required unordered pairs are 00,01,02,11,12,22, one of each. This is a reduced double-two set.
- Draw boundaries so each tile covers exactly two orthogonally adjacent cells. Every cell must belong to one tile. The two printed digits determine that tile’s pair; 01 and 10 are the same pair.
- Use every required pair once. Two neighbouring zeros elsewhere do not entitle you to use a second 00. Cross out a pair on the inventory only after recording its two coordinates.
| A | B | C | D | |
|---|---|---|---|---|
| 3 | 1 | 2 | 2 | 2 |
| 2 | 0 | 2 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 |
| Pair | Cell 1 | Cell 2 |
|---|---|---|
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
Domino pair cover · Host key — keep separate
Horizontal pairs A1B1,C1D1,A2B2,C2D2,A3B3,C3D3 use every pair once.
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 · Double-three number chain: rules and printable materials