Disjoint number paths
Connect matching endpoints without crossing, branching or sharing a cell.
Logic & rule checking
- Players
- 1–3
- Time
- 15–25 minutes
- Materials
- Printed puzzle, pencil and separate host key
Prepare
Use the 4×4 board with pair 1 at A1,D1; pair 2 at A2,D2; pair 3 at A3,D4. Keep every endpoint fixed. Work together rather than erase another player’s path as a competitive move.
Follow the rule
Draw a path through cell centres with orthogonal steps between each matching pair. A path may turn but may not revisit a cell. It must not pass through any other numbered endpoint.
Check each step
Different paths cannot share a cell, cross or branch. This kit does not require all unnumbered cells to be used: do not add that condition from another app or puzzle variant.
Worked example
Pairs 1 and 2 can each run straight along their own rows. Pair 3 can take A3–B3–C3–C4–D4. These paths leave several white cells unused; that is allowed here.
Finish and adapt
Check each endpoint degree one and every internal used cell degree two; confirm that the three routes are separate. Accept any legal set of routes. Copy to a clean sheet for another attempt; the supplied answer demonstrates feasibility, not uniqueness.
Purpose, observation and provenance
Within this activity: Connect matching endpoints without crossing, branching or sharing a cell.
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.
Disjoint number paths · Player sheet
Before you begin
- Use the 4×4 board with pair 1 at A1,D1; pair 2 at A2,D2; pair 3 at A3,D4. Keep every endpoint fixed. Work together rather than erase another player’s path as a competitive move.
- Draw a path through cell centres with orthogonal steps between each matching pair. A path may turn but may not revisit a cell. It must not pass through any other numbered endpoint.
- Different paths cannot share a cell, cross or branch. This kit does not require all unnumbered cells to be used: do not add that condition from another app or puzzle variant.
| Proposed cells / boundaries | Constraint checked |
|---|---|
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |
Disjoint number paths · Host key — keep separate
1 A1–B1–C1–D1; 2 A2–B2–C2–D2; 3 A3–B3–C3–C4–D4.
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 |
|---|---|
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |