Pearl turn loop
Build one loop that treats black and white pearls with different turn rules.
Logic & rule checking
- Players
- 1–3
- Time
- 15–25 minutes
- Materials
- Printed puzzle, pencil and separate host key
Prepare
Use the 4×4 board. Black pearls sit at A1,D1,A4,D4; white pearls at B1,C1. Draw between cell centres by orthogonal steps. Coordinates increase from bottom to top.
Follow the rule
The loop must pass through all pearls, close into one component and never cross, branch or revisit a cell. It may leave other cells unused. A border drawn around cells is not the route: the route runs through centres.
Check each step
At a white pearl go straight and turn in at least one immediately neighbouring route cell. At a black pearl turn 90 degrees, then go straight through the next route cell on both sides of that turn.
Worked example
The perimeter-cell route A1–B1–C1–D1–D2–D3–D4–C4–B4–A4–A3–A2–A1 works. At B1 the nearby turn is A1; at C1 it is D1. Both cells beside each black pearl are straight.
Finish and adapt
Check every pearl locally and then trace the whole route globally. A pair of separate valid-looking loops fails the one-loop rule. The host route is one valid answer; this small page is not a random puzzle generator or uniqueness certificate.
Purpose, observation and provenance
Within this activity: Build one loop that treats black and white pearls with different turn rules.
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.
Pearl turn loop · Player sheet
Before you begin
- Use the 4×4 board. Black pearls sit at A1,D1,A4,D4; white pearls at B1,C1. Draw between cell centres by orthogonal steps. Coordinates increase from bottom to top.
- The loop must pass through all pearls, close into one component and never cross, branch or revisit a cell. It may leave other cells unused. A border drawn around cells is not the route: the route runs through centres.
- At a white pearl go straight and turn in at least one immediately neighbouring route cell. At a black pearl turn 90 degrees, then go straight through the next route cell on both sides of that turn.
| Proposed cells / boundaries | Constraint checked |
|---|---|
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |
Pearl turn loop · Host key — keep separate
Use all 12 perimeter cells as one centre-to-centre loop; inner four cells remain unused.
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 · Single-loop clue squares: rules and printable materials