L-piece reposition
Reposition an L-shaped piece while preserving one legal space for the next turn.
Logic & rule checking
- Players
- 2
- Time
- 15–25 minutes
- Materials
- 4×4 board; two L tetrominoes; two neutral squares
Prepare
Two players each own one L made of three cells in a line plus one attached at an end. Number cells A1–D4. Start W on A1,A2,A3,B1; B on D2,D3,D4,C4; neutrals on B2,C3. Pieces may not overlap or leave the board.
Play
On a turn lift your entire L and replace it in a different set of four cells, rotating or reflecting it if desired. Every destination cell must be empty after lifting your own piece. The opponent and neutral squares stay fixed during that placement.
Worked example
After a legal L move, optionally move exactly one neutral square to any empty cell. You may leave both neutrals unchanged. Moving only a neutral without relocating your L is not a turn.
Finish and check
For the starting W move, B1,B2,B3,C1 is blocked by neutral B2; it is illegal. A2,A3,A4,B4 is empty after lifting W and forms a legal L. After placing there, neutral B2 may move to A1.
Adaptation and limits
If the active player has no legal different L placement, that player loses. For a short session stop after 40 turns and call it a draw if neither is trapped. Record each L’s four coordinates and any neutral move; paper outlines can replace cut pieces.
Purpose, observation and provenance
Within this activity: Reposition an L-shaped piece while preserving one legal space for the next turn.
A partner can replay each legal action and explain the stopping condition; this is an observable task, not evidence of lasting improvement.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
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.
Rules to keep beside the materials
- Two players each own one L made of three cells in a line plus one attached at an end. Number cells A1–D4. Start W on A1,A2,A3,B1; B on D2,D3,D4,C4; neutrals on B2,C3. Pieces may not overlap or leave the board.
- On a turn lift your entire L and replace it in a different set of four cells, rotating or reflecting it if desired. Every destination cell must be empty after lifting your own piece. The opponent and neutral squares stay fixed during that placement.
- After a legal L move, optionally move exactly one neutral square to any empty cell. You may leave both neutrals unchanged. Moving only a neutral without relocating your L is not a turn.
- For the starting W move, B1,B2,B3,C1 is blocked by neutral B2; it is illegal. A2,A3,A4,B4 is empty after lifting W and forms a legal L. After placing there, neutral B2 may move to A1.
- If the active player has no legal different L placement, that player loses. For a short session stop after 40 turns and call it a draw if neither is trapped. Record each L’s four coordinates and any neutral move; paper outlines can replace cut pieces.
L-piece reposition — player materials
| Turn1–40 | L four cells | Optional neutral move |
|---|---|---|
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
Host check — keep separate
W may move to A2,A3,A4,B4; B1,B2,B3,C1 is blocked at B2.
Examples are stipulated model cases, not measured experimental or learning outcomes.