Corner-only polyominoes
Place whole shapes while distinguishing corner contact from shared edges.
Shape & spatial thinking
- Players
- 2 players
- Time
- 15–25 minutes
- Materials
- 8×8 grid and five shapes per player drawn on squared paper.
Prepare
Each has a monomino 1, domino 2, straight triomino 3, L triomino 3 and 2×2 square 4. Draw or cut one of each in two labelled sets. On the 8×8 board, white’s first shape must cover A1; black’s must cover H8. A shape may be rotated or flipped.
Play
White goes first. Alternate placing one unused whole shape on empty cells. After your first placement, it must touch at least one of your earlier shapes at a corner, and must share no edge with any of your own occupied cells. Contacts with the opponent may be by edge or corner. Shapes cannot overlap or leave the board.
Worked example
If white begins with a single cell at A1, a white domino occupying B2,C2 is legal: B2 touches A1 only at a corner. A domino at A2,B2 is illegal because A2 shares an edge with A1. Every square of a new piece is checked, not just one anchor cell.
Finish and check
If no legal placement remains for any unused shape, pass. End when both pass consecutively or all pieces are placed. Fewer unplaced unit squares wins; the total starting area is 13 per player. Equal unused area is a draw; no bonus for the monomino.
Adaptation and limits
Mark each cell with W or B as well as optional colours. Large drawings with outlines can replace cut pieces. The small piece set is our teaching game, not a copied commercial board or balance claim. Use tracing to check an uncertain orientation.
Purpose, observation and provenance
Within this activity: Place whole shapes while distinguishing corner contact from shared edges.
Ask which own corner connects a piece and whether any own edge also touches.
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.
Player materials · Corner-only polyominoes
Each set: single; domino; straight 3; L3; square 4. Starting area 13.
Example white A1; candidate B2,C2 versus A2,B2.
Cards / pieces · prepare before play
Trace or cut at one identical scale: unit squares must match board cells. Two labelled sets; cut each full outline.
Player record · keep the host key separate
| Piece | Cells | Corner contact | Edges checked |
|---|---|---|---|
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
Host key · separate from players
B2,C2 legal after A1; A2,B2 illegal. Total 1+2+3+3+4=13.
Run the round
Each has a monomino 1, domino 2, straight triomino 3, L triomino 3 and 2×2 square 4. Draw or cut one of each in two labelled sets. On the 8×8 board, white’s first shape must cover A1; black’s must cover H8. A shape may be rotated or flipped.
White goes first. Alternate placing one unused whole shape on empty cells. After your first placement, it must touch at least one of your earlier shapes at a corner, and must share no edge with any of your own occupied cells. Contacts with the opponent may be by edge or corner. Shapes cannot overlap or leave the board.
If white begins with a single cell at A1, a white domino occupying B2,C2 is legal: B2 touches A1 only at a corner. A domino at A2,B2 is illegal because A2 shares an edge with A1. Every square of a new piece is checked, not just one anchor cell.
If no legal placement remains for any unused shape, pass. End when both pass consecutively or all pieces are placed. Fewer unplaced unit squares wins; the total starting area is 13 per player. Equal unused area is a draw; no bonus for the monomino.
Mark each cell with W or B as well as optional colours. Large drawings with outlines can replace cut pieces. The small piece set is our teaching game, not a copied commercial board or balance claim. Use tracing to check an uncertain orientation.
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