Patches is a tiling puzzle — cover the entire grid with non-overlapping squares and rectangles, each containing exactly one numbered clue. The number tells you the area (cell count) of that rectangle. This guide covers clue prioritization, shape constraints, and layout planning.

## How clues work

Each numbered cell is a **clue** — it must sit inside exactly one rectangle, and that rectangle's total cell count must match the number.

Some clues also show a **shape hint**:

| Hint | Meaning |
|------|---------|
| Square | Rectangle must be a perfect square (e.g. 4, 9 cells) |
| Tall | Height greater than width |
| Wide | Width greater than height |
| Any | No shape restriction beyond area |

A clue with number **1** is always a 1×1 square — place it immediately.

## Solve strict clues first

Prioritize clues in this order:

1. **Area 1** — single-cell rectangles.
2. **Clues with shape hints** — few legal dimensions (e.g. area 4 + square = only 2×2).
3. **Large area clues** — they consume significant grid space and constrain neighbors.
4. **Ambiguous small clues** — multiple rectangle shapes fit; save for last.

Every rectangle you place **removes** cells from the grid. Strict clues shrink the remaining space and make ambiguous clues easier.

## Dimension table for common areas

| Area | Possible rectangles (w×h) |
|------|---------------------------|
| 2 | 1×2, 2×1 |
| 3 | 1×3, 3×1 |
| 4 | 1×4, 4×1, 2×2 |
| 6 | 1×6, 6×1, 2×3, 3×2 |
| 8 | 1×8, 8×1, 2×4, 4×2 |
| 9 | 1×9, 9×1, 3×3 |

Shape hints eliminate rows from this table. Area 4 with a square hint → only 2×2.

## Large rectangles anchor the grid

A 6-cell or 8-cell clue often dominates a corner or edge. Placing it early prevents smaller clues from fragmenting that zone.

Before drawing a large rectangle, check:

- Does it block another clue from fitting any legal shape?
- Does it leave odd-sized gaps that cannot be tiled?

If a large placement creates an isolated 1- or 2-cell gap with no clue, undo and try a different dimension.

## No overlaps, no gaps

The grid must be **perfectly tiled**. Common failure modes:

- Two rectangles overlap — the board rejects the overlap.
- Unclued cells remain — every cell belongs to exactly one rectangle.
- A clue sits outside its rectangle — the clue cell must be inside the shape you draw.

## Work from corners and edges

Corners and edges limit rectangle orientation:

- A clue in the corner cannot extend outside the grid — only one or two orientations work.
- Edge clues cannot grow past the boundary — use that to fix width or height.

## Undo and hints

Patches rewards trial and error within logic bounds:

- Draw a rectangle, see what gaps remain, undo if the layout fails.
- **Get hint** suggests a rectangle with an explanation.
- **Full solution** reveals placements one at a time.

## Practice path

| Step | Link |
|------|------|
| Rules | [Patches how-to-play](/patches/how-to-play) |
| Demo | [Patches demo](/patches/demo) |
| Practice | [Random Patches](/patches/random) |
| Archive | [Patches archive](/patches/archive) |

Patches combines spatial reasoning with arithmetic — the best solvers think in areas and dimensions, not individual cells.