How to Solve Parcel (Shikaku): Rectangle Packing from Number Clues

Parcel is a rectangle-partition puzzle in the Shikaku family. Drag to outline rectangles that tile the entire grid. Each rectangle must contain exactly one clue, and that clue is the rectangle's exact area. A 6 can be a 1 by 6 rectangle or a 2 by 3 rectangle, in either orientation, provided it fits without crossing another rectangle.

The useful object is not the clue by itself. It is the set of all rectangles that could belong to that clue. Parcel becomes manageable when you compare those candidate sets and look for cells they all share.

Build a candidate list for the constrained clues

Prime numbers have only a 1 by N shape. Corner clues lose many orientations because rectangles cannot leave the board. Clues near other clues lose candidates that would contain both numbers. Start with those restricted cases.

You do not need to draw every candidate. Mentally test the factor pairs and note whether the clue can grow left, right, up, or down.

Look for overlap, not just a unique rectangle

A clue may have three possible rectangles, but all three may include the same cell. That cell is guaranteed to belong to the clue even before you know the final border. Guaranteed ownership can rule out candidates for neighboring clues.

This is often stronger than waiting for a clue to have exactly one complete shape.

Use other clues as hard walls

A rectangle cannot contain a second clue. When you test a candidate, stop its growth before it swallows another number. Dense clusters of clues therefore create many implied boundaries even when no rectangle has been drawn.

Small clues are especially useful walls. A 1 owns exactly its single cell, and a nearby 2 has very few ways to extend around it.

Read the remainder after every placement

Once a rectangle is fixed, forget its interior and study the new outline of the empty region. Has a clue become trapped in a strip of a particular width? Has an empty corner been created that only one clue can reach?

Parcel's best deductions often come from the shape you have not filled. A candidate that leaves a clue-free pocket or a one-cell orphan is impossible, even if the candidate itself has the correct area.

Large clues need room, so budget it early

A 12 or 16 can consume a substantial part of the board. Identify where its factor shapes could fit before surrounding small clues claim the space. This does not mean drawing the large rectangle immediately; it means preserving at least one legal footprint for it.

A disciplined way to test a rectangle

1. Does its width times height equal the clue?
2. Does it stay inside the grid?
3. Does it contain exactly one clue?
4. Does it avoid every fixed rectangle?
5. Can the remaining cells still be partitioned among the remaining clues?

Example: why a correct area can still be wrong

Imagine a clue of 6 near the left edge. Both a vertical 1 by 6 and a horizontal 2 by 3 rectangle fit the clue and stay on the board. The vertical option, however, might leave a single empty corner cell above a neighboring clue of 4. That clue cannot claim the corner and still form a rectangle of area 4, so the vertical 6 is impossible.

Nothing was wrong with the area calculation. The error appeared only when you inspected the remainder. This is why strong Parcel solving alternates between candidate generation and leftover-region analysis.

The fifth question separates a plausible rectangle from the right rectangle. If a draw turns out to be wrong, tap the finished rectangle to clear it and return to the candidate list. With practice, you will reject bad partitions before they ever reach the board.

A new Parcel puzzle is available every day. For more repetitions with the same rules, open Practice and choose Parcel.