CoverletHow to solve a 5x5 Shikaku puzzle step by step
A 5x5 board is small enough to see as a whole and rich enough to teach the habits that scale to larger Shikaku puzzles.
By Mourad Hamdi · Last reviewed
Try the logic
Paint four patches. Leave no gaps.
Choose a number, tap the cells that belong to it, then check the board. The areas are 6, 4, 3, and 12—together they cover every square exactly once.
Choose 6, then paint its six cells.
1. Start with the board, not a favourite clue
Before placing anything, scan all 25 cells. Mark the clues at corners and edges, note any 1s, and look for numbers whose factor pairs are limited by the five-cell width. A quick whole-board scan prevents you from committing to a shape just because it looks convenient.
2. Use area and factor pairs
Write the possible dimensions beside each clue. For example, a 6 can be 1x6, 2x3, 3x2, or 6x1, but a 1x6 rectangle cannot fit across a five-column board. A 4 has 1x4, 4x1, and 2x2; a 3 has only a strip. Remove dimensions that run off the board before considering neighbours.
3. Lock the forced edges
A corner clue must own the corner cell, so its rectangle can only extend in two directions. An edge clue cannot extend through the outside of the board. If one candidate is the only shape that covers an exposed corner or avoids another clue, it is a deduction, not a guess. This is where small boards become teachable: the boundary does much of the work.
4. Propagate from finished patches
After confirming a rectangle, treat every cell it covers as unavailable to the remaining clues. Recalculate nearby candidates and ask which empty cell has only one possible owner. A 5x5 example with areas 6, 4, 3, and 12 is available in the interactive rectangle guide; use the check button to see how a local placement affects the complete partition.
5. Check the final cover
A solved Shikaku board has one rectangle per clue, the correct area for every rectangle, no overlapping cells, and no empty cells. Count the areas as a final sanity check: on a 5x5 board they must add to 25. If the total is right but a gap remains, one rectangle boundary is still wrong; return to the closest unresolved clue instead of guessing at the last square.
See the whole board before placing a rectangle
A 5x5 Shikaku board is small enough to inspect as one object, which is exactly why it is a useful practice board. Before drawing a boundary, count the 25 cells and note where every clue sits. Mark corners, edges, isolated cells, and any clue that has very few possible dimensions. The first goal is not to solve the most interesting number. It is to understand the spaces that are already constrained by the board boundary. A rectangle must contain exactly one clue, its area must equal that clue, rectangles cannot overlap, and the rectangles must cover the board without gaps. Keep those four rules visible while you scan. If a clue is near a corner, it has fewer directions in which its rectangle can extend. If a clue is in the centre, it may have more choices, so leave it until surrounding deductions reduce them. The board is a set of relationships, not a collection of independent mini-problems.
List the factor pairs for each clue
Area gives you the first shortlist. A clue marked 1 can only be a one-cell rectangle. A clue marked 2 can be a 1x2 or 2x1 strip. A clue marked 3 can be a 1x3 or 3x1 strip. A clue marked 4 can be a 1x4 strip, a 4x1 strip, or a 2x2 square. For a clue marked 6, the mathematical options include 1x6, 6x1, 2x3, and 3x2, but a 5x5 board immediately removes the six-cell strips because they cannot fit in either dimension. Do this removal before you think about neighbouring clues. Then draw each remaining candidate lightly in your notes or imagine its occupied cells. A candidate is useful only if it fits inside the board and contains no other clue. The factor pair is not the solution; it is the beginning of a finite list. Writing the list prevents a common mistake: treating the first shape that looks plausible as if it were forced.
Lock deductions at corners and edges
Boundary clues often provide the cleanest deductions. A corner cell must belong to the rectangle of one clue, and a rectangle that owns that corner can extend only along the two directions available inside the board. An edge clue cannot cross the outside boundary, so some orientations disappear immediately. For each candidate, ask whether it covers a required corner or edge cell, whether it would include another clue, and whether it would leave a neighbouring cell with no possible owner. If only one candidate survives those questions, place it. This is a proof, not a guess. Keep the rectangle boundary exact: if a clue has area 4, a long strip and a 2x2 square are different candidates even though both contain four cells. On a small board, one forced edge can remove several candidates nearby. That propagation is the reason to solve the boundary first rather than spending time debating a central clue with many symmetrical options.
Propagate every confirmed patch
Once a rectangle is confirmed, treat all of its cells as unavailable to the remaining clues. Then rescan the board. A clue that previously had three candidate shapes may now have one because a neighbouring cell is occupied. An empty cell may also become informative: if only one unresolved clue can reach it with a valid area, that clue must own it. This is often more reliable than asking which number looks easiest. Continue alternating between candidate lists and empty-cell coverage. If a proposed rectangle leaves a nearby clue with no legal shape, reject it before it spreads confusion. The Coverlet Patchwork board uses the same satisfying area-and-boundary idea, while the interactive rectangle guide gives a compact example of checking a local placement against the whole partition. The habit to practise is not speed. It is updating the board after every certain move so that old possibilities do not remain in your head after they have become impossible.
Finish with an exact cover check
A solved 5x5 Shikaku must pass four checks. Every rectangle contains exactly one clue. Every rectangle's area matches its clue. No rectangles overlap. No cells are left uncovered. The clue areas should also add to 25, the total number of board cells, but the arithmetic is only a sanity check: matching totals cannot reveal an overlap paired with a gap. Inspect the boundaries row by row and column by column. If the last empty cell does not fit, do not invent a tiny patch to make the picture look complete. Return to the nearest unresolved clue and review which candidate was removed and why. A late contradiction usually points to an earlier assumption, not to a mysterious exception in the rules. With practice, the board becomes a chain of small certainties: a corner forces an orientation, an edge removes a factor pair, a finished rectangle limits its neighbours, and the final cover confirms that the whole chain is consistent. That is the transferable skill a 5x5 board teaches. If you are practising on paper, use a light pencil or a separate candidate list so that a rejected boundary does not become a false rule. If you are using an interactive board, prefer an undo action and a clear check state over an opaque error sound. Then replay the solve once after completion and name the deductions that actually forced the answer. That short review builds a reusable method: area first, boundaries next, propagation throughout, and exact coverage at the end. This review also makes future boards faster without turning speed into the goal today.
For more practice, compare this 5x5 method with the full beginner strategy, then try Patchwork when you want a fresh daily board.
References
APA 7 references for the research discussed in this article. Last checked 21 Aug 2026.
Frequently asked
Questions about this puzzle
Why practise on a 5×5 board?
A 5×5 board is small enough to scan at once, but it still teaches factor pairs, edge constraints, propagation, and the final area check.
What should the clue areas add up to?
They should add up to 25, the total number of cells on a 5×5 board. The sum is a useful final check, but it does not replace checking each boundary.
What if I reach the last empty cell and it does not fit?
Return to the nearest unresolved clue and review its candidate rectangles. A late gap usually means an earlier boundary was assumed rather than proved.
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