From your first 3×3 to Legend-tier 8×8 boards — the techniques that turn staring into solving.
Shikaku has only four rules, so getting better is not about learning more rules — it is about learning to see constraints faster. The tips below are ordered from the moves you should make on every board to the deeper deductions that separate Master-level solvers from everyone else. If you need a refresher on the basics first, read the complete Shikaku rules or the beginner's guide, then come back here and play with these in mind.
A 1 is always a single cell — draw it immediately. A 2, 3, 5, or 7 can only be a straight strip, because primes have no other rectangular factorisation. That means a prime has at most two orientations, and if it sits near an edge, often only one fits. On most beginner boards, placing the 1s and primes alone reveals half the solution.
A number in the middle of the grid can extend in four directions. On an edge it has three. In a corner, two. Fewer directions means fewer candidate rectangles, which means faster certainty. Scan the perimeter first, resolve what you can, then let those placements push constraints toward the centre.
Counter-intuitively, big numbers are often easier than mid-sized ones. An 8 on a 6-wide board cannot be 1×8, so it is 2×4 or 4×2 — and a block that size collides with almost everything around it. List the possible positions, strike out each one that overlaps another number or runs off the grid, and you will usually find one survivor. The same is true of 9 (always 3×3 on boards under 9 wide) and 12 (2×6 or 3×4).
Before committing a rectangle, count its cells. On GridPaw the game rejects a wrong-sized rectangle, but on paper — and in your head while planning — miscounting a 2×3 as 5 cells is the most common beginner error. Say the dimensions out loud: "two by three, six." It sounds trivial. It prevents the majority of early mistakes.
All the numbers on a valid board add up to the total cell count. When you are unsure whether a region of the grid can be tiled by the numbers inside it, add them up. If the numbers in the bottom two rows sum to more than 2 × width, at least one of them must extend upward. Simple arithmetic, powerful constraint.
This is the single most important Shikaku technique. Pick an empty cell and ask: which unplaced numbers could possibly include this cell in a legal rectangle? Check each candidate — can a rectangle of that number's area reach from the number to this cell without crossing another number or a placed rectangle? If exactly one number can, that number must cover the cell. You now know one cell of its rectangle for certain, which usually pins the shape. Cells in tight corners and cells far from any number are the best places to look.
When two numbers both have several candidate shapes, look for cells that every candidate of one number must include. Those cells are certain for that number, so no other number's rectangle may use them. Strike them out of the neighbours' candidate lists. Frequently this collapses a neighbour to a single option, which then collapses the next one — you have started a chain.
Each rectangle you draw changes the board. Make a habit of re-scanning the numbers adjacent to your last rectangle before looking anywhere else. The new wall you just created is the most likely place for a number to have lost all but one of its options.
When one placement forces another, do not stop after two steps. Keep asking "what does this force?" until nothing new is forced. On Medium and Hard boards, a single well-chosen prime can trigger a chain that resolves six or seven rectangles in a row. Solvers who stop chains early end up re-deriving the same facts later.
On a 5×6 or 7×8 board, the two orientations of a shape are not symmetric. A 1×5 strip fits horizontally on a 5-wide board but leaves no slack, while vertically on a 6-tall board it has two positions. Always note the grid dimensions before you begin and remember which axis is the tight one.
When a number has exactly two candidate shapes and nothing directly eliminates either, place one mentally and follow the consequences for three or four moves. If you reach an impossible situation — a cell nothing can reach, a number with no legal shape — the candidate you tested is wrong, and the other one is proven. This is not guessing: you are constructing a proof by contradiction. With practice you can run these tests entirely in your head; on GridPaw you can also draw the test rectangle and Undo if it fails.
For each unplaced number, imagine the union of every legal rectangle it could still form — its "shadow." Cells outside every number's shadow are impossible and signal a mistake elsewhere. Cells inside exactly one shadow are orphan cells (Tip 6) in disguise. Cells where two shadows overlap are the contested territory where the real decisions live. Seeing the board as overlapping shadows rather than as isolated numbers is what lets strong players read a Legend board in under a minute.
Sometimes a placement is legal now but leaves a region whose remaining numbers cannot tile it. Before committing a rectangle that closes off part of the grid, count the cells in the closed region and the numbers trapped inside it. If they do not match, the placement is wrong even though nothing overlaps yet. This partition check catches errors two or three moves before they would surface.
On dense boards, find the area with the highest ratio of numbers to empty cells. Constraints there are strongest, and resolving it releases information outward. Working from the loosest region inward is the classic way to end up with an unsolvable-looking corner that was in fact determined from the start.
Certain configurations recur constantly: a 4 in a corner next to a 2 on the edge (the 4 is almost always the square); two primes on the same edge pointing at each other; a large number in the centre whose only fit is symmetric. Each time you resolve a pattern, name it. Named patterns become instant recognitions, and instant recognitions are what speed is made of.
| Stage | Play these levels | Focus on |
|---|---|---|
| Week 1 | Tutorial & Easy (1–10) | Tips 1–5. Never draw without counting. |
| Week 2 | Medium (11–16) | Tip 6 only. Find one orphan cell per board before anything else. |
| Week 3 | Medium-Hard & Hard (17–30) | Tips 7–10. Follow every chain to the end. |
| Week 4+ | Expert, Master, Legend (31+) | Tips 11–15. Zero hints as the goal. |
Progress on GridPaw is saved automatically, so you can follow this plan in short sessions. The Daily Challenge is a good benchmark: when you can finish it without hints on most days, you are solving at an advanced level.
Place every 1 as a single cell, then look at prime numbers (2, 3, 5, 7) sitting in corners or on edges. Primes can only form straight strips, and edges cut their options in half, so these are the most reliable opening deductions.
Practise one technique at a time. Spend a few boards only looking for orphan cells (empty cells that just one number can reach). Then spend a few boards only counting area. Isolating techniques builds recognition faster than solving casually.
List every shape (for 12: 1×12, 2×6, 3×4 and their rotations), then eliminate each one that runs off the grid or contains a second number. Large numbers usually have only one or two survivors because they collide with so many neighbours.
Stop looking at the numbers and look at the empty cells instead. Find the empty cell farthest from any unplaced number, or in the tightest corner, and ask which numbers could reach it. Usually only one can, and that gives you a forced placement.
Advanced solvers sometimes test a placement mentally to find a contradiction, but this is still logic, not guessing: you follow the consequences until something breaks, then rule that shape out. On GridPaw you can use Undo to test safely, but aim to do it in your head.
