How to Solve Shikaku (Rectangles) Puzzles
Shikaku looks intimidating at first - a plain grid scattered with numbers, and somehow you are meant to slice it into neat boxes. But the whole puzzle rests on two tidy rules, and once you see them clearly the grid almost solves itself. There is no arithmetic to grind through and no luck involved: every rectangle has a home that pure logic can find. This guide shows you how to read the numbers, how to spot the boxes that can only go one way, and how to keep carving without ever stranding a cell or letting two rectangles collide.
What Shikaku actually asks of you
Shikaku - the name is Japanese for "divide into squares" - hands you a rectangular grid with numbers sprinkled across some of its cells. Your job is to cut the entire grid into rectangles (and squares count as rectangles too), following just two rules. First, every rectangle must contain exactly one number. Second, that number must equal the rectangle's area - how many cells it covers. A 6 lives in a box of six cells; a 4 in a box of four.
When you are done, the whole grid is tiled with no gaps and no overlaps, and each number sits alone inside its own correctly sized box. Because the cells all have to be used and each number owns exactly its area, the totals always balance: add up every number on the board and you get the exact number of cells in the grid. There is only one valid way to carve a well-made puzzle, and you can reach it by reasoning alone.
Factor every number into its possible shapes
This is the idea that turns a wall of numbers into a list of choices. Each number can only form rectangles whose width times height equals it, so before placing anything, work out what shapes a clue is even allowed to take. A 6 can be 1×6, 2×3, 3×2, or 6×1. A 12 has more options - 1×12, 2×6, 3×4, 4×3, 6×2, 12×1 - and is therefore harder to pin down early.
The gift hiding in this step is the prime numbers. A 5 can only be 1×5 or 5×1 - a single straight strip, never anything chunkier. The same goes for 2, 3, 7, 11, and 13. Those clues are nearly decided before you start: you only have to choose which direction the strip runs and where along the line it sits. Hunt down the primes first; they are the cheapest information on the board.
Sketch the options. When a number stumps you, mentally list its factor pairs and check each one against the space around the clue. In Mochi Rect you can simply drag out a candidate box and watch its running area print in the middle - a fast way to feel which factor pairs actually fit before you commit to one.
Place the forced rectangles first
Some clues have only one legal home, and finding them is the heart of solving. A clue is forced when every shape it could take but one is blocked - by the edge of the grid, by another number it would swallow, or by a wall of cells that no other rectangle can reach.
Walls and corners are where forced clues hide. A number tucked in a corner has two of its directions cut off immediately, so a corner 4 can usually only stretch one way. A clue pressed against the top edge cannot grow upward, which often leaves a single shape that fits. And a number can never overlap another number, so if a 3 sits two cells away from a 2 along a row, neither can spread into the other's lane - that mutual blocking frequently leaves exactly one option each.
Place those certain rectangles before anything speculative. Each one you lock in becomes a new wall for its neighbours, and clues that looked open a moment ago suddenly have nowhere left to go but their one true home.
Watch for cells that would be stranded
Because every cell must end up inside some rectangle, a cell that no clue can reach is a contradiction - and spotting those near-orphans is one of the most powerful tools you have. Look at the corners and edges of the grid especially: a corner cell can only be covered by a number whose box can physically extend to touch it.
Run the question in reverse. Instead of asking "where can this number go?", ask "which numbers could possibly cover that lonely cell in the top-left?" Often only one clue is close enough and large enough to reach it. The moment a single cell can be claimed by just one number, that number's rectangle is forced to include the cell - which usually nails down its whole shape. Any candidate box that would leave a cell with no possible owner is wrong, even if the box itself looks legal in isolation.
Let the cell choose. If you stall, stop staring at the numbers and stare at an empty cell instead - the one in a tight corner is best. In Mochi Rect the boards are built backward from a real partition and validated for full coverage, so every cell genuinely has one owner waiting to be found, and the bulb hint will outline the smallest box you still need if you want a nudge.
Eliminate boxes that overlap or trap
Once a few rectangles are down, most of your progress comes from ruling options out rather than guessing them in. Two tests catch almost every bad placement, and walking them through is faster than untangling a mistake later.
- The overlap test. No two rectangles may share a cell, and none may contain a second number. If a shape you are considering would cross a committed box or engulf another clue, discard it - that direction is dead, which often leaves only one survivor.
- The trap test. After imagining a box in place, glance at the cells just outside it. If placing it would wall off a pocket of cells that no remaining number can fill, the box is wrong even though it broke no rule on its own.
- The reach test. A number can only cover cells within its own row and column span. If a stretch of cells sits too far from every clue large enough to reach it, you have mis-shaped a nearby rectangle - back up and re-cut.
Each elimination tightens the board. When a clue is left with a single shape that survives all three tests, you have not guessed it - you have proven it.
A simple solving routine
Put the pieces together and you have a loop that cracks the great majority of boards:
- Factor the clues. Note the primes and the corner and edge numbers - these have the fewest shapes and decide first.
- Place every forced rectangle. Lock in any clue with only one legal home, starting from the walls and working inward.
- Re-scan after each box. A committed rectangle is a new wall; clues beside it often drop to a single option the instant it lands.
- Chase stranded cells. When numbers stall, find a cell only one clue can reach and let it force that clue's shape.
- Eliminate the rest. For undecided clues, throw out every shape that overlaps, traps, or cannot reach - keep the survivor.
- Loop until every cell sits inside exactly one box; the areas will add up because they always do.
Guessing never appears in that list, and in a properly built puzzle it never has to. If you feel cornered, you have probably missed a forced clue against a wall - re-walk the edges and the lonely corner cells before you reach for a coin flip.
Where to go next
The quickest way to make all of this automatic is to play small boards until factoring a clue and spotting a forced corner feel like reflexes. Mochi Rect keeps things gentle on purpose - it has no timer and no lives, dragging a fresh box simply replaces whatever it overlaps, and a quick tap lifts any rectangle back off, so untangling a tangle costs nothing. Start in the roomy 5×5 Berry world, let the denser 10×10 boards stretch you, then turn to Endless for an unlimited supply. If you enjoy the "what is already forced?" feeling of a Shikaku, the pure-logic puzzles below scratch the very same itch.