Spatial Partitioning

What is the Spatial Partitioning?

Spatial partitioning means dividing a space into parts that fit together with no gaps and no overlaps. Puzzles built on it, like Shikaku from the Japanese puzzle magazine Nikoli, are pure deduction: every piece has to be worked out from the clues, and each piece you fix limits what the pieces around it can be. Solving them exercises planning, spatial reasoning and the habit of weighing several constraints at once.

Spatial Partitioning on Neuroptimize is a Shikaku-style puzzle with shape rules. You cover the grid with rectangular patches, each holding exactly one clue. A clue’s outline gives the patch’s shape (square, tall, wide or any), and its number, when it has one, how many cells the patch covers. As you level up, the grid grows from 4 by 4 to 7 by 8 and the clues give away less: first numbers disappear, then shapes, until some clues only mark where a patch is.

How to play the Spatial Partitioning

1. A grid appears with several dark clue tiles. The pills above it show the board’s par time, your time so far and how many cells are covered, and the legend under the board names the clue shapes in play.
2. Drag across the grid to lay a patch. The rectangle runs from the cell where you start to the cell under your finger, snapping to whole cells, and the pill above shows its width, height and size as you drag. It must hold exactly one clue: a rectangle with no clue, or two, is not laid.
3. A square clue needs a patch as wide as it is tall, a tall clue one taller than it is wide, a wide clue one wider than it is tall, and a round clue allows any rectangle. A number is the patch’s size in cells; a clue without one can be any size that fits.
4. Laying a new patch for a clue replaces its old one and lifts any patch it overlaps. Tap a patch to lift it, or tap a clue to give it a single-cell patch. Undo steps back (Backspace or Z on a keyboard), and Clear empties the board.
5. When every cell is covered and every patch keeps its rule, the board is solved. If a full board breaks a rule, the patches that do are outlined and marked with "!", and the board counts as a miss; you can still fix it to go on, or skip it.
6. A session is 4 boards. A clean solve scores points, more for bigger boards with fewer giveaways, plus a time bonus that is whole on par and fades to nothing at twice par. Clean solves in a row build a combo that multiplies them.
7. The grid is 4 by 4 at first, 5 by 5 from level 4, 6 by 6 from level 10, 7 by 7 from level 19 and 7 by 8 from level 25. Hidden numbers start at level 4, any-shape clues at level 8, and clues with neither a number nor a shape at level 13.

Strategies and tips

The science behind the Spatial Partitioning

Shikaku, invented by Yoshinao Anpuku and published by the Japanese puzzle magazine Nikoli in 1989, asks you to divide a grid into rectangles that each hold one clue. Yasuhiko Takenaga and colleagues (2013) proved it NP-complete: no known shortcut solves every board, so each has to be reasoned out. Studying Sudoku, a puzzle of the same pure-deduction kind, Louis Lee, Geoffrey Goodwin and Philip Johnson-Laird (2008) found that newcomers picked up deductive tactics within minutes, and that a deduction is harder the more constraints it has to combine. Here every patch you pin down narrows what its neighbours can be.

Frequently asked questions