LITS, formerly known as Nuruomino (ヌルオミノ), is a binary determination puzzle published by Nikoli.

Rules

''LITS'' is played on a

rectangular grid A regular grid is a tessellation of ''n''-dimensional Euclidean space by congruent parallelotopes (e.g. bricks). Its opposite is irregular grid. Grids of this type appear on graph paper and may be used in finite element analysis, finite volume ...

, typically 10×10; the grid is divided into

polyomino A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling. Polyominoes have been used in po ...

es, none of which have fewer than four cells. The goal is to shade in a

tetromino A tetromino is a geometric shape composed of four squares, connected orthogonally (i.e. at the edges and not the corners). Tetrominoes, like dominoes and pentominoes, are a particular type of polyomino. The corresponding polycube, called a tetracu ...

within each pre-printed polyomino in such a way that no two matching tetrominoes are orthogonally adjacent (with rotations and reflections counting as matching), and that the shaded cells form a valid

nurikabe The ''nurikabe'' (塗り壁 or 塗壁) is a ''yōkai'', or spirit, from Japanese folklore. Its name translates to "plaster wall", and it is said to manifest as an invisible wall that impedes or misdirects travelers walking at night. Sometimes re ...

: they are all orthogonally contiguous (form a single polyomino) and contain no 2×2 square tetrominoes as subsets.

History

The puzzle was first printed in ''

Puzzle Communication Nikoli A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together ( or take them apart) in a logical way, in order to arrive at the correct or fun solution of the puzzl ...

#106''; the original title is a combination of 'nuru' (

Japanese Japanese may refer to: * Something from or related to Japan, an island country in East Asia * Japanese language, spoken mainly in Japan * Japanese people, the ethnic group that identifies with Japan through ancestry or culture ** Japanese diaspor ...

: "to paint") and 'omino' (

). In issue #112, the title was changed to the present one, which represents the four (of five) tetrominoes used in the puzzle: the L-shape, the straight, the T-shape, and the skew (square tetrominoes may never appear in the puzzle as they are a direct violation of the rule).

Solving Strategies

There are some simple, and difficult, strategies for this puzzle.

Instantly solvable/Chains

There are 4 different "instantly solvable" cases, the L, S, T, and I can all be instantly solved in boxes that only have 4 blocks. There are also "chains" or 4 blocks eliminating a block from a 5 block box, creating another location for the next tetromino.

Inherent locational placements

If you see 5 pieces, you will always be able to place at least one block inside of the pentomino(like tetromino, but for 5). Like if you see a t with an extra block on the top, the two spots in the middle can be filled in, since every possible tetromino takes place in those 2 blocks. Every other location can be inherently assumed based on the amount of possible tetrominoes, and the overlapping tiles of all of them.

External links