Hitori is a great logical teaser. You start will a square grid filled with numbers (from 1 to the size of
the grid). One must colour the least number of cells so the following three rules are satisfied:
Numbers must not appear more than once in each row or column
Painted (black) cells are never adjacent in a row or a column
Empty (white) cells create a single continuous area, undivided by painted cells.
Key points
Appeals to a logical mind, but requires no arithmetical skills. Pure pattern recognition. Penmanship
merely involves circling numbers and colouring certain squares in black. Sizes can range from simple
to large and this grades the puzzle. We guarantee only one solution.
Grid Sizes
A 'normal' Hitori board is 8 x 8 cells. Sample and instructional boards may be 5 or 6 cells to a side.
The largest Hitori we can produce are 12 x 12. However, 10 x 10 is also a good publishing size and 9 x 9 and 11 x 11 are
also possible.
Strategies
Whenever you fill in a black cell you will get four white ones around it. Always mark the known white cells
around a black with circles so you know they are committed to be being white.
Unique numbers. All cells will either be black or white at the end. We can be certain that some
cells are white just because they are unique in both their row and column. It's conventional to mark white
cells in a circle.
Triples. Start by looking for any triple numbers, ie, any number that occurs three times adjacently
in any row or column. We can mark the outer two numbers as black. Why? If an outer cell of the three were
white then according to Rule 1 the other two are black (to make the number unique) but rule 2 says black
squares can't be adjacent. The center cell is probably white, but only provisionally.
Corner 4s. If there is a block of four identical numbers in a 2 by 2 arrangement in the corners
then there must be two black cells. To prevent an isolated white cell the black cells can only be arranged
in one configuration - diagonally from the outermost corner.
Pair and Single. Given three numbers in a row or column something useful can be deduced from
them if two are adjacent and one isolated. The isolated one must be black. If it were white we'd be committing
the other two to be adjacent blacks and we can't allow that.
Known removes Unknown. Any cell marked as white must mean that all other occurrences of that
number in the row and column must be black. This is very productive strategy and you should apply it at
all times.
Contiguous White. Take advantage of Rule 3. If an unknown cell is the only way for the whites to
remain joined up then it can't be black.
