Advanced Hitori Techniques for Harder Grids

The advanced Hitori techniques are not new rules. They are ways to read a larger grid faster, and one extra check, the connection rule, that small grids almost never need. This article uses a real hard grid (8 x 8) from the LogikLand generator and follows the solution from the first scan to the last square, so every technique is shown on numbers you can check. If the basics are not automatic yet, start with how to solve Hitori.

What changes on 8 x 8 and 9 x 9

The LogikLand generator only keeps a grid if a program can solve it with logic alone. At the hard level (8 x 8) it also requires at least one square that can only be settled by the connection rule. At the expert level (9 x 9) the connection rule must be used at least three times, and at most 40 % of the squares may be settled right at the first scan, by lonely numbers and by the patterns "a b a" and "a a". So an expert grid gives you fewer easy squares at the start and more work in the middle.

The grid we use

Rows are counted from the top and columns from the left, starting at 1. The solution is on the right.

At the first scan, 30 of the 64 squares (47 %) are settled by lonely numbers and the two patterns. Everything below comes from that start. In total the solution shades 19 squares.

Triples

Three equal numbers in a line are a triple. At most one of them can stay white, and two shaded squares may not touch, so the two outer ones must be shaded and the middle one stays white. In this grid, column 5 reads 5, 6, 6, 6 and so on from the top: the three 6s in rows 2, 3 and 4 form a triple. Shade rows 2 and 4, and circle row 3. There is no other 6 in that column, so nothing else follows from it. These three squares are settled at the very first scan.

Sandwiches that start a chain

A sandwich is a number between two copies of another number, as in 1, 7, 1. One of the two 1s has to be shaded, and a shaded neighbour would touch it, so the middle number stays white. In column 4, rows 4, 5 and 6 read 1, 7, 1. The 7 in row 5, column 4 is therefore white. A white square is the starting point of a chain, because every other copy of its number in its row and its column must be shaded. That is exactly what happens next.

The cascade

A white square shades its twins, and a shaded square whitens its neighbours. Each result can feed the next. The table follows one chain through this grid, from one sandwich to eight squares.

Nothing in this chain is a guess. When you are stuck on a big grid, do not scan again from the top: pick the newest circled or shaded square and ask what it forces. The most recent square is usually where the next move is.

The connection rule

In this grid, simple moves settle 63 of the 64 squares. One square is left: row 4, column 8 (a 6). Nothing on its row or column forbids shading it. The only reason it cannot be shaded is the third Hitori rule.

Look at the 1 in row 3, column 8. Above it, the 2 in row 2 is shaded. To its left, the 2 in row 3, column 7 is shaded. The only way out for this 1 is downward, through row 4, column 8. If that square were shaded, the 1 would be cut off from every other white square. So it stays white, and the grid is finished.

This is the connection rule in its simplest form: before you shade a square, check that every white neighbour still has another way out. The harder form is a long wall of shaded squares touching at corners. A wall that closes into a loop locks the white squares inside it away from the rest, so the last square of the loop cannot be shaded. Expert grids need the rule at least three times, in simple or more complicated forms.

Corner traps

A corner square has only two neighbours. A shaded square makes its neighbours white, so if a corner is shaded, its two neighbours are white. Now suppose both neighbours of a corner were shaded: the corner could not be shaded (it would touch them), so it would be white and completely walled in. That breaks rule 3. So you can never shade both neighbours of a corner: once one of them is shaded, the other and the corner stay white. It is a quick check to run each time you shade a square beside a corner.

Practice

To drill the early moves on small grids, solve printable easy Hitori puzzles. The connection rule needs the larger levels: the LogikLand Hitori assistant makes hard and expert grids once you create a free account to make a full book. For the rules in one page, see Hitori rules.