### Hitori - Solving with pairs

Posted:

**Fri 04 Sep, 2015 3:51 am**I've been refreshing myself on Hitori logic this week, before the LMI test this weekend.

For practice you can solve some handmade Hitoris online at Nikoli or Puzzle Picnic.

The main rule to start with is:

* If a cell is between two identical digits, then it must be white.

But I came across a few ideas regarding pairs of identical digits touching each other which I thought were interesting.

Obviously a pair cannot be both white or both black, so they are always one white and one black.

* If a row contains a pair of 1s, then all other 1s in that row must be black.

* If there is a pair in a corner of the grid, then an adjacent cell must be white (see first diagram).

Words are too hard. I'll draw some diagrams, and then show afterwards which cells must be white or black.

In each diagram there are some pairs, represented by small digits (like 1s and 2s).

The big digits are spread around filling in space, and aren't linked to each other.

Have a look and decide what can be deduced in each case, some cells must always be unshaded (orange) or shaded (blue).

(click each image to expand it)

Even a single unshaded cell is useful, it might cause a shaded (plus 4 more unshaded) on the far side of the grid. Every little bit helps in Hitori.

These diagrams are fairly simple, they're highlighting how much can be learnt from a pair or two. Obviously more complicated patterns exist.

Heyawake logic can be seen in a few places too.

Hopefully that'll make sense, you're welcome to ask questions or point out mistakes.

For practice you can solve some handmade Hitoris online at Nikoli or Puzzle Picnic.

The main rule to start with is:

* If a cell is between two identical digits, then it must be white.

But I came across a few ideas regarding pairs of identical digits touching each other which I thought were interesting.

Obviously a pair cannot be both white or both black, so they are always one white and one black.

* If a row contains a pair of 1s, then all other 1s in that row must be black.

* If there is a pair in a corner of the grid, then an adjacent cell must be white (see first diagram).

Words are too hard. I'll draw some diagrams, and then show afterwards which cells must be white or black.

In each diagram there are some pairs, represented by small digits (like 1s and 2s).

The big digits are spread around filling in space, and aren't linked to each other.

Have a look and decide what can be deduced in each case, some cells must always be unshaded (orange) or shaded (blue).

(click each image to expand it)

Even a single unshaded cell is useful, it might cause a shaded (plus 4 more unshaded) on the far side of the grid. Every little bit helps in Hitori.

These diagrams are fairly simple, they're highlighting how much can be learnt from a pair or two. Obviously more complicated patterns exist.

Heyawake logic can be seen in a few places too.

Hopefully that'll make sense, you're welcome to ask questions or point out mistakes.