Hitori - Solving with pairs

Rules and Tips for standard puzzle types, and their variants
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Hitori - Solving with pairs

Post by kiwijam » 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)
Hitori samples 1.png
Hitori samples 1.png (9.66 KiB) Viewed 23881 times
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.
Hitori samples 2.png
Hitori samples 2.png (7.68 KiB) Viewed 23881 times

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Re: Hitori - Solving with pairs

Post by PuzzleScot » Fri 04 Sep, 2015 2:12 pm

Thanks James.

Once I've isolated the pair+single and pairs separated by 1, I tend to look for anything that is not duplicated in a row/column - these must always be white. While that doesn't appear to help much, it can be very useful to ensuring connectivity of white areas, and deducing which of another (separated) pair can be shaded. eg, if the 3 cells surrounding a corner are unshaded, the corner cell must be shaded (to avoid ambiguity). If that act leaves its partner unduplicated, then that partner must be unshaded too.

After that, I'd look at the situations you outline above and for each cell in that region say "if this was shaded, would it cause a problem". If so, it must be unshaded.

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