How to Solve Hitori Puzzles

The Japanese puzzle magazine Nikoli first published Hitori (short for Hitori ni shite kure, literally “leave me alone”) in March of 1990. It uses an interesting variation on the sudoku formula of non-duplicate numbers in every row and column. The difference is that the puzzle already has duplicate numbers. Your job is to figure out which ones to eliminate.

Rules
Basic Techniques to Solve
Solving the Puzzle

Rules

From the grid of numbers, shade out cells so that no row or column contains a duplicate digit.

Rows and columns do not have to contain all possible numbers.
Shaded cells may not be orthogonally adjacent to another shaded cell.
Unshaded cells must form one contiguous orthogonally connected area.

Because of duplicates, not all rows and columns will have all numbers.
You may not shade a cell adjacent to another shaded cell.
Unshaded cells must be orthogonally contiguous in the solution.

Basic Techniques to Solve

Look for unique numbers.
Look for adjacent pairs of the same value.
Find number pairs separated by one cell.
Follow the basic routine.

Look for Unique Numbers

This technique is much easier in smaller grids, of course. Since the goal of the puzzle is to shade duplicates, any unique numbers you find must be unshaded.

So, when you find a number that only occurs once in a given row AND column, you can mark it as unshaded. Be careful! Sometimes a number might seem unique along one axis, but it’s actually a duplicate along the other.

This 1 is unique in both its row and column, so it is definitely unshaded.

These 1s are unique in their columns. However, since they’re in the same row, one of them must be shaded.

Adjacent Pairs

When you see adjacent numbers of the same value, one of them must be unshaded. This is due to the rule that no two shaded cells may be adjacent. This results in two effects:

In the corners, you can deduce at least one unshaded cell next to the pair. This unshaded cell either provides an exit path, or it’s simply located next to the shaded cell of the pair.
Look in that row or column, and shade any extra copies of the number in the pair, because they’re definitely duplicates.

Here, we have a pair of 2s in the corner. One of them must be shaded.

If it’s the bottom 2, then the adjacent numbers must be unshaded. Remember the 3.

If the other 2 is shaded, then the 3 must still be unshaded. Otherwise, you’d isolate the 2 in the corner.

So no matter what, we know the 3 must be unshaded.

Have a Sandwich

Look for a value sandwich – a single cell between matching numbers. This cell must be unshaded, because, at least one of the number pair will be shaded. Whichever one it turns out to be (maybe even both), all orthogonally adjacent cells must remain unshaded.

No matter which 2 is shaded, the 3 must be unshaded because it’s adjacent.

Follow the Routine

As we just demonstrated, marking unshaded cells makes finding shaded cells much easier. Use the three techniques above to find your break-in points, then follow this basic algorithm, which will get you through the majority of Hitori puzzles.

Mark all cells orthogonally adjacent to a known shaded cell as unshaded.
When you know an unshaded cell, look in that row and column, and shade any duplicates of that number.
Always provide an exit path for unshaded cells.

We’ll start with our known unshaded cells. Notice we have another sandwich in the middle. So the 2 in the center is unshaded, and the others must be shaded.

From there, we can mark the cells around them as unshaded.

Next, these duplicate numbers must be shaded.

Again, cells around shaded ones must be unshaded.

And this 5 must be unshaded, so that the 1 in the corner doesn’t get isolated.

Solving the Puzzle

Now we have our techniques, so let’s tackle the larger example. If you’d like to give it a shot before following the walkthrough, you can attempt it here.

A Strong Start

We’ll start by spotting all the adjacent pairs. Notice that these 10s have duplicates in their row? Those must be shaded.
Next, we use the sandwich technique to find many unshaded numbers.
Now we search for duplicates of the unshaded numbers. I’ve circled the ones we found repeats of.

Running the Routine

With several shaded cells, we can use the algorithm. First, these adjacent numbers mist be unshaded.
This 7 must also be unshaded to avoid isolating the 8.
Next, we check again for duplicates. The circled numbers have shaded clones in their row or column.

We have several cells that are mostly surrounded. So we must provide an unshaded escape path for them.
Again, we’ll mark the numbers around the shaded cells as unshaded.
Check again for possible isolation. This 3 and 6 must provide exit paths.

Lather, Rinse, Repeat

And so it goes, back and forth. Look for duplicates of unshaded cells.
Then mark the numbers around shaded cells as unshaded.
After that, make sure that any potentially isolated cells have an unshaded exit to connect with the group.

Look for duplicate numbers to shade.
Mark unshaded cells around them, and connect isolated groups.
We’ve solved the Hitori puzzle!

Rules