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Hitori Sandwich: A Number Between Two of the Same

The sandwich technique says: a number between two of the same, like 4 2 4, stays unshaded. If the middle were shaded, neither outer number could be (shaded squares can’t touch), so both would stay unshaded, and repeat.

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This is the first of the Hitori techniques.

The rule

  1. Look along every row and down every column for three squares in a row whose outer two numbers match.
  2. Circle the middle one: it stays unshaded.
Sandwich: a number between two of the same stays unshaded A 3 by 3 grid whose top row is 4 2 4. The 2 between the two 4s stays unshaded. 4 2 4 1 3 2 2 1 3
4 2 4: the 2 stays unshaded.

In a real puzzle

On the 9×9 every technique page follows, it’s the first move. Row 1 starts 6 7 6, so the 7 stays unshaded.

Step 1: sandwich Hard level 5 at step 1, with the squares this step reasons from and settles highlighted. 6 7 6 1 7 2 8 1 4 6 3 8 2 5 4 8 8 7 5 1 8 6 7 5 4 2 1 8 4 9 5 3 5 7 2 1 7 6 3 8 3 9 5 1 5 7 4 2 6 8 1 3 7 9 1 1 2 4 2 7 2 9 3 4 5 7 3 2 5 1 9 9 7 9 2 7 3 3 6 5 8 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
Step 1: 6 7 6 at the start of row 1, so the 7 is circled.

How often you’ll need it

On every one of the game’s 150 levels, which all have at least one sandwich on the empty grid. On the 9×9 here it’s 6 of the 55 moves, and on a Hard level about 3 to 4 on average. Most come at the start: sweep for them all before anything else.

Next steps

Questions

Does it work down columns too?

Yes. Any three squares in a row or column, where the outer two have the same number, make a sandwich.