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Hitori Cut-Off: Keep the Grid Joined Up

The cut-off technique says: a square whose shading would wall in an unshaded square, or cut the unshaded squares in two, stays unshaded. All the unshaded squares must join up.

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This is the fifth of the Hitori techniques.

The rule

  1. Look at a square that isn’t settled yet, especially near shaded squares, edges and corners.
  2. Imagine it shaded. Would any unshaded square be walled off from the rest?
  3. If so, it stays unshaded. Circle it.

In a real puzzle

On the 9×9 every technique page follows, it’s first needed at step 27. The top-right corner square is circled, and the square beside it, in row 1, column 8, is shaded. Shading the square below the corner, in row 2, column 9, would wall the corner in. So it stays unshaded.

Step 27: cut off Hard level 5 at step 27, 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 27: shading row 2, column 9 would wall in the top-right corner.

How often you’ll need it

Almost always: on 48 of the 50 Easy levels and every Medium and Hard one, about 3, 6 and 9 times per puzzle. On the 9×9 here it’s 6 of the 55 moves, including the last two: it’s often what settles the last few squares, the ones the chain doesn’t reach.

Next steps

Questions

Where do cut-offs usually happen?

Near the edges and corners, where a square has fewer neighbours to stay joined through. On the game’s levels, cut-off squares are on the edge more often than the edge’s share of the grid.