Slant techniques

Slant is mostly about two things: what the numbers allow, and which lines would close a loop. Start at the edges, where numbers touch fewer squares, and work inward.

In each picture, the cells the technique decides are outlined in blue.

1. Corners of the grid

   A corner of the grid touches only one square. A 1 there means that square’s line runs into the corner. A 0 means it runs the other way.

2. Numbers on an edge

   A number on the edge of the grid touches two squares. A 2 means both lines point into it, making a peak or a valley. A 0 means both point away.

3. A 4 is an X

   A 4 needs every one of its four squares to point at it, so it always sits at the center of an X. That’s also why you’ll never see a 0 in the middle of the grid: keeping all four lines away from a corner would draw a closed diamond around it.

4. Count what’s left

   Once a number has as many lines touching it as it asks for, every other square around it points away. If it needs every square that’s still open, they all point in. Here the 1 is already satisfied by the top-left line, so the other three squares point away.

5. Never close a loop

   When three sides of a diamond are drawn, the last square has to take the other diagonal, or it would close a loop. Late in a puzzle this is the move you’ll make most often, and it works on bigger loops too: never join two points that are already connected.

When nothing seems forced, follow a line along its connections. If two corners are already joined by a path, no square may draw the diagonal between them.