The Diagonal 3s Pattern: A Key Technique

The Magic of Diagonal 3s

You already know that two adjacent 3s (sharing a side) force three lines. But what about when they touch only at a corner? This "Diagonal 3s" pattern is slightly more subtle but just as powerful.

The Setup

Look for two cells containing "3" that are diagonally adjacent—they share a single vertex but no edges. This configuration creates a unique stress on the shared corner.

The Deduction

The two outer edges that meet at the shared vertex MUST be lines.

Here is why: The shared vertex must have exactly 2 lines passing through it (to continue the loop). If the loop didn't grab the outer edges of the 3s, it would have to zig-zag strictly between them, which creates a contradiction with the requirement to fill 3 sides of both cells without branching. The math forces the loop to "wrap around" the far sides of both 3s.

·───·   ·
│ 3      
·   ·   ·
    │ 3 │
·   ·───·

The "Zigzag"

This pattern often creates a zigzag shape. The loop comes in, grabs the outer edge of the first 3, passes through the shared vertex, and grabs the outer edge of the second 3.

·───·   ·
│ 3      
·   ·   ·
    │ 3 │
·   ·───·

Chaining Diagonals

If you have a chain of diagonal 3s (3-3-3), this logic extends. You effectively get a long, forced snake of lines along the outer boundary of the chain. This is extremely common in computer-generated hard puzzles.

Practice Tip

Scan for diagonal pairs of 3s early in the game. They are independent of their neighbors. You can fill in those two lines instantly, which often gives you a foothold to solve the adjacent cells.