SK Loops

SK Loops (Stephen Kurzhal Loops) is an advanced technique that identifies locked sets distributed across eight cell pairs surrounding four solved cells. The loop structure enables eliminations in aligned units.

Understanding the Pattern

The Core Structure

SK Loops requires:

Four solved cells in a 2×2 box arrangement (spanning 2 bands and 2 stacks)
Eight cell pairs (up to 16 cells) forming a continuous loop around them
Candidate links connecting consecutive pairs

The 2×2 Box Pattern

The four solved cells must be in boxes that form a rectangle:

     Stack 1    Stack 2
     ┌─────┐    ┌─────┐
Band │Box 0│    │Box 1│
  1  │  ●  │    │  ●  │
     └─────┘    └─────┘
     ┌─────┐    ┌─────┐
Band │Box 3│    │Box 4│
  2  │  ●  │    │  ●  │
     └─────┘    └─────┘

The four solved cells (●) create the framework.

The Loop Cells

Eight pairs of cells surround the solved cells, forming a continuous loop:

    ╭──[P1]──[P2]──╮
    │              │
  [P8]    ●    ●  [P3]
    │              │
  [P7]    ●    ●  [P4]
    │              │
    ╰──[P6]──[P5]──╯

Each pair [Pn] contains 1-2 cells with shared candidates.

How It Works

Link Connectivity

Each consecutive pair must share candidates:

Pair 1 links to Pair 2 through shared digits
Pair 2 links to Pair 3 through shared digits
... and so on around the loop
Pair 8 links back to Pair 1

The Size Constraint

Total link sizes must be ≤ 16

Each link has a "size" (1-3 cells). The sum of all eight link sizes cannot exceed 16.

Locked Set Property

When the loop is complete:

The candidates within the loop form a locked set
They must stay within the loop cells
External cells sharing units with the loop lose those candidates

Elimination Rule

Cells that:

Share a unit (row, column, or box) with loop cells
Contain candidates that appear in the loop
Are NOT part of the loop themselves

...can have those candidates eliminated.

Example Structure

Solved cells: R2C2, R2C5, R5C2, R5C5 (in boxes 0, 1, 3, 4)

Loop pairs around them:
P1: R1C2-R1C3 = {2, 5}
P2: R1C5-R1C6 = {5, 7}
P3: R2C7-R3C7 = {7, 3}
P4: R5C7-R6C7 = {3, 9}
P5: R7C5-R7C6 = {9, 4}
P6: R7C2-R7C3 = {4, 8}
P7: R5C1-R6C1 = {8, 1}
P8: R2C1-R3C1 = {1, 2}

Loop candidates: {1, 2, 3, 4, 5, 7, 8, 9}

Each pair shares a candidate with its neighbours, completing the loop.

Complexity

SK Loops is an expert-level technique:

Extremely rare: Appears in less than 0.05% of puzzles
Complex structure: Four solved cells + eight pairs
Many constraints: Connectivity, size limits, box arrangement
Difficult to spot: Requires recognising the full pattern

Why "SK Loops"?

Named after Stephen Kurzhal, who first described this pattern in Sudoku solving forums.

Tips

Look for solved rectangles — Four solved cells in 2×2 box pattern
Don't search manually — The pattern is too complex
Trust the hint system — SK Loops are found automatically
Understand the logic — Helps verify the eliminations

Relationship to Other Techniques

Technique	Structure
X-Cycles	Alternating chains for one digit
Almost Locked Sets	N cells with N+1 candidates
SK Loops	Multi-cell loop around solved rectangle

SK Loops creates a locked set through loop connectivity rather than unit constraints.

More Puzzles

Related Techniques

X-Cycles — Chain-based eliminations
Almost Locked Sets — Locked set concepts
3D Medusa — Complex chain networks