SK Loops Explained: The 16-Cell Hidden-Pair Loop
An SK Loop is a closed loop of eight hidden pairs, sixteen cells across four boxes arranged in a 2x2 rectangle. Because those sixteen cells must hold exactly the sixteen loop candidates, any other cell in the loop's rows, columns or boxes cannot take them. It is a last-resort technique for extreme puzzles, first documented while solvers attacked the Easter Monster. Reading it well depends on two basics: hidden pairs and strong and weak links.
Step 1: Start With the Box Rectangle
An SK Loop begins with four boxes, not four cells. The boxes sit in two bands and two stacks, so together they form a rectangle of boxes. Inside each of those four boxes, look for a given or already solved cell that sits where the loop's row and column cross; that cell acts as a pivot. If the four boxes do not form that layout, the chain cannot close, so this is the cheapest check and the one to make first. Most failed attempts stop here, which is a useful result in itself.
Step 2: Read the Eight Hidden Pairs
Around the pivots sit eight pairs of cells, two in each box. Each pair behaves like a hidden pair: two digits are confined to those two cells within their unit, so one digit must go in each cell. The difference from an ordinary hidden pair is that each pair constrains the next. Once you decide which way a pair resolves, the pair that shares its row or column inherits the consequence, and the chain carries that pressure all the way around the loop. Reading the pairs is the slow part; nothing here can be guessed from the shape alone.
Step 3: Trace the Loop in Either Direction
The loop is bidirectional. Start at any pair and trace clockwise or counter-clockwise, and you must return to the starting pair without a break. Between pairs, the links alternate between strong and weak, which is what gives the pattern its forcing power: a false candidate in one pair forces a true candidate in the next, and the alternation keeps that inference alive. If the chain dead-ends, you are looking at unrelated hidden pairs, not an SK Loop. The full link logic is covered in our guide to strong and weak links and Sudoku chains.
Step 4: Apply the Elimination Rule
Once the loop closes, count what it holds: sixteen cells and sixteen loop candidates. That is an exact fit, so all sixteen cells are locked by the loop and every candidate in them is accounted for. Any loop digit that also appears in another cell of a loop row, column or box has nowhere to go, because the loop has already claimed every slot. Remove it. The result can be a dozen eliminations at once, which is why the pattern can crack a grid that looked completely frozen.
Step 5: Know When to Look
SK Loops live at the top of the difficulty scale. They need a crowded candidate grid, usually around 10 to 11 on Sudoku Explainer-style ratings, and they are almost never present in puzzles that fall to singles and pairs. Treat them as a last resort: exhaust X-Wing, Y-Wing, colouring and chains first, and only then ask whether the four-box rectangle exists. The Easter Monster, the puzzle that made the pattern famous, remains the canonical example.
Step 6: Build the Habit Without Memorising Diagrams
You do not need to memorise a picture. Run three checks in order. First, does the candidate grid offer a 2x2 box rectangle with four pivots? Second, do the eight cell pairs each look like a hidden pair for two digits? Third, does the chain of pairs close when traced in either direction? A no at any step means the pattern is not there, and you can return to simpler work without second-guessing yourself. When the checks all pass, the eliminations usually arrive faster than the search that found them.
- Check the box rectangle before you check individual candidates.
- Trace the loop both ways; a genuine loop closes in both directions.
- Keep pencil marks complete, because a missing candidate breaks the chain.
Key Facts
- ▪An SK Loop is a continuous loop of eight hidden pairs across sixteen cells.
- ▪The four boxes involved form a 2x2 rectangle in two bands and two stacks.
- ▪Each box contributes two pairs of cells, one along its loop row and one along its loop column.
- ▪A pivot in each box is a given or solved cell where the loop row and column cross.
- ▪The link chain alternates strong and weak links and reads in either direction.
- ▪The sixteen loop cells must contain exactly the sixteen loop candidates.
- ▪Eliminations remove loop digits from other cells in the loop rows, columns and boxes.
- ▪SK Loops appear almost exclusively in the hardest puzzles, rarely below an extreme rating.
- ▪The pattern became known while solvers were attacking the Easter Monster puzzle.
- ▪Simpler techniques should always be exhausted before you look for a loop.
Frequently Asked Questions
What is an SK Loop in Sudoku?
An SK Loop is a continuous loop of eight hidden pairs, sixteen cells in total, spread across four boxes that form a 2x2 rectangle. Each pair constrains the next, and the loop's candidates can be removed from the rest of its rows, columns and boxes.
How many cells and boxes does an SK Loop use?
Sixteen cells and four boxes. The boxes sit in two bands and two stacks so they form a rectangle, and the loop links one pair of cells in each box with one link in each row and each column.
Why is it called an SK Loop?
The name honours the online handle of the solver who popularised the pattern after it emerged while solvers were attacking the Easter Monster puzzle.
When should I look for an SK Loop?
Only in the hardest puzzles, after singles, pairs, pointing pairs and wings have failed and many cells still carry crowded candidate lists. SK Loops are effectively unknown in easy or medium grids.
How does an SK Loop eliminate candidates?
The sixteen loop cells must hold exactly the sixteen loop candidates, so every loop cell is locked by the loop. Any other cell in a loop row, column or box therefore cannot take those digits.
Do I need an SK Loop to solve most hard puzzles?
No. It is a last-resort pattern for extreme grids such as the Easter Monster. Most hard puzzles yield to singles, pairs, box-line reduction and wings before a loop is needed.