Solving order
Which technique, and when.
Knowing twenty techniques doesn't help much if you don't know which one to look for. Each has a point in the puzzle where it's the right move, and a point where hunting for it just wastes ten minutes. This page is a map of which is which.
It goes from the easy stuff to the moves that need the whole grid. The higher up the list, the quicker it is to check.
The order
The solving order.
Numbers are going in easily.
Keep going. Count what's missing from a row, column or box and fill in any cell that can only take one number.
You're stuck, but your pencil marks are complete.
Clear out candidates before trying to place anything. A digit trapped in one line, or two cells sharing the same pair, is usually what gets things moving again.
Stuck again, with all your marks filled in.
Look for sets of three, then for a digit that only fits in two spots in each of two lines. After this, nothing is quick to spot.
You've tried everything above and nothing moves.
Change how you're looking. Stop reading cells and follow one digit across the whole grid, or look for a shape made of three cells instead of a line.
A really hard puzzle, still stuck.
Go bigger. Four lines instead of three, a chain of links instead of one pattern, or use the fact that the puzzle has only one solution.
Look-alikes
Techniques that look like each other.
Some techniques are easy to mix up. These are the pairs people ask about most, and how to tell them apart.
- Single candidate or hidden single?
- Same idea, from opposite ends. A single candidate reads one cell and counts the digits left in it; a hidden single reads one digit and counts the cells left for it in a unit. Use whichever the grid makes easier. Both are certain, so there's never a reason to guess. Single candidate, Hidden single
- Naked pair or hidden pair?
- Both are two digits in two cells of one unit, and they're mirror images. A naked pair is found by reading the cells: two cells that each hold only those two digits, which removes the digits from the rest of the unit. A hidden pair is found by reading the digits: two digits that can only go in those two cells, which removes every other candidate from those cells. A naked pair is easier to spot, so it's usually found first, and a unit rarely shows both. Naked pair, Hidden pair
- Naked triple or hidden triple?
- Same difference as with pairs, one size up. The naked triple reads cells whose candidates add up to three digits and removes those digits from the unit; the hidden triple reads three digits confined to three cells and clears the other candidates out of them. Both are rarer than their pair versions, and the hidden one is the rarer of the two. Naked triple, Hidden triple
- X-Wing or swordfish?
- How many lines. An X-Wing is two rows in which a digit has exactly two homes, and both rows use the same two columns. A swordfish is three rows whose homes for that digit use only three columns, and the rows may hold two or three homes each. If two rows line up, take the X-Wing: it's easier to verify and it clears the same two columns. Go for the swordfish when an X-Wing scan comes up empty. X-Wing, Swordfish
- Swordfish or jellyfish?
- Three lines or four. A swordfish spans three rows and three columns; a jellyfish spans four of each, and its rows may hold two, three or four homes for the digit. A jellyfish clears four columns at once, which is why it can crack a puzzle nothing smaller could. It's also rare. Swordfish, Jellyfish
- XY-Wing or XYZ-Wing?
- How many candidates the pivot has, which changes what you can remove. In an XY-Wing the pivot holds two candidates, so it forces one of its two wings to take the shared digit, and the digit can be removed from anything that sees both wings. In an XYZ-Wing the pivot holds three, so the pivot might be the shared digit itself, which narrows the removal to cells that see the pivot as well as both wings. XY-Wing, XYZ-Wing
- XY-Wing or W-Wing?
- What holds the three cells together. An XY-Wing is three cells that all see each other through one pivot. A W-Wing is two cells holding the same pair, which don't need to see each other at all. They're joined by a strong link instead: two cells that are the only homes for one of the pair's digits in their unit. If the two pairs happen to see each other, you have a naked pair and should use that instead. XY-Wing, W-Wing
- Unique rectangle or BUG?
- How big the pattern is, and what it removes. A unique rectangle is four cells in two rows and two columns that must not all hold the same two digits, and it removes candidates from those four cells. A BUG is the whole grid: every unsolved cell holding two candidates except one, which means the exception must take its third digit. Both rest on the puzzle having exactly one solution. Unique Rectangle, BUG
- Skyscraper or X-Wing?
- How much the two rows share. An X-Wing needs both rows to have their two homes in the same two columns, and it clears those columns completely. A skyscraper needs the rows to share only one column, and gets a weaker result: the digit comes out of the cells that can see both of the far ends. If the rows match in both columns, it's an X-Wing and you should take the stronger elimination. Skyscraper, X-Wing
Stuck
When nothing works.
- Check the marks before the technique. Most "impossible" grids just have a pencil mark missing or one that should've been erased. Clear your marks and redo them: it takes a minute and unsticks more puzzles than any technique.
- Restart the order from the top. A number you placed five minutes ago might have opened up a single somewhere you already checked. Go back to counting before trying anything harder.
- Read the digit, not the cell. Every technique past X-Wing means following one digit across the grid, or spotting a shape made of a few cells. You won't see either by staring at one cell.
- It isn't the puzzle's fault. A proper sudoku can always be solved with logic alone. If it feels like you need to guess, you've missed something.
New to sudoku? The rules of sudoku take two minutes to read, and the first-puzzle walkthrough only uses the first two moves above.
Every technique
All 17 techniques.
The eight lessons from the game come first, in teaching order. The rest are for tougher puzzles.