Strategy guides › Sudoku

Which Sudoku techniques our Easy to Expert puzzles really need

Eigengames team · 6 October 2026 · 5 min read

▶ Play Sudoku🎯 Try Hard puzzle 15

Twenty minutes in, pencil marks everywhere, and not a single cell with one candidate left. Every row has been scanned twice. This is the moment most players start guessing, and it is also the moment where knowing which tool comes next is worth more than staring harder.

To find out which tools our puzzles call for, we wrote a solver that works like a person. It always uses the simplest technique that makes progress, in this order: naked singles, hidden singles, pointing and claiming, pairs, triples, X-wing, XY-wing, swordfish. We ran it on 200 daily puzzles of every difficulty, the actual dailies from the first 200 days of the game, and recorded the hardest technique each one needed.

Each column adds up to 200 puzzles, counted by the hardest step each one needed; “trial needed” means none of the techniques was enough. Easy puzzles have 39 or 40 givens, Medium 32 or 33, Hard 27 or 28, and Expert 23 to 27. Triples and swordfish never turned out to be the missing piece. The last row is the interesting one, and we will get to it.

Singles carry Easy and Medium

Our generator starts from a full grid and removes cells in mirror-image pairs for as long as the solution stays unique. It never asks how hard the result is. What decides the difficulty is how many givens are left, and with 39 or 40 of them the singles do nearly everything. On Easy, 196 of the 200 puzzles fell to naked singles alone: cells where only one digit is still possible. On Medium the picture changes. Only 102 fell to naked singles; another 89 needed hidden singles.

A hidden single is a digit that has only one home in a row, column or box, even though that cell has other candidates. You find it by scanning a digit, not a cell.

The habit to build: pick a digit, look at each box, and let the rows and columns that already contain it rule out squares. On Medium, 191 of our 200 dailies need nothing more than this and the naked singles.

Pointing: a digit stuck in one line of a box

Once singles dry up, the first new idea is intersection. If every possible place for a digit inside a box lies on one row, that digit must go on that row inside that box, so it can be crossed off the rest of the row. The same works the other way round: if a row’s only places for a digit all sit in one box, the digit can be crossed off the rest of that box. Players call the first pointing and the second claiming; the SudokuWiki page on intersection removal has more examples.

It sounds small. On Hard it is the step that unlocks 13 of our 200 dailies, and on Expert 23.

Pairs: two cells, two digits, case closed

If two cells in the same row, column or box both have exactly the same two candidates, those two digits belong to those two cells, in some order. Nobody else in that unit can have them. That is a naked pair. The hidden version is the mirror image: two digits that can only go in the same two cells of a unit, which lets you wipe every other candidate from those cells.

Here are both ideas at work in the middle band of Hard puzzle 15, after the singles have filled 31 cells.

After those removals, the two yellow cells are themselves a 5-6 pair. That is typical: each elimination tends to set up the next one, which is why pencil marks pay for themselves on Hard and Expert. Our game’s Notes mode helps here, because placing a digit removes it from the notes of its row, column and box for you.

When nothing works: the two-candidate test

Now the last row of the table. On Hard, 33 of the 200 dailies got stuck even after X-wing, XY-wing and swordfish; on Expert, 76 did. Our generator only promises a unique solution, and a unique solution does not have to be reachable with the classic techniques. One Easy daily out of 200 and three Mediums were in the same boat.

What rescued every single one was the same move. Find a cell with only two candidates. Pencil in one of them, and follow the consequences with the ordinary techniques. If that leads to a contradiction (a cell with no candidates left, or a digit with no home in some row), the other candidate is the answer. This is proof by contradiction, not a guess: you only keep a digit you have shown must be there.

On Hard, 20 of the 33 stuck puzzles needed one such test and the other 13 needed several. On Expert, 30 needed one and 46 needed several. In all 800 puzzles, there was never a stuck position where no two-candidate cell gave a contradiction within a test or a few. Two tips make it cheaper. Pick a two-candidate cell with many empty peers, because its consequences spread fastest. And use Undo freely: the game lets you take back as many moves as you like, so you can try a line and roll it back without rubbing anything out.

Practice

Hard puzzle 15 is a good workout: after the hidden single above and a run of other singles, it needs two pointing-or-claiming steps and one naked pair, and no trial at all. Solve it once with pencil marks, then try a fresh Expert and see how long you last before you need a two-candidate test.

Scan by digit, mark by cell, and only test what you can disprove.

▶ Play Sudoku🎯 Try Hard puzzle 15