Technique library

Every technique, explained.

44 techniques across eight families, each with a written explanation and worked examples you can step through. No order imposed — if the solver just showed you a Sue de Coq, start there.

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Foundations

2 techniques · none read

Reading the GridThe first stop on the path. How a sudoku grid is built from rows, columns and boxes, how every cell gets its name, what givens are, and the one rule that decides which digits a cell can still take.3 min read Pencil MarksWhat a candidate is, how to write pencil marks and where this site puts each digit, when to mark every cell and when one box is enough, and how to cross marks out when a digit goes in.4 min read

Singles

3 techniques · none read

Last Possible NumberA cell whose row, column and box have used eight digits between them has one digit left, and no pencil marks are needed to find it.Easy6 min read Naked Single vs Hidden SingleA naked single is a cell with one digit left. A hidden single is a digit with one cell left. They often land on the same square, and the difference is which question you asked.Easy6 min read Hidden SingleA digit with only one place left in a house goes there, whatever else the cell still shows.Easy7 min read

Locked candidates

2 techniques · none read

Pointing Pairs and TriplesWhen a box can only put a digit on one row or column, that digit comes out of the rest of the line. Pairs and triples work the same way, and one stray pencil mark stops both.Easy7 min read Claiming Pairs and TriplesWhen a row or column can only put a digit inside one box, that digit comes out of the rest of the box. Pairs and triples work the same way, and one stray pencil mark stops both.Easy8 min read

Subsets

4 techniques · none read

Naked PairTwo cells in a house holding nothing but the same two candidates take both of those digits, so every other cell in the house has to give them up.Medium7 min read Hidden PairTwo digits with nowhere else to go in a house own the two cells they share.Medium6 min read Naked TripleThree cells in a house that hold only three digits between them take all three, even when no cell shows all three. How to count a triple, and why three short cells are not always one.Medium8 min read Hidden TripleThree digits in a house that can only go in the same three cells own those cells, even when no digit can use all three. How to count a hidden triple, and why three digits with two homes each are not always one.Hard11 min read

Fish

3 techniques · none read

X-WingOne digit with only two places in each of two rows, lined up in the same two columns, clears those columns. How to find the rectangle, why it works, and why two places in each row are not always one.Hard8 min read SwordfishOne digit whose places in three rows all fall inside the same three columns clears those columns. How to find it, why rows with only two places still count, and how a fourth column breaks it.Hard9 min read JellyfishOne digit whose places in four rows all fall inside the same four columns clears those columns. How to find it, why it only pays off on a digit open in eight rows, and how a fifth column breaks it.Expert9 min read

Wings

3 techniques · none read

Y-WingA pivot cell with two candidates and two wings that share a third digit clear that digit from every cell that sees both wings. How to find one, why either case gives the same strike, and why two wings on the same digit prove nothing.Hard9 min read XYZ-WingA pivot with three candidates and two wings that share one of its digits clear that digit from every cell that sees all three. How to find one, why the pivot has to be seen too, and why a cell that sees only the wings keeps its candidate.Hard9 min read W-WingTwo cells with the same pair of candidates, tied together by a digit with exactly two places in a house, clear the other digit from every cell that sees both. How to find one, why only one cell needs to be forced, and why three places break the link.Hard9 min read

Chains & coloring

20 techniques · none read

Simple ColoringFollow one digit through every house where it has exactly two places, and color the cells in two. One color holds the digit everywhere. How to build the chain, the two ways it removes candidates, and why three places break a link.Hard9 min read X-ChainFollow one digit along links that alternate strong and weak, from a strong link to a strong link. At least one end holds the digit, so a cell that sees both ends loses it. How to build the chain and where a weak link cannot go.Expert9 min read X-Chain Cell GroupsAn X-chain with cell groups lets two or three cells of one box stand as a single node. That carries the chain through a box with three places for the digit. How to build one, why a group links like a cell, and the group that breaks it.Expert9 min read Short AICA short AIC is the shortest X-chain: two strong links on one digit, joined by a weak link. Four cells, three links, and any cell that sees both ends loses the digit. How to find one by pairing strong links, and the pair that fools you.Expert8 min read

Short AIC Cell GroupsComing laterExpert8 min read

XY-ChainAn XY-chain links cells with two candidates. Inside each cell one digit or the other is true, and the digit passed between cells changes as you go. One end holds the digit both ends carry. How to build one and the cell that breaks it.Expert9 min read

XY-Chain Cell GroupsComing laterExpert9 min read

AICAn AIC, or alternating inference chain, links candidates with strong and weak links in turn. Strong links run between cells or inside one, so the digit can change. When both ends carry the same digit, one holds it. How to follow one and the two-ends rule.Expert10 min read AIC Cell GroupsA grouped AIC is an alternating inference chain where one node can be two or three cells in a box. The group turns a house with three places into a strong link. A worked chain, how group nodes link, and the two-ends rule.Expert10 min read 3D Medusa3D Medusa colors candidates, not cells, so the color can pass from one digit to another inside a cell with two candidates. How to build the cluster step by step, the three color rules, and what it adds to simple coloring.Expert8 min read X-CycleAn X-cycle is an X-chain that closes into a loop on one digit. When the links alternate all the way round, every weak link strikes. When two weak links meet at one cell, that cell loses the digit. A worked loop and a quiz.Expert9 min read

X-Cycle Cell GroupsComing laterExpert9 min read

XY-CycleAn XY-cycle is an XY-chain that closes into a loop of cells with two candidates. Every link between its cells has its digit at one end, so each one can strike. A worked six-cell ring, how it differs from an XY-chain and an X-cycle, and a quiz.Expert9 min read

XY-Cycle Cell GroupsComing laterExpert9 min read

Bi-Directional CycleComing laterExpert10 min read

Bi-Directional Cycle Cell GroupsComing laterExpert10 min read

NishioNishio tests one candidate: assume it, fill in only the singles it forces, and strike it if the grid breaks. A worked trial with two forced digits, the three ways a trial breaks, and why it is not guessing.Expert8 min read Digit Forcing ChainA digit forcing chain follows one candidate as true and as false, with singles only, and keeps whatever both branches agree on. A worked example, how it differs from Nishio, what the in-game hint shows, and a quiz.Expert10 min read Cell Forcing ChainA cell forcing chain tries each candidate of one cell as its value, tracks each with naked and hidden singles, and strikes any candidate every branch removes. With a worked three-candidate example, its ties to digit and unit forcing, and a quiz.Expert10 min read Unit Forcing ChainA unit forcing chain puts one digit in each place it has in a row, column or box, follows each with singles only, and keeps what all the branches agree on. Includes a worked example, a comparison with digit forcing and Nishio, and a quiz.Expert10 min read

ALS & exotics

7 techniques · none read

BUG+1BUG+1, the bivalue universal grave plus one: when every empty cell has two candidates but one, the digit seen three times in that cell's houses goes in. A worked grid, why it needs a puzzle with one solution, and how to spot it.Hard5 min read Restricted Common CandidateAn almost locked set is N cells in one house with N + 1 candidates. Two of them with a restricted common candidate (ALS-XZ) remove a shared digit. A worked grid, the link to Y-wings and naked subsets, and a quiz.Expert8 min read Aligned Pair ExclusionAligned pair exclusion lists every combination two cells that see each other could take, strikes the ones a repeated digit, a bivalue cell or an almost locked set rules out, and removes a candidate left in none. Worked grid and quiz.Expert8 min read

Aligned Triple ExclusionComing laterExpert9 min read

ALS ChainAn ALS chain links almost locked sets through restricted common candidates, a new digit at each joint, and removes a digit both end sets hold. A worked grid, why it works, its link to XY-chains and Y-wings, and a quiz.Expert10 min read Sue de CoqSue de Coq pairs two cells where a line crosses a box with a bivalue cell in the line and another in the box, then clears digits from both houses. A worked grid, why it works, its link to the rcc move, and a quiz.Expert10 min read Death BlossomA death blossom gives a stem cell one almost locked set per candidate, then removes a digit every petal holds. The two-petal form, a worked three-petal grid, why it works, and a quiz.Expert11 min read