Source: Levelica Canonical: https://www.levelica.com/en/guides/sudoku # Sudoku ## Summary Settling every empty cell with logic instead of guesswork, from singles to chains and puzzle design. ## Description Sudoku is a logic puzzle where the given digits force every remaining cell to a single answer. It starts from one constraint: no digit repeats in a row, a column, or a 3x3 box. From there your toolkit grows, from scanning by eye to pencil marks, to patterns that read two rows against two columns, to chains that follow an assumption to its end. Difficulty comes from the highest technique a puzzle demands, not from how long you took. The higher you go, the more your seat shifts from solver to setter. --- ## Level Overview | Level | Proficiency Stage | Hashtags | | ----- | ---------------------------------------------- | ---------------------------------------------------------------------- | | Lv.1 | Rules and Singles (HoDoKu Easy) | #SudokuRules #NakedSingle #FullHouse #GridScanning | | Lv.2 | Unaided Finish (HoDoKu Easy) | #HiddenSingle #Crosshatching #EliminationScan #UnaidedSolve | | Lv.3 | Candidate Control (HoDoKu Medium) | #PencilMarks #LockedCandidates #NakedPair #HiddenPair | | Lv.4 | Crossing Patterns (HoDoKu Hard) | #NakedTriple #HiddenTriple #XWing #SpeedSolving | | Lv.5 | Chain Reasoning (HoDoKu Unfair) | #Swordfish #XYWing #ChainLogic #SudokuGrandPrix | | Lv.6 | Construction and Verification (HoDoKu Extreme) | #ForcingChain #AlmostLockedSets #PuzzleConstruction #DifficultyGrading | | Lv.7 | Technique Creation | #TechniqueCanon #VariantInvention #RatingStandard #SudokuPedagogy | > Proficiency mapping source: the stages are based on the five difficulty grades HoDoKu, an open-source sudoku solver, assigns to solving techniques: Easy, Medium, Hard, Unfair, Extreme. HoDoKu holds that a puzzle's grade can never sit below the grade of the hardest step its solution needs, so which grade you can finish without guessing tells you which techniques you actually hold. That is why each level carries, in parentheses, the grade its technique repertoire first opens. Easy closes on singles alone, so it covers both Lv.1 and Lv.2; Lv.7 carries no grade because the scale has already hit its ceiling by then; and the top two stages take the Sudoku Grand Prix run by the World Puzzle Federation as their destination. The parenthetical is a band alignment that lays the grade order beside the acquisition order, not a literal technique-by-technique match. The stage names themselves come from the core behavior at each level. Sudoku has no internationally recognized ranking for individual solvers, so no grade code is used as a stage name. > **Integrative Framework:** The seven levels here are not one difficulty table copied over. They divide where four independent axes meet. HoDoKu's five-grade system (Easy, Medium, Hard, Unfair, Extreme) supplies the **technique repertoire axis**, the order of acquisition that climbs from singles to locked candidates and pairs and triples, then to X-Wing and Swordfish, then to chains and almost locked sets. Pelánek's work on difficulty rating supplies the **search cost axis**, the amount of sweeping and backtracking a puzzle costs and how that relates to real human solving time. The World Puzzle Federation's Sudoku Grand Prix supplies the **speed axis**, how many puzzles you clear inside a time limit while holding accuracy. The puzzle generation half of the same HoDoKu document supplies the **construction and verification axis**, the reverse job of guaranteeing one answer and grading the difficulty. Level boundaries fall where all four axes step up at once. > **Cross-Validation:** Level boundaries were set by checking whether separate sources converge on the same point. The baseline is HoDoKu's own rule. A puzzle's grade can never sit below the grade of the hardest step its solution needs, so what raises difficulty is one more technique becoming necessary, not more sweeping. Boundaries split where that technique gets added. > > - **Lv.2 to Lv.3 boundary**: the Easy band that closes on singles and hidden singles ends and the Medium band that needs locked candidates, pairs and triples begins, and that lands on the same spot where working by eye alone stops getting you anywhere without written candidates. The weapon changes from a tool that fills cells to a tool that erases them. > - **Lv.3 to Lv.4 boundary**: techniques that close inside one line or one box step back, X-Wing arrives to read two rows against two columns, and the grade band moves from Medium to Hard. Pelánek's overview tests several difficulty metrics against real human solving time. From this boundary on, finish time is decided by the height of the techniques you called on rather than by how much you swept, and the speed axis finally means something. > - **Lv.5 to Lv.6 boundary**: the ceiling of competition that the World Puzzle Federation's Grand Prix defines by ranking solvers across several rounds points to the same spot as the turn in HoDoKu's document, where puzzle generation follows the solving techniques. The grade band climbs from Unfair to the topmost Extreme. The role passes from solving what others set to owning the uniqueness and difficulty of what you set. > - **Lv.6 to Lv.7 boundary**: above this, no technique list and no competition rulebook names the next step. HoDoKu's grades stop at Extreme and the Grand Prix standings close with a season, so Lv.7 is defined only by the techniques and standards other people inherit and use, not by results. --- ## Level 1 #SudokuRules #NakedSingle #FullHouse #GridScanning ### Summary Learning the rules and filling cells where only one candidate fits. ### Description You've just stepped into sudoku. You pick up the constraint that no digit repeats in a row, a column, or a 3x3 box. Then you fill the spots where only one cell is left in a unit. You also fill cells whose candidates narrow to one, a naked single. On the technique repertoire axis you use the lowest tier only. On the search cost axis you sweep the whole grid over and over because you don't know where to look. Cover the hints and the next move stops coming. ### Checklist - [ ] Can explain the rule that each row, column, and 3x3 box holds the digits 1 through 9 exactly once - [ ] Can find a row or a box with only one empty cell left and fill that cell in - [ ] Can point to a cell whose candidates narrow to one and lock in the digit - [ ] Can finish one puzzle at the easiest difficulty from start to end with hints to lean on - [ ] Can catch and fix your own error when the same digit repeats in a line or a box - [ ] Can mark where you got stuck and write down which clue you were missing > If you've checked off most of this list, you're ready to enter the Lv.2 Unaided Finish stage and take on closing a puzzle with no hints. HoDoKu's technique ranking puts hidden singles right after naked singles, which flips the question you ask from cell first to digit first. Pick one digit at a time from 1 to 9 and sweep the whole grid for that digit alone. Do it in short repeated bursts and the flip settles in before anything else. --- ## Level 2 #HiddenSingle #Crosshatching #EliminationScan #UnaidedSolve ### Summary Finishing easy puzzles unaided through crosshatching. ### Description Your first independence shows up here: you close a puzzle with no hints. You find the spots where a digit has only one home inside a line or a box, called a hidden single. Crosshatching two lines against each other narrows its position inside a box. On the search cost axis your sweeps gain an order, and the same puzzle takes noticeably less time. You still carry it all by eye, with no candidates written down. ### Checklist - [ ] Can find the spots where a digit has only one possible cell inside a line or a box - [ ] Can crosshatch two lines to narrow where a digit sits inside a box - [ ] Can complete 10 puzzles in a row at the easiest difficulty with no hints - [ ] Can fix your own scan order for the digits 1 through 9 and apply it the same way every time - [ ] Can time 10 finished puzzles and record your own average - [ ] Can mark which cells you guessed and which ones you reasoned out > If you've checked off most of this list, you're ready to enter the Lv.3 Candidate Control stage and take on solving by writing candidates down and erasing them. Chase & Simon(1973) showed that skilled chess players read a board as meaningful units rather than separate pieces. The same shift in perception takes time in sudoku scanning, and until it lands, writing candidates on the grid is faster. Pick 10 puzzles your eyes alone can't close and write out every candidate. --- ## Level 3 #PencilMarks #LockedCandidates #NakedPair #HiddenPair ### Summary Tracking pencil marks to clear medium puzzles without guessing. ### Description This is where dependence turns into autonomy. You keep pencil marks, writing every possible digit into every empty cell. Then you clear the cells around them with locked candidates, where a box's candidates for one digit all sit in a single line. Naked pairs, two digits trapped in two cells, do the same work. On the technique repertoire axis your tools move from filling in to erasing, and medium puzzles close with no guessing. ### Checklist - [ ] Can write the candidates for every empty cell and update them each time a digit is locked in - [ ] Can spot a box whose candidates for one digit all sit in a single line and erase that digit from the rest of the line - [ ] Can find two cells left with the same two candidates and clear the candidates around them - [ ] Can find a hidden pair, two digits that appear in only two cells, and erase the rest of their candidates - [ ] Can finish 20 medium puzzles on logic alone with no guessing - [ ] Can recover from a broken pencil mark by recalculating only the line it affects - [ ] Can name the one technique that decided the final placement in a puzzle you finished > If you've checked off most of this list, you're ready to enter the Lv.4 Crossing Patterns stage and take on eliminations that read two rows against two columns. HoDoKu's table puts X-Wing after pairs and triples because the stage your reasoning plays on widens from inside one line to the crossing of rows and columns. Solve the same puzzle twice and cut your pencil marks in half on the second pass, and your view widens from the line to the grid. --- ## Level 4 #NakedTriple #HiddenTriple #XWing #SpeedSolving ### Summary Opening hard puzzles with triples and X-Wing. ### Description You stop running a set procedure and start picking tools by reading the position. Naked triples, three digits locked in three cells, and X-Wing, built from two rows and two columns, open puzzles at the hard grade. The speed axis enters for the first time: you time your finishes at one difficulty and manage the spread. You also judge the point where scanning by eye has nothing left to give and switch over to pencil marks. ### Checklist - [ ] Can find three cells left with only three digits between them and clear the candidates around them - [ ] Can spot a hidden triple, three digits that appear in only three cells - [ ] Can find an X-Wing built from two rows and two columns and erase the candidates in those columns - [ ] Can finish a hard puzzle with no guessing and list the techniques you used in order - [ ] Can log finish times for 20 puzzles at one difficulty and check the gap between your fastest and slowest - [ ] Can set the order of techniques to try when you stall and follow it as written - [ ] Can judge the point where scanning by eye has nothing left to give and switch to pencil marks > If you've checked off most of this list, you're ready to enter the Lv.5 Chain Reasoning stage and take on following an assumption to its contradiction. The Sudoku Grand Prix packs a round into 90 minutes, so when you drop a puzzle counts toward your score. Ericsson(1993) found that gains come from repetition aimed at weaknesses, not from comfortable practice. Collect the puzzles that stopped you, solve 20 in a row needing the same technique, and note where you stall. --- ## Level 5 #Swordfish #XYWing #ChainLogic #SudokuGrandPrix ### Summary Running chain logic and competing in timed rounds. ### Description Your reach widens from your own solving to the people around you. Swordfish across three rows and three columns, XY-Wing linking three cells, and simple coloring bring you into chain reasoning. Coloring splits one digit's candidates into two colors until one side contradicts itself. You learn to judge which puzzles to take and which to leave in a timed international round, and you coach people who have just started, step by step. ### Checklist - [ ] Can find a Swordfish across three rows and three columns and erase the candidates it rules out - [ ] Can find an XY-Wing linking three cells and erase the candidate from the cells all three see - [ ] Can alternate two colors across one digit's candidates and find the cell where a contradiction appears - [ ] Can follow a chain between two candidates and lock in a cell where both branches agree - [ ] Can enter a timed international round and submit your answers inside the limit - [ ] Can coach three or more beginners step by step, from crosshatching through locked candidates - [ ] Can pick which puzzles to solve first and which to skip in a round, judging by points and difficulty - [ ] Can review a round that went badly and name, puzzle by puzzle, where you lost time > If you've checked off most of this list, you're ready to enter the Lv.6 Construction and Verification stage and take on building puzzles that hold exactly one answer. HoDoKu covers solving techniques and puzzle generation in one document because the two jobs run the same knowledge in opposite directions. Take a puzzle you solved, pull the clues out one at a time, and watch for the point where difficulty climbs a step. That experiment opens the setter's eye. --- ## Level 6 #ForcingChain #AlmostLockedSets #PuzzleConstruction #DifficultyGrading ### Summary Working forcing chains and building puzzles with one answer. ### Description Your seat moves from solver to setter. Almost locked sets and forcing chains carry you through the hardest puzzles with no guessing, and you leave the path behind in a form other people can retrace. The construction and verification axis opens: you build puzzles whose single answer is guaranteed, and you grade their difficulty by the hardest technique they demand. ### Checklist - [ ] Can apply an almost locked set elimination in a real puzzle - [ ] Can assume each of a cell's two candidates in turn and trace the chain that lands on the same conclusion - [ ] Can finish a puzzle at the top difficulty with no guessing and record the solving path so others can retrace it - [ ] Can build a puzzle whose single answer is guaranteed and verify that uniqueness yourself - [ ] Can grade the difficulty of a puzzle you built by the hardest technique it demands - [ ] Can place in the standings of an international event that ranks solvers across several rounds - [ ] Can review another setter's puzzle and point out a second answer or a gap in the logic > If you've checked off most of this list, you're ready to enter the Lv.7 Technique Creation stage and take on widening the technique list. HoDoKu's grades stop here, and so do the Grand Prix rules. Ericsson(1993) set immediate feedback as a condition of deliberate practice, and once the fixed sequence ends, you have to arrange it yourself. Write your method up as a named procedure, give the same puzzle to three or more solvers, and collect the points where they split. --- ## Level 7 #TechniqueCanon #VariantInvention #RatingStandard #SudokuPedagogy ### Summary Leaving techniques and variants that later solvers take as standard. ### Description You leave a mark on how sudoku itself is spoken about. Other communities adopt the technique or notation you wrote up exactly as it stands. The variant rules you designed settle in as a competition category or a regular slot on a setting list. No technique list and no competition rulebook names a step beyond here, so the evidence of arrival is only how long the methods you left keep being cited. ### Checklist - [ ] Can confirm that a technique or notation you wrote up is in use in three or more other communities - [ ] Can show that a variant you designed was adopted as a competition category or a regular setting slot - [ ] Can show that your puzzles or commentary have been cited as learning material for five years or more - [ ] Can point to your own contributions to a difficulty grading standard or a competition rulebook - [ ] Can confirm that five or more people you coached now set puzzles or compete internationally on their own - [ ] Can record where a new technique changes the existing grading system, in a form later solvers can reproduce > If you've checked off most of this list, you stand where you leave behind the language that explains sudoku rather than one more way to solve it. Standings change every year, but named techniques and grading standards stay, and they decide what someone facing a grid for the first time looks at first. What this stage produces shows up in the puzzles other people solve with that language, not in the ones you solved yourself. --- ## References - [Difficulty Rating of Sudoku Puzzles: An Overview and Evaluation](https://www.fi.muni.cz/~xpelanek/publications/sudoku-arxiv.pdf) — Radek Pelánek, Masaryk University - [HoDoKu — Sudoku Solving Techniques and Puzzle Creation](https://hodoku.sourceforge.net/en/docs_cre.php) — HoDoKu (open-source Sudoku solver) - [WPF Sudoku Grand Prix — Rules and Rankings](https://gp.worldpuzzle.org/content/rules) — World Puzzle Federation (WPF) - [Perception in chess](https://doi.org/10.1016/0010-0285(73)90004-2) — Chase & Simon (Cognitive Psychology) - [The role of deliberate practice in the acquisition of expert performance](https://doi.org/10.1037/0033-295X.100.3.363) — Ericsson, Krampe & Tesch-Römer (Psychological Review)