LOGIC PUZZLES
Sudoku Solving Techniques: From Scanning to Pairs
Every well-made Sudoku has exactly one answer, which means you never need to guess. This guide walks through the techniques in the order you will need them, from your first scan of an Easy grid to the patterns that unlock Expert puzzles.
What you are really doing
A Sudoku grid is a set of constraints. Each of the nine rows, nine columns and nine 3×3 boxes must contain the digits one to nine exactly once. Every technique below is just a way of noticing that a constraint leaves only one possibility somewhere on the board.
Beginners often think of solving as finding the next number. Experienced solvers think of it as removing possibilities until a number has nowhere else to go. That change of mindset is what separates a puzzle that feels like luck from one that feels like logic.
Start by scanning, not thinking
Pick the digit that appears most often among the clues and look for where its missing copies must go. If a digit already sits in two of the three rows crossing a box, the third row is often the only place left for it in that box. Do this for one digit across the whole board before moving to the next.
Scan rows and columns that are nearly full as well. A row with seven digits filled in needs only two more, and the two missing numbers give each empty cell in that row a tiny set of candidates. Work through each digit from one to nine; it takes a minute and often fills several cells.
Single candidates: the workhorse
A cell is a naked single when only one digit can legally go there, because the other eight already appear in its row, column or box. A digit is a hidden single when a row, column or box has only one cell left where that digit fits, even if that cell could hold other digits too.
Most Easy and Medium puzzles fall to these two ideas alone. When you feel stuck, go digit by digit and ask for each unit, where can this go? Then go cell by cell and ask, what can go here? Alternating between the two questions finds most of the available moves.
Use pencil notes on purpose
Notes are not a place to dump every possibility in the grid. Write candidates only in the region you are currently working on, usually a box that is already half full. Filling the whole board with tiny numbers creates visual noise and hides the patterns you are trying to see.
A good rhythm is to scan for singles until you stall, add notes to the most constrained region, then look for the patterns below. Keep notes honest: when you place a number, remove it from the notes in its row, column and box. PlayDapple does this clean-up for you when you enter a full number, but it is worth understanding why.
Naked pairs and triples
If two cells in the same row, column or box can contain only the same two digits, those digits must occupy those two cells, in some order. You can therefore remove both digits from every other cell in that unit. The same idea extends to triples, where three cells share three candidates between them, even if no single cell shows all three.
Pairs are easiest to spot with notes. Look for two cells that show the identical two numbers, then check which other cells in the unit still list one of them. Each elimination can reveal a new single, so apply the pair and then return to scanning.
Pointing pairs and box-line reduction
Sometimes every place a digit can go inside a box lies on a single row or column. That digit must be in that line within the box, so you can remove it from the rest of the line outside the box. This is called a pointing pair, or a pointing triple when three cells are involved.
The reverse also works. If a digit in a row can only appear inside one box, it can be removed from the other cells of that box. Between them these two eliminations unlock many Hard puzzles, and they are much easier to find than they sound once you look at where candidates line up.
Recovering from a mistake
If a row suddenly has no legal place for a digit, an earlier entry is wrong. Do not erase everything. Look for the most recent entry that was not completely forced, undo back to it, and replace it with a more careful deduction.
Use the Check feature when you suspect an error, since it flags entries that differ from the solution without replacing them. Use Hint sparingly. A hint tells you a value but not why it belongs there, so study what changed and try to find the reasoning yourself.
A practice plan
Spend a few puzzles on Easy until singles are automatic. Move to Medium and force yourself to use notes only when you are stuck. When Hard feels comfortable, try Expert and look for pairs and pointing pairs. Speed arrives later; accuracy and pattern recognition come first.
Keep an eye on the timer only if it motivates you. Many people enjoy Sudoku most when they ignore it. Pausing for a break is also a useful technique, because a fresh look often shows a single you missed.
X-Wing: your first advanced pattern
When a digit can appear in exactly two cells in each of two different rows, and those cells share the same two columns, you have an X-Wing. The digit must occupy one diagonal pair or the other, so it can be removed from every other cell in those two columns. The same pattern works with rows and columns swapped.
X-Wings are rare in Easy and Medium puzzles but turn up in Expert grids. Finding one is easiest with notes for a single digit: scan each row for exactly two candidates and look for a matching row.
Common beginner mistakes
The most common error is entering a number because it looks plausible rather than because it is forced. A forced move can always be explained in one sentence, such as this is the only place a 7 can go in this box. If you cannot say the sentence, hold off.
The second mistake is neglecting to update notes. A stale note shows a candidate that is no longer possible, and a stale note can hide a single you would otherwise have seen. Make a habit of clearing notes immediately after placing a number.
The third is tunnel vision. If one region has stopped giving you moves, move to another instead of staring at it. A move elsewhere often changes the constraints in the region you left.
Why unique solutions matter
A properly constructed Sudoku has exactly one solution. This is not a stylistic preference but the property that makes logical solving possible: if two solutions existed, no amount of deduction could choose between them. The puzzles on PlayDapple are generated with a solver that verifies uniqueness before a puzzle is shown, which is why you can trust that every deduction you make is leading somewhere.