Naked pair
Level: Beginner+ When to use it: When two cells in the same row, column or box have exactly the same two pencil-mark candidates.
How it works: If two cells in one unit can only hold the same two digits — say {3, 7} and {3, 7} — then those two digits must go in those two cells, even though we don't know which goes where. That means we can erase 3 and 7 from every other cell in the same unit.
★ Example: In a row, cell A is {3, 7} and cell B is {3, 7}. Cell C nearby is {3, 5, 7}. We can confidently erase 3 and 7 from C, leaving C as {5} — a brand-new naked single!
💡 Pro tip: Naked pairs unlock more naked pairs and hidden singles. One little spotted pair often opens the whole puzzle.
Hidden pair
Level: Beginner+ When to use it: When two digits can only fit in the same two cells of a row, column or box — even though those cells have other candidates listed too.
How it works: Inside one unit, find a pair of digits that appear as candidates in only two specific cells. Those two digits must take those two cells. You can erase every other candidate from those two cells, leaving just the pair behind.
★ Example: In a 3×3 box, the digits 4 and 8 only show up as candidates in two cells, A and B. Cell A's candidates are {2, 4, 8} and cell B's are {4, 6, 8}. Erase the extras: A becomes {4, 8} and B becomes {4, 8}.
💡 Pro tip: Hidden pairs are like naked pairs in disguise. Once spotted, you've created a naked pair you can keep using.
Pointing pair (or triple)
Level: Beginner+ When to use it: When all the candidates for a digit inside a 3×3 box sit in one row or one column.
How it works: Pick a digit and a box. If every place that digit could go in the box lines up in the same row or column, then it must go somewhere in that line — but inside the box. That means the digit can't go anywhere else along that row or column outside the box. Erase those extra candidates.
★ Example: In the top-left box, the digit 2 can only fit in the cells of row 1. So the 2 in that box has to live in row 1. Now you can erase the candidate 2 from every other cell in row 1 outside the top-left box.
Box-line reduction
Level: Beginner+ When to use it: When all the candidates for a digit inside a row or column sit inside a single 3×3 box.
How it works: It's the mirror of a pointing pair. If a digit can only fit a row or column inside one box, the digit must be in that box — so you can erase it from the other cells in that box.
★ Example: In row 4, the digit 5 can only go in the three cells that fall inside the centre box. The 5 must therefore be inside the centre box, in row 4 — so other cells of the centre box (rows 5 and 6) can't be 5.
💡 Pro tip: Pointing pairs erase candidates outside the box. Box-line reductions erase candidates inside the box. Same idea, different angle.
Naked triple
Level: Beginner+ When to use it: When three cells in the same unit share only three candidates between them.
How it works: If three cells of a row, column or box together can only hold three particular digits — for example {2, 5, 9}, {2, 5}, {5, 9} — then those three digits live in those three cells. You can erase all three digits from every other cell in the same unit.
★ Example: Three cells in a column are {1, 4}, {1, 4, 6} and {4, 6}. Together they cover only {1, 4, 6}. Any other cell in the column with 1, 4 or 6 as a candidate can have those numbers erased.
💡 Pro tip: Naked triples are a step up. If you can spot pairs reliably, triples are the natural next thing to learn.