Naked Pairs and Pointing Pairs Explained

Why pairs matter

Singles find a value for a single cell, one at a time, and they carry you comfortably through easy and medium boards. Pairs do something different and far more powerful: they let you remove candidates from many cells at once, and those bulk eliminations frequently create the very singles you were missing a moment earlier. This is the moment most players stop feeling permanently stuck on hard boards, because it hands them a way to make progress when no cell can yet be filled directly. Instead of staring at a grid full of two-candidate and three-candidate cells with no obvious next move anywhere, you start using the relationships between cells to prune the possibilities down, and the puzzle begins to open up in front of you again. Pairs do not usually finish a board by themselves, but they reliably break the deadlock, and breaking the deadlock is exactly what a hard puzzle demands of you when the simple methods have run completely dry.

Naked pairs, step by step

A naked pair occurs when two cells in the same group, meaning the same row, column, or box, both hold the exact same two candidates and nothing else besides them. For example, imagine two cells in a row that each show only the triangle and the heart as possibilities. You do not yet know which of the two cells will ultimately take the triangle and which will take the heart, and you do not need to know that to make progress. What you do know for certain is this: between them, those two cells will use up the triangle and the heart completely, because each cell must be one of the two and no cell can be both. That shared certainty is the entire basis of the elimination that follows, and it holds no matter how the pair eventually resolves. Once you see a naked pair, you can act on it immediately, long before you can tell which cell is which.

A naked pair worked example

Take row 3 of the board. After keeping careful notes, r3c1 shows only the triangle and the heart, and r3c7 also shows only the triangle and the heart, with no other candidates in either cell. Neither cell can be anything else, so between them they will consume the triangle and the heart within row 3. That means neither shape can legally appear anywhere else in the row, so you confidently erase the triangle and the heart from the notes of every other cell in row 3, including r3c4 and r3c9. Now suppose r3c4 previously read the triangle, the heart, and the circle as its three candidates. After the erasure it reads only the circle, which makes it a naked single, so you place the circle at r3c4 straight away. One pair you could not immediately resolve just handed you a completely certain placement two cells over, and that placement will likely unlock the next move in turn. Notice that you never had to decide which of r3c1 and r3c7 was the triangle and which was the heart, because the eliminating power of the pair came entirely from the fact that they were the only two homes for both shapes, not from resolving them.

Pointing pairs, step by step

A pointing pair lives at the intersection of a box and a line, and it works in the opposite direction to a naked pair. Suppose that within one box a particular value can only be penciled into two cells, and both of those cells happen to sit in the same row. Since that value must appear somewhere inside the box, and its only two possible homes there both lie on that one row, the value is guaranteed to end up in that row within this box. That local guarantee reaches beyond the box itself, which is what makes the technique so useful: because the value is locked into that row here, it cannot appear in the same row anywhere outside the box. As a worked example, look at the top-left box, where the moon can only go in r1c2 and r1c3, both in row 1. The moon must be in one of them, so it is certainly in row 1, and you can erase the moon from r1c5 and r1c8 elsewhere along that row.

How to find them, and why one deduction unlocks many

• Keep accurate, up to date notes, because pairs are almost impossible to spot without candidates written down.
• Scan each row, column, and box for two cells sharing the same two candidates, which is a naked pair.
• For each box, check whether a value is restricted to two cells on a single line, which is a pointing pair.
• After any pair lets you erase candidates, immediately re-scan the affected group for freshly created singles, then place them and try a Hard board in Shapedoku with Notes mode on to practice the chain reaction.