Pointing pairs and triples

What it is

Pointing is the first technique that removes candidates rather than placing a digit. It works like this: if, inside one box, a digit can only go in cells that all lie in the same row, then the digit must end up in that row within that box. That means no other cell in that row, outside the box, can hold that digit. The same applies to columns.

The candidates in the box “point” along the row or column, ruling the digit out further along. If two cells are involved, it is often called a pointing pair. If three, a pointing triple. The logic is the same either way.

Some books call this “locked candidates (type 1)”. It means the same thing.

How to spot it

You need pencil marks, or at least a clear picture of where a digit can go in a box. Then:

1. Pick a box and a digit that is missing from it.
2. Find every cell in the box where that digit is a candidate.
3. Check whether all of those cells are in a single row, or a single column.

If they are, look along that row or column outside the box. Any cell there with that digit as a candidate can have it removed.

A fast way to find these is to cross-hatch a box, as in our scanning guide. When the hatching leaves two or three cells in a straight line, you have a pointing pattern.

A worked example

Look at box 4, which covers rows 4 to 6 and columns 1 to 3. The digit 6 is missing from it.

After checking the box, you find that 6 is only a candidate in two cells: row 5, column 1 and row 5, column 3. Every other empty cell in box 4 is blocked, either by a 6 elsewhere in its row or column.

Both of those cells are in row 5. So wherever the 6 goes in box 4, it will be in row 5. Row 5 can only hold one 6, so the 6 for row 5 is locked inside box 4.

Now look along row 5 outside box 4. Say row 5, column 6 (in box 5) and row 5, column 8 (in box 6) both have 6 among their notes. You can remove 6 from both.

Suppose row 5, column 8 had notes of 2 and 6. After removing the 6, only 2 is left, so it becomes a naked single and you can place the 2.

Why it works

Every box needs a 6, and every row needs a 6. In this example, box 4’s 6 has to be in row 5. If another cell in row 5 also held a 6, row 5 would have two of them, which breaks the rules. So the other cells in row 5 cannot be 6.

A common mistake

The most common error is getting the direction wrong. Pointing removes candidates from the row or column outside the box. It does not tell you anything about the other cells inside the box, which already had no candidates for the digit.

Another slip is missing one candidate cell. If 6 could also go at row 6, column 2, the candidates are no longer in a single row and nothing can be removed. Check every empty cell in the box carefully before making any removals. If your notes are out of date, the pattern can look real when it is not.

When you will need it

Pointing is one of the techniques added at Medium level on sudoku.ie, alongside claiming and pairs. You will meet it on Tuesday, Wednesday and Sunday puzzles, and it is used all the time on Hard and Expert days. Claiming is its mirror image, so read that guide next.