Pointing

There is a pointing pattern when, inside a box, a number can only go in cells of the same row (or the same column). You don't know yet which one, but you do know that the row's copy of that number is there. So it is removed from the notes of the other cells in the row, outside the box.

It is the first Medium technique and the first that doesn't place a number: it removes candidates. The name comes from the picture: the cells left in the box are lined up and point at the rest of the row. It belongs to a family called locked candidates: the number is locked where a box and a row cross.

An example

1. There are no singles left in this grid: the Easy techniques make no progress. Let's look at the 9 in box 4, on the left, in the middle. The box has five empty cells and no 9 yet.
2. The same principle as in scanning applies. The 9 in column 3, at the top, rules out the empty cell in row 4. The 9 in row 6, in column 8, rules out the two in row 6.
3. Two cells are left, in row 5. In other words, the 9 of box 4 is in row 5.
4. Row 5 has only one 9, and it is in one of these two cells. The notes of the other empty cells in row 5 can be updated accordingly.
5. What did we gain? In column 5, the 9 only had two places: rows 4 and 5. Without the one in row 5, there is one left, in row 4. It is a hidden single that wasn't there before the pointing.

This is the usual pattern at Medium level: pointing doesn't place a number directly, but it helps remove candidates and, that way, a hidden single often appears.

Rows and columns

In the example the cells ended up in the same row. If they end up in the same column, the reasoning is the same: the number is removed from the rest of the column, in the other two boxes it crosses. There can be two or three cells. There can't be more than three, because a box only has three cells in each row and each column.

With or without notes

Pointing can be spotted while scanning the Sudoku. When looking for where a number fits in a box, you may find only two or three cells left, all in the same row or the same column. That is the pattern to use.

Without notes, just remember that the 9 of row 5 has to be in box 4, and use that when scanning box 5 or column 5. With the notes written, the pattern looks different: in a box, a number is noted in only two or three cells of the same row or column.

How to search

• When scanning, don't throw away the near misses. When a number is left with two or three cells in a box, check whether they are all in the same row or the same column.
• Check whether it removes anything. Pointing only lets you remove candidates if the number is still in the notes of other cells of that row or column, outside the box. If it isn't, the pattern is valid, but there is nothing to remove.
• After removing, look for singles. In the row or column where the candidate was removed, and in the boxes it crosses, a number may have been left with a single possible place.
• The question the other way round (in a row or column, a number that can only go inside one box) is claiming, the other half of locked candidates.

Your turn

Find a pointing pattern and cross out the candidates it removes: tap each cell, choose the number and, at the end, press «Check».