Sudoku Solving Techniques

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Pointing Pairs - Intersection Removal

Pointing Pairs - Intersection Removal

We’re already familiar with Pairs, Triples and Quads but previously we were only looking for them in a single row, column or box (unit). There are sound logical reasons for looking at the overlap of two units now which is where the name ‘intersection removal’ comes from.
The intersection of two units.

Before we formulate the rule, we’ll identify the principle – which is very easy to spot and apply. In the bottom section of this Sudoku we have lots of 3’s, particularly in row G. However, in the middle box we have only two 3’s. These are the only two places in that whole box where 3 is permissible. Luckily they are aligned on a row which is our intersection.

Fig. 10.1

Logically, if those two cells are the only place a 3 can go in that box then any other 3 on that row must be illegal and we can remove them. The 3’s marked in grey squares are the eliminations. We say that the 3 Pair in box 8 are pointing along the row at the illegal 3’s, hence “Pointing Pairs”. Pointing Triples are also a possibility:

Fig. 10.2

Here there are three 3’s in box 3 and aligned row A which tells us we can remove them from the rest of the box.

Rows and columns intersect on three cells with boxes but between a row and a column the overlap is confined to one cell – so the principle of intersection must always involve a box. This also puts a maximum on the size of the intersection. We can’t find Pointing Quads since only three cells in a box can be aligned on row or column. If we were playing Jigsaw Sudoku the restriction is lifted. Boxes can be very elongated and therefore Quads and Quintets are possible.

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