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If any one number occurs twice or three times in just one unit (any row, column or box) then we can remove that number from the intersection of another unit. There are four types of intersection: A Pair or Triple in a box - if they are aligned on a row, n can be removed from the rest of the row. A Pair or Triple in a box - if they are aligned on a column, n can be removed from the rest of the column. A Pair or Triple on a row - if they are all in the same box, n can be removed from the rest of the box. A Pair or Triple on a column - if they are all in the same box, n can be removed from the rest of the box.

Pointing Pairs, Pointing Triples Looking at each box in turn there may be two or three occurrences of a particular number. If these numbers are aligned on a single row or column (as a pair or a triple) then we know that number MUST occur on that line. Therefore, if the number occurs anywhere else on the row or column outside the box WHICH THEY ARE ALIGNED ON then it can be removed. The pair or triple points along the line at any numbers which can be removed. Here are two Pointing Pairs at the same time on this tough rated puzzle. The 3s in B7 and B9 are alone in box 3 and they are aligned on the row. So looking along the row we can remove all the 3s in Box 1. In a similar manner the 2s in G4 and B7 point along the row to G2.

Pointing Pairs: Load Example or : From the Start

Now this is a rather special puzzle and a little extreme, but if we look at the whole board you can see I have highlighted a whole cluster of Pointing Pairs. It is obviously not necessary to spot everyone to progress the board but there are so many good examples it is worth looking at. The eliminations are highlighted in yellow. You should be able to see which eliminations belong to which Pointing Pair.

Pointing Pairs Example 2: Load Example

Box Line Reduction This strategy involves careful comparison of rows and columns against the content of boxes (3 x 3 squares). If we find numbers in any row or column that are grouped together in just one box, we can exclude those numbers from the rest of the box. For example: This Sudoku contains numerous Pointing Pairs and Box/Line Reductions and is worth stepping through from the start. Consider row A. The only 2s left are in A4 and A5 which means we should should check the rest of the box. 2 has to go someone on row A and it will be in one of those two cells. So we can eliminate 2 from B5, C4 and C5.

Box/Line Reduction: Load Example or : From the Start

In the very next step of the same puzzle we have two 4s alone in column 8. That fixes 4 to be in either cell A8 or B8. We can remove the other 4s in box 3 and get our next solved cell: 2 in C7.

Box/Line Reduction: Load Example or : From the Start

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