Solver App for Android and iPhone Strategies for Number Puzzles of all kinds
Print Version
Basic Strategies
Tough Strategies
Diabolical Strategies
Extreme Strategies
Depreciated Strategies
The Logic of Sudoku
Order Str8ts Book 1
Order Now!
Order Str8ts Book 2
Order Now!
  Intersection Removal
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:
  1. A Pair or Triple in a box - if they are aligned on a row, n can be removed from the rest of the row.
  2. A Pair or Triple in a box - if they are aligned on a column, n can be removed from the rest of the column.
  3. 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.
  4. 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 G5 point along the row to G2.
Pointing Pairs
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. A couple are consequences of a previous elimination.
Pointing Pairs Example 2
Pointing Pairs Example 2: Load Example

Here is a Pointing Triple found in a tough grade puzzle containing many wholesome and nutritious Pointing Pairs. All the 3s are found in G6, H6 and J6 and nowhere else in box 8, so they point up the column to another 3 which can be removed.
Pointing Triple
Pointing Triple: Load Example or : From the Start
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 somewhere 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
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
Box/Line Reduction: Load Example or : From the Start

I've rolled two examples into one diagram here, I hope it wont be confusing. The one involving 6s follows on immediately from the first one found among the 3s (purely because it searches in order from 1 to 9). They are both 'triple' versions of Box/Line reduction.

In column 1 the 3s occupy G1, H1, J1 (shorthand = GHJ1) which are all in box 7. The solution is pinned to column 1 so the other 3s in the box must go.

The 6s are likewise pinned by column 2. You can see there are other 6s in column 3, in A3 and J3) which is why it's okay to remove the 6s in DEF3. You won't run out.
Triple BLR
Triple BLR: Load Example or : From the Start

If you are a fan of Jigsaw Sudoku puzzles, you may want to read the articles on Double Pointing Pairs and Double Line/Box Reduction which extend the ideas here but are strategies possible only in the Jigsaw variant of the puzzle.

Go back to Hidden CandidatesContinue to X-Wings


Your Name/Handle

Email Address - required for confirmation (it will not be displayed here)

Your comment or question

Please enter the
letters you see:
Enter these letters Remember me

Please keep your comments relevant to this article.
Email addresses are never displayed, but they are required to confirm your comments. When you enter your name and email address, you'll be sent a link to
confirm your comment. Line breaks and paragraphs are automatically converted no need to use <p> or <br> tags.

Subject Comments - Talk
Comments here pertain to corrections to the text, not the subject itself

Wednesday 11-Sep-2013

... by: Hassieb Wali

I can see pairs in the examples but no triples. Could you give an example of triples.

Andrew Stuart writes:

Good idea, done

Saturday 1-Dec-2012

... by: Brandon

In the second paragraph of "Box Line Reduction", "someone" should be changed to "somewhere". Very nice explanations nevertheless!

Andrew Stuart writes:

Fixed, ty!

Sunday 30-Aug-2009

... by: W Gerald

Why isn't your printed version the same as the site version with no changes in layout and only background and text colours reversed? The site version display is superb.

Andrew Stuart writes:

It should be identical. It removes the side menu - not required for printing - and it horizontally flexes since the printer driver decides on the actual width.

Post a Comment using Facebook...

Article created on 3-April-2008. Views: 290250
This page was last modified on 12-September-2013, at 02:02.
All text is copyright and for personal use only but may be reproduced with the permission of the author.
Copyright Andrew Stuart @ Syndicated Puzzles Inc, 2013