





Double Pointing Pairs When it comes to Jigsaw Sudoku, it can't be emphasised too much how important Pointing Pairs and Line/Box Reduction are for candidate removal and general puzzle cracking. They are important for normal Sudoku puzzles but excel in Jigsaws because the shapes allow for many more instances. And not just Pairs and Triples but Quads and upwards. This extension is very easy to spot  so I have put it before Law of Leftovers in the solver. Experienced Jigsaw solvers are probably using this all the time! The strategy family of Intersection Sets looks at how rows and columns intersect or overlap with boxes (or shapes in Jigsaw). It is fascinating to know that precisely because Jigsaws are very odd shapes  often elongated, we can improve the one box/one line Intersection Removal technique just for Jigsaws. We can 'double up' using two boxes and two lines (two rows or two columns). Pointing Pairs and Line/Box Reduction are flip opposites of each other, and same goes for their double versions. Pointing Pairs look for a box containing candidates X that all line up on a row or column. The solution must exist in the box so it excludes X from the rest of the line or column. What if we find two boxes where all the candidates line up on exactly two rows (or two columns)? Then we know any other candidate pointed at can't be the solution.
By doubling up the first strategy I'm begging the question, can you triple up as well? There is no logical reason why not, but this is rare as it would require five different shapes to intersect in a row or column. I have chosen not to implement it in the solver as I'd need to insert much further down the list of strategies but at some future point I will code it up and see if it is useful at all. If you work out an example, please let me know and I'll add it to this page. (The word "Pair" in this strategy name strains credulity since it will be a rare occasion when exactly two pairs are involved. The limit is this length or width of a Jigsaw shape and often there will be different numbers involved in each "pair". "Set" is perhaps a better word, but I retain "pair" because I want to associate it with the single one line/one box version where pairs are most common). Double Pointing Pairs are only half the story. Do read the next article on Double Line/Box Reduction for the complete picture. I am grateful for Brian Hobson for putting me on the track for these strategies. He says he's been using them for years to great success and I agree they are easy to spot. 
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