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Improve your Sudoku Skills (Advanced)
Turning up the Heat
This tutorial is primarily for advanced solvers who have done a good deal of sudokus and would like to further improve their skills with some advanced theory. If you don't feel confident in your skills yet, take a look at the intermediate or beginner hub in this three part series.
These rules are applied the least often out of the various sudoku skills that are used. The beginner skills account for most of the steps in any sudoku, so most of them the really advanced skills are used.
However, in the difficult and fiendish puzzles, you'll probably come across one of these skills at a pivotal step. Make sure you're well versed with the intermediate and beginner skills before you try these.
The following three tactics are best explained by example, and are quite difficult to spot in any puzzle. However, you should probably expect one of these tricks in the hardest ranked puzzles.
(1) The Box
In picture A, we have labeled the squares where a 4 could possibly go. In particular, we take a look at rows C and G. There are only four squares where a 4 can go (highlighted green), and they actually form a box. The fact that they share pairs of columns/rows (aka boxlike) means that there must be two 4s on opposing corners of the box. Why? For example if there was a 4 in 'Bf,' there couldn't be a 4 in 'Cf' or 'Gf' which means there must be a 4 in both 'Ca' and 'Ga' which is not possible. For this reason all other 4s can be eliminated as possibilities in the rows and columns of the box sides (in purple).
(2) Double Box
In picture B, we have outlined the double box structure in red, with the possibilities for 9 in blue. We have three pairs of possibilities for 9 in columns b, e and h. These three columns have coinciding end squares so the same box rule applies. See if you can convince yourself why, using the same logic as above. This proves that the possibilities for 9 in green can be eliminated. This technique is very rarely used, but if you can successfully use it, you know you've become a true sudoku master!
The last and most annoying method is a technique that always works. Nearly all the puzzles in existence won't require this and a lot of solvers will probably tell you it's not the right way to go about it. However, I have stumbled across puzzles that probably require this technique or a type of triple box or multiple induction that basically requires working ahead ten steps anyway. The idea is to keep filling out boxes until you reach a contradiction. This is usually only useful if you've exhausted all the other methods and you have a box that has only two choices. Choose one of the choices and complete from there. If you reach a contradiction, you know it's the other choice. If you don't reach a contradiction, check that the other choice does lead to a contradiction.