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Improve your Sudoku skills (Intermediate)
Improving your solvability
If you're a sudoku enthusiast like me, you probably have come across two types of sudokus. Those that are too easy and those that are way too hard. It seems like there's never anything in between. However, I've recently come across a few strategies to help organize my thinking when I'm searching horizontally, vertically, whether thinking "in the box" or even "out of the box" (a metaphor for the more advanced sudoku techniques). Things often get a lot more exciting the better you get at them, so I hope these tips reignite your sudoku solving experience!
This tutorial is primarily for intermediate solvers who have done a few sudokus here and there and are looking for an extra weapon in their arsenal to solve the slightly trickier puzzles. one thing to note is that you should be especially confident in the skills at the beginner level before attempting these intermediate skills, as these skills are only really used if the beginner tactics have been used and exhausted in the puzzle. Most intermdiate puzzles use a majority of the beginner rules and a few intermediate steps here and there to bring the puzzle up to the intermediate level. If you feel confident with this skills, you can try taking a look at the advanced hub in this three part series.
(1) Subgroup Exclusion
The sub-group exclusion rule is quite useful, and you have probably applied it without knowing it at one point or another. A subgroup is a collection of three squares in a row or column in a sudoku region (box). In the picture to the right (picture 1), in the upper left box, there are three columns that are subgroups (purple, red, green), as well as the three rows A, B, C. Every square belongs to one row and one column (two subgroups). This strategy is applied when you prove that a number must be in one subgroup and not the other two (you won't necessarily figure out which square it's in, but it should narrow down your possibilities). If you know that a number is in a particular subgroup, you can ignore that number as a possibility for the other two subgroups.
Here's an example (Picture B):
Look at the row F. The number 5 can only go in the 'd' and 'f' spots since the other spots already have 5 in their column. Thus, 5 can only be in the central box for row F, which almost begs us to apply the subgroup exclusion rule. In the central box, since there must be a 5 in row F, there can't be a 5 in row E, so we eliminate it as a choice for each of the squares in row E. This eliminates a few possibilities that is critical to solving the sudoku even though no squares have been completed.
(2) Hidden Twin
As a slightly more difficult exclusion rule, it should be applied after subgroup has been exhausted. For this rule, you must find a situation where two numbers can only go in two particular squares. Although we don't know which number goes in which, we can eliminate any other numbers that were previously choices for the twin squares. You can also apply this rule for triples (three numbers can only go in three squares in a region, eliminating any other numbers).
Try an example:
In the picture below (Picture C), you can see a simplified 4x4 grid for demonstration purposes (numbers 1-4). Look at the upper left box, where 2 & 3 must go somewhere in the region, but can only go in column 'a' since column 'b' already has both 2 & 3. Thus we have two twin squares 'Aa' and 'Ba'. This means all other choices can be disregarded (1 & 4). You can see that this elimination is pivotal to solving the entire puzzle ('Ac' eliminates the possibility of 2 in 'Aa', so 'Aa' must be 3).
(3) Lonely Twins
The lonely twin rule can be used to eliminate other possibilities in the same row, column or box as the twin. This is most times the logical next step after applying "Hidden Twin" and similarly can be applied to triples.
Check out the example (Picture D):
A lonely twin is observed in Ca and Cb. This twin prevents 2 & 3 from being in their row (since this twin is oriented along a row) or the box. Thus we can eliminate 2 from 'Da' and 2 from 'Cc' (which solve those wo respective squares).
That's it for the article. Try applying these rules to your sudoku solving. It might take a while for you to get use to them, but it's absolutely necessary for the intermediate and advanced sudokus. Happy solving!