Lesson #10: X-Wings and the Rectangle Rule for Solving Medium to Hard Sudoku Puzzles

hello and welcome to this video on x-wings also known as the rectangle rule it's actually a two by two rectangle that forms an x pattern take a look at this grid we see that all the candidates are filled in and in column 4 the 2 can only appear in rows a and c but in column 7 the 2 also appears only in rows a and c this creates a rectangle pattern where the corners of the rectangle all have one candidate in common the two we can also identify an x pattern here since if this is the two in row a then this has to be the other two in column c but if this is the two in row a then this would be the other two in row c and so this forms an x pattern as you see here let's go through the logic of this pattern one more time and then we'll see how to use it as a solving strategy if this 2 in row a column 4 is true then this 2 in the same row row a column 7 can't be true so the 2 in column 7 must therefore be in row c so in this scenario this is what the twos would look like however if row a column 4 is not a 2 then the 2 in the same row column 7 must be true and therefore the 2 in column 4 must be in row c and this forms the other wing of the x which is why it's called an x-wing in either case the true twos will be at opposite ends of the x or opposite ends of the rectangle alright now that we understand what the x-wing pattern looks like how can we use it as a solving strategy well if this 2 is true then this 2 is also true and if this 2 is true then this 2 is also true so either way we have a 2 in row a and another 2 in row c already spoken for so there can't be another two in row a or row c so now we can eliminate all the other two candidates in row a and all the other two candidates in row c in this example we found the matching candidates the twos down the columns forming an x-wing or rectangle and then eliminated all the other twos in those rows this rule also applies when we find candidates across the rows we can then eliminate the penciled in candidates down the columns here's an example of that in this case the number 4 forms the corners of the 2x2 rectangle in row d the only place a 4 can go is in either columns three or six and in row f the only place a four can go is in either columns three or six so now we can eliminate all the fours as candidates in column three and all the fours as candidates in column six so how do you spot this x-wing pattern the trick is to look for a number that only appears twice in a line either a row or a column and then look to see if there's a corresponding row or column where that same number also appears twice if the four cells form a rectangle then you have an x-wing pattern and you can eliminate all the other same numbers in the row or column this pattern appears often and is a powerful tool for eliminating candidates keep doing sudoku puzzles every day and you'll soon learn to recognize this pattern as you get more practice i'll continue adding to the solve me episodes playlist and you'll see this and other strategies being used as i think out loud while solving i hope you enjoyed watching this video and i hope you learned something

Channel: Learn Something

Views: 47,106

Keywords: sudoku tutorials, sudoku tricks, sudoku guy, cracking the cryptic, cracking the cryptic classic sudoku, classic sudoku, sudoku solving techniques, sudoku solving tricks, sudoku for the frustrated, sudoku for seniors, what are x wings in sudoku, what are x-wings in sudoku, xwings, sudoku for beginners

Id: ooMuXjuOF1E

Length: 4min 28sec (268 seconds)

Published: Sat Oct 23 2021