Sudoku Solving Tip - X Wing Technique

in this episode we'll cover the x-wing technique which is used in solving some of the hardest puzzles now x-wings come in two variations the column variation and the row variation well in this episode we'll cover the column variation so let's start with our first example in an x-wing we're looking for a formation where the same candidate appears at four corners of a rectangle like you see here in this example each of the highlighted cells contains an eight as a candidate and forms the corners of a rectangle now let's look at the rows in row five the candidate eight does not appear anywhere else except in these two cells the same is true for row eight the eight does not appear anywhere else except in these two cells so this is a typical example of an x-wing pattern now the x-wing rule suggests that we'll have an eight in this cell in this cell or in this cell and this cell notice how these two diagonal lines form an X and that's why we call this technique x-wing now based on the x-wing technique if this cell isn't eight then across the row this cell cannot be an eight and down the column this cell cannot be an eight therefore if this cell is an eight it's opposite cell must be an eight now let's check the opposite case if this cell is an eight then across the row this cannot be an eight and looking down the column this also cannot be an eight therefore if this is an eight it's opposite cell must be an eight so in either case you'll end up with AIDS in opposite corners now we don't know which diagonal the AIDS will lie on but we do know that eight will be in opposite corners and one of the AIDS will be in column one and the other will be in column nine so based on this knowledge we can eliminate eight as candidates from all the other cells in columns one and nine as indicated by the green rings so let's go ahead and eliminate the eight once we do that we're left with a single choice over here so this cell must be a two now x-wings can be quite confusing to understand so let's look at a couple more examples to fully understand this technique so this is example two here the highlighted cells form the four corners of our rectangle each of the highlighted cells contains a for forming our x wing notice there are no other force in Row 2 and row 9 outside the highlighted cells so based on the x-wing rule we can eliminate fours from all the other cells in columns 3 & 9 as indicated by the green rings so let's remove the fours from the three cells as soon as we do that were left with a naked pair over here in Row 4 which will hopefully help us make further progress now let's look at one last example here in example three we'll explore some formations which look like x-wings but are really not x-wings now do you think these highlighted cells form an x-wing well at first glance it does look like an x-wing because each of these cells contains a seven and forms a rectangle but if you look carefully row two contains these other sevens which violates the x-wing rule therefore this is not an x-wing now how about this formation do you think this is an x-wing well it sure looks like an x-wing because once again each of these cells contains a seven and forms a rectangle but it's not an x-wing because there's also these other sevens in rows two and five for it to be a true x-wing there should not be any sevens in rows two and five except for the highlighted cells so be very careful in identifying x-wings now how about this last formation well this time we do have an x-wing and it's an x-wing because we have a seven in all the highlighted cells which form a rectangle but this time we don't have any of the sevens in rows three and four outside the highlighted cells so this is a true x-wing now based on the x-wing rule we can eliminate the sevens from columns three and nine once these sevens are eliminated were left with a single choice over here and here so sells 23 must be a six and sell 53 must be a nine so that's all there is to x-wings now all these examples we just saw were column variations we use rows to determine our x wing and then eliminate it candidates from the columns now the reciprocal case is also possible where we'll use columns to identify our x wing and then eliminate candidates from the rows so the row variation of x wings is next

Channel: SudokuVideoTutorials

Views: 1,922,321

Keywords: Sudoku, Solving, Wing, Solver, Tips, Video, Tutorial

Id: pi7QLXW5Z3M

Length: 7min 16sec (436 seconds)

Published: Thu Apr 16 2009