How to solve sudoku puzzles pdf

Same deal as Naked triples, only its between 4 cells and numbers. You know the drill Removes all numbers but the 4 from the 4 cells. An X-wing occurs when within 2 rows or columns there are only 2 instances of a number and they share the same column or row forming a rectangle. Erase all other instances of that number in line with any of the four numbers making the rectangle.

In the example above, there is an X-wing formed with 4's and all the ones in line with them get erased. The logic being, in both rows, there are only two possibilities that can be a 4, and since they form a perfect rectangle, if you choose one on the first line, then you would have to choose the one to the diagonal of it to satisfy that line, and same deal if you chose the other to start.

No matter which one you start with, all cells in line with the 4 main corners of the rectangle would be proven to not possibly be the same number. The unique rectangle occurs when there is a rectangle made entirely of pairs where one of them happens to have an extra number along with the pair. That extra number is the value of the cell. The logic being, sudokus are usually made with only one possible solution and if the rectangle of pairs occurs without an extra number, then the opposing corners would share the same value, and so would the other pair of corners.

OR the numbers could be switched around and still create a working solution. The swordfish occurs when there are 3 lines, either vertically or horizontally, which have 2 or 3 cells each of one number, which also has all of the cells within exactly 3 lines perpendicular to the first ones. Erase any of the number in question in line with the numbers making up the swordfish. The logic being the same as the X-wing, there are only 3 possible rows for the number in question to be in either horizontally or vertically and since the perpendicular of it was also limited to 3 lines, each row and column has to have that number at least once so any cells in line with them can be erased.

XY-wing is like naked triples but only 1 of the cells is related to both and the other 2 are exclusive of each other. In the example above, there is an XY-wing of the numbers 1, 2 and 7, and since the exclusive blocks share a 1, all other 1's in the same block as the 1 and 2, and the same row as the 1 and 7 get erased.

The logic being, if you choose the 1 in one side of the XY-wing, then any 1's in line with it would be erased, but if you chose the 7, then it would force the middle block to be a 2, then forcing the other side of the wing to be a 1. Those are the only 2 possibilities so you know that any cells intersecting the both of them can not be a 1.

Forced chaining is more of a guessing game than an actual trick, when a board is down to mostly doubles it allows you to force chains, pick a value in one square then follow it through, then pick the other and follow it through. If any cells result in the same value in both chains, then that cell gets that value. In the examples above i show both chains starting from the 1 and 2 cell and ending on the 5 and 7 cell, but on both chains that cell becomes a 5 so that one cell can be filled in.

The logic being, there are only two possibilities in the starting cell, and if both lead to the same result in another, then that other cell has no choice but to be that number.

XY-chain is a combination of forcing chains and XY-wing, you start a chain and stop when you come across another cell in a different row, column, AND block that gets forced into the second option you had in the first cell. Letting you erase that number from any cells that the two ends of the chain intersect. In the example above, it starts at the 2 and 3 cell, ending on the 3 and 9 cell, thus erasing the 3's that were in the same block as the end and the same column as the start.

The logic is the same as forcing chains and Xy-wing, the first could be the number in question or another one, and by chaining that into another cell forced to have the number in question, you can be sure that any cells intersecting both can not be the number. This trick is probably the last one you'd want to do on a sudoku, it involves forcing chains to look for contradictions.

In the example above, I start on the 1 and 2 cell and the chains force the 5 and 6 in the bottom right block both out thus creating a contradiction as that cell would no longer have any possibilities.

As a result of finding a contradiction, we can know that the first chain can not be the number we started with and would have to be the other, possibly even forcing another chain all on its own. However, I will stress again that great care must be taken with this trick to avoid messing up your puzzle completely; all it takes is a single mistake to make a sudoku impossible. The logic being, if the one choice you made results in a contradiction, then you know that that one choice is wrong, but also, if the one choice makes no contradiction then you still have to undo all of the chain and try another because just because it doesn't contradict itself doesn't mean it is the solution.

Question 1 year ago on Step This guide is amazing. I have just started out with sudoku and can do a few easy puzzles but I need to improve my skills. If you're a beginner check out Rich Goodwin's sudoku series-- it's a nice intro.

If you get stuck on a sudoku puzzle and need some help, we have a website that can help you get hints: Sudoku Beginner. I often mark in the number in smaller writing in cells like these as a note to myself that there is a candidate line In the example there are only 2 spaces for a 1 in the bottom right block and the line formed cuts off more possibilities letting you figure out that the red square is the only cell in the middle right block that can have a 1.

All the other numbers but the doubles can be erased from the 2 cells In the example above, the 2 and 9 are exclusive to the corner cells and so the other numbers in the cells got erased.

The logic being the same as the naked pairs. Logic being same as Hidden doubles. Thank you for taking the time to read through my guide. Did you make this project? Share it with us! I Made It! Answer Upvote. Does an XY-wing have to have the pairs in either 2 columns or 2 rows? This means that the empty space circled in blue in the bottom row cannot contain 7 or 6, and must contain number 5.

This square also has only three empty spaces. By checking to see which numbers are already in place 1, 2, 4, 6, 8 and 9 , we know that the missing numbers are 3, 5 and 7.

If we look above, we can see a 5 and 7 in the central row of the square circled in red , so that means that the top center space must contain a 3 in blue. Also, if we look to the left, we can see 5 circled in red , which means that the upper left space of the square cannot contain 5, so that means the 5 has to go in the left-center space marked in blue and the last remaining empty space has to be a 7. Please read part 2 of this series on how to solve Sudoku puzzles, using this actual game as an example.

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