Hard Sudoku Puzzles are designed for experienced players. In this difficulty level, the number of allocated clues at the start of the game is considerably reduced and finding the solution for the remaining cells requires high doses of concentration and logic.
At this point, pencil notes are no longer an option but rather a necessity to be able to work through the grid. Advanced techniques will also be required to eliminate candidates and find the solution for each cell.
Advanced techniques used in hard Sudoku levels are designed to eliminate candidates and help clear the grid. The three most used in this level are called X-Wing, Swordfish, and XY-Wing. These then branch out into other advanced techniques used mostly for the evil and impossible levels.
You can apply the X-Wing strategy when you find the same candidate in four different cells within the grid, united by row and column, and forming a square or rectangle when tracing an imaginary line between them. By mentally connecting the two diagonal extremities of this, you can determine that only two pairs of possibilities can come out of this link. If one is true, then the other becomes impossible. The goal is to test these sets and eliminate that candidate from any cells in the grid that would become impossible under both.
With the Swordfish technique, you must have three rows that contain two cells each with the same candidate. The position of the cells does not need to be symmetrical, but each must be connected to at least another by column. When united, these blocks create a closed chain that reveals only two possible sets out their combination. Like with the X-Wing technique, you should then test both of them and eliminate that candidate from cells that become impossible when both sets are applied..
The XY-Wing is applied when you find three cells, each with only a pair of candidates, that share at least a digit between them (e.g. XY/YZ/XZ). Their shape roughly resembles a Y shape, with a cell that works as the stem and two branches. Each branch must share a candidate with the stem. To make it easier, trace a line over the column of the stem and another two over the rows of the branches. If the cell where the lines meet one another contains the digit shared by the stem and the branch, you can safely eliminate it from being a candidate to it.