You can also write in the margins outside of the cells (the individual boxes of 9 squares inside of larger puzzle). Feel free to take notes or jot down reminders to yourself. Using pencil also allows you to draw on the puzzle. If you use any patterns or uniqueness tests, you may want to visually track what you’re doing by circling or drawing around given cells.
Candidates refer to the potential solutions for a given square. If you know that square has to be a 6, 4, or 8, then 6, 4, and 8 are all candidates. It may feel like you’re making things harder by writing down every candidate, but the more information you have, the easier it will be to identify patterns and rule out incorrect answers. Some sudoku enthusiasts will “rank” their potential solutions by putting numbers they’re fairly confident in at the top corners, and numbers they’re less confident in at the bottom.
There are two popular scanning techniques: one direction and two directions. Scanning in one direction involves viewing the cells from left-to-right and up-to down. Scanning in two directions involves looking at perpendicular rows and columns together to process early combinations. If anything stands out to you as exceptionally obvious once you’re done scanning the given numbers, go ahead and fill in the squares you’re 100% confident in.
Cells refer to the collection of 9 squares that are inside of each sudoku puzzle. For example, if there’s a 6 in the middle square of the center cell and a 6 in the righthand column of the top-center cell, but there is only one available square in the left-hand column of the bottom-center cell, then a 6 has to go there!
Keep doing this over and over again until you’ve exhausted all of the potential singles on the board.
For example, let’s say you’ve got two 3s written down in the top two rows of squares in the top right cell. This is a naked pair. On the top left cell, a 3 may be able to go in any square right now. Since your pair rules out the bottom row in the top left, you can cross those candidates out. If this reveals a single, you’ve got a new square to fill in![7] X Research source
Quads are much rarer, and they’re less helpful in a way since they don’t let you narrow down a large number of candidates all at once, but if you spot one, it’s worth investigating. Solving single squares can also turn quads into triples or pairs, so don’t forget about these!
Corners (a collection of 4 solved squares in any of the 4 corners). Corner patterns help eliminate a ton of potential candidates in the rows and columns connected to it. Revisit these regularly to make sure you don’t provide a false solution. [10] X Research source Skyscrapers (two rows or columns of a given candidate that are unequal in length). This pattern can help you isolate rows and columns to solve entire rows or columns of the puzzle. [11] X Research source Right angles (any 3 given numbers in an L-shape inside of a cell). Right angles give you a lot of information regarding the empty columns and rows in the cell they’re in, which can help you cancel out incorrect candidates in the adjacent cells. [12] X Research source
Remember, this only works if the candidates are located in different cells. You cannot use an x-wing if one of the wing pairs are in the same cell. This is easiest to visualize when the candidates are really close together, but the rectangular pattern required to use this technique could theoretically involve the 4 outermost corners of the puzzle.
Finding swordfishes can be kind of challenging since it requires a closed chain of 6 candidates with a redundant candidate in each row and column. [15] X Research source
If only one square in a given cell contains multiple candidates, you can eliminate the other candidates from that cell. This is the simplest version of a uniqueness test. If you have two triples in a cell, but one of the candidates appears a third time in a different square in that cell, you can eliminate it from the triples to reveal a naked pair. If you have two cells in a rectangle with one extra candidate, you can eliminate that candidate from any rows or columns in the adjacent cells.
It can also just help to return to an area with a fresh eye. If you get stuck, you’re going to get frustrated. Taking a break and moving on will allow you to return with a new attitude that may help you find a solution.
If you did make a mistake somewhere, it can create a snowball effect where you suddenly have incorrect answers everywhere. If it’s a super difficult sudoku, calculate each row, column, or cell as soon as you solve it to make sure you haven’t made an obvious mistake.
