How to Solve Sudoku Puzzles (beginner and Advanced)
Introduction: How to Solve Sudoku Puzzles (beginner and Advanced)
In this guide I will explain all of the tricks I have found to reduce the possibilities in a sudoku puzzle and ultimately solve it. Each step in this instructable will be of a different trick so if you come across any you already know of then feel free to skip ahead to the later ones.
**For beginners** let's get to know the puzzle itself, a sudoku puzzle is a grid of 9 small squares horizontally by 9 small squares vertically. where after every 3 there is a thicker line and throughout the puzzle various numbers are placed. The object of the puzzle is to figure out the places where you have to place the numbers 1-9 in order to have every single row, column, and block filled up with a 1, 2, 3, 4, 5, 6, 7, 8, and a 9. Most sudoku puzzles are made so that there is only one final solution after sifting through all the options and filling in all the blocks. **For beginners**
The last thing for this introduction will be my order of doing things:
1. I use 4 terms regularly, a block is the 3x3 area of squares separated by the thicker lines, a row is the horizontal line of numbers, a column is the vertical line of numbers, and a cell is any individual square on the board.
2. each trick will be given *'s for how annoying I think they are to find and use, but they will be ordered by similarity (ie. 74
the pairs/triples/quads will be together but it may be more conducive to move onto the later tricks before thinking in quads.)
3. on each trick I will first explain what to do, then show how it works in the example image, and finally the logic behind why it works.
4. I like to enjoy myself while solving them, so the steps may seem a bit inefficient as i voice my own standards.
Step 1: Visualization*
Look for single cells within the blocks that do not intersect any horizontal or vertical lines that could be drawn from one of the numbers on the board, then place that number when you find them. An easier way to think of this is find all of the 1's on the board, draw mental lines vertically and horizontally off all of them, then see if you can find any blocks where all but one cell is either crossing these lines or filled by other large numbers. When you do, you would know that you can fill in that cell with a 1; this can be done with any number.
In my example given I drew the lines off of every 8 on the board and in the upper right block there is a single cell that does not cross any of them, so that block has to be an 8. Take care to not fill in the middle 2 blocks however, they both already have an 8 and the puzzle would be wrong at that point.
The logic behind this move is that in order for every row, column, and block to have the numbers 1-9, absolutely no row, column, or block can hold the same number twice, so by visualizing lines off of every single instance of a number, you effectively show yourself all the places a number can't go.
Step 2: Candidate Lines*
Sometimes while visualizing for places to put numbers you come across blocks where 2 or 3 cells in a line could possibly be that number but none of the others in the block. This is a useful piece if information because the line formed by those cells also cannot hold the number in question. 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.
The logic behind this is that when the candidates are in a row but nowhere else in the block, it doesn't matter which of the 2 or 3 it is, on that one line the slot will be filled and no others in any other block on that same line can share the number.
Step 3: (Optional) Counting*****
To fill in more possibilities you could look through each cell and count all the numbers in the same block, column, and row, but I personally find this to be too much work with too little gain and cannot be bothered to show it.
Step 4: Repetition!
the previous steps don't end once you've done every number, a large majority of puzzles are easy enough that they can be solved with just the first two steps, you just have to keep going back through the cycles as more and more numbers get filled in until you finally can't find any more. 242