There are many ways of solving a Sudoku. Here, we present three ideas that encapsulate the most important ideas on how to solve Sudokus. We have two rules of thumb for you: “follow the logic” and “follow the crowd”. The first two tips are about following the logic.
Cell logic: this is a method of figuring out which number can fit in a particular free cell. We start with a free cell and try to find out which numbers can be used to fill it.
Number-logic: this is a method of finding where a particular number can fit in a row, column or box that is missing that number. So, we start with a number, from 1 to 9, and try to find out where, in a square, row, or column, it can fit in.
Follow the crowd: stated simply, the easiest pickings (free cells to fill in) are in rows or columns or boxes which already have many givens. Imagine a row with 8 givens. Find the number missing (the 9th number) and plug it in the free cell in that row. Similarly for a column or a box with 8 givens. Now, imagine a row with 7 givens. You may find that one of the two free cells will only allow one of the two possible numbers. So, then, you can now plug in that free cell with that one possible number.
Most Sudoku puzzles have at least some easy wins: free cells which can be filled in without much difficulty, followed by cells which require some thought and strategy to fill in. Remember that Sudokus are made up of 3 units: rows, columns, and boxes. The easiest way to solve Sudokus is to start with any one of these methods:
Use cell logic:
Say, we decide to start with rows. We will first scan the first row and apply cell logic on each free cell in this row. That is, we will take each cell in the row, and (based on the numbers already used up in the row, column and box to which this cell belongs), try to figure out which remaining numbers can fit here. If there is only one such number, we will fill it in. We will move on to the next cell in the row if more than one number can fit in the cell.
This process is then repeated for each column, and then for each of the 9 boxes. The repeated application of cell logic will get a few free cells filled in for most puzzles except the hardest ones.
Use number logic:
Say, we decide to start with rows. We will first scan the first row and apply number logic on each free cell in this row. That is, we will take each row, and (based on the numbers already filled in, in the remaining cells of the row, column and box to which this cell belongs), try to figure out in which free cell, the numbers from 1 to 9 can fit. If there is only one such cell, we will fill it in with the number. If the number can fit in more than one cell, we will move on to the next number in sequence.
This process is then repeated for each column, and then for each of the 9 boxes. Once again, after doing this, some more free cells would get filled.
Now, after both cell logic and number logic has been employed once and some free cells have been filled in, it is possible that the process can be repeated many times.
This process can be continued until no more cells get filled.
To summarize the above:
- Use number-logic (find where a certain number can fit in a particular box or row or column).
- Use cell logic (find which number can fit in a particular cell in a box or row or column).
Look for free cells in partially filled rows or columns or boxes. Free cell in rows or columns or boxes that are mostly filled are the easiest to crack. It is a lot more challenging to fill free cells in rows/columns/boxes that are wide empty.