How to solve sudoku problems

How To Solve SuDoku Puzzles

Introduction

The SuDoku grid has three main elements. There are 9 columns, 9 rows and 9 blocks. Using the numbers 1 through 9, the 81 cells in the sudoku grid must be filled so that every column, row and block contains the numbers 1 through 9. No number can repeat within any column, row or block. Certain numbers are given and the puzzler must then fill in the remainder in order to solve the puzzle. The amount of numbers given, which ones, and their placement within the grid determine the difficulty of the puzzle.   For this tutorial we’ll begin with a very easy puzzle which will introduce you to some basic sudoku solving strategies.   Here is an easy grid to get you started. To begin, look for a number which has a high frequency within the puzzle In our example, the number 8 appears five times so we’ll begin by pencilling in the rest of the 8s wherever they can possibly go. We know that no number can repeat in any block so we need to put 8s in blocks 2, 3, 6 and 7. After lightly entering all possible 8s, we discover that there is only one square in blocks 6 and 7 where we can place an 8. (Remember! The 8 cannot appear twice in any column or row.) Now we can safely enter the two 8s in blocks 6 and 7. Now, identify another number with a high frequency rate. The number 5 also appears five times within the puzzle so now we'll follow the same procedure for the 5s. Once again, we have only a single cell in blocks 3 and 5 where a 5 can possibly be placed. Now we enter the number 5 in block 3 and 5. Now, here's where it gets interesting.   Since we know that numbers cannot repeat in any column, we can logically ascertain (now that we've entered 5s in blocks 3 & 5) that some of the 5s we pencilled in for blocks 8 and 9 are no longer possibilities. So let's remove those 5s. And lo and behold, now we have only one possible placement for 5 in those two blocks. That completes the number 5 since every block now contains a 5. So where do we go from here?  Now, we'll follow the same procedure for the 7s. Again, we have only one possible placement fo the 7 in blocks 3 and 4. Now we can safely enter those numbers and remove any 7s from the corresponding rows or columns. And that leaves only one possibility for the 7 in block 6. And it also nails down the 8 in block 3! Now, we're making progress. Now, we'll fill in the 7 in block 6 and the 8 in block 3. Again, we can eliminate one of the 8s in block 2. That leaves a single square for the 8 in block 2. So we can enter the 8 and that completes the 8s for this puzzle. Now, it's time to change our solving strategy.  Up to now, our strategy has been to enter all the possibles for any number with a high frequency rate within the puzzle. Now, we've got enough numbers entered into the grid that we can use a different solving strategy. Let's look at block 3. We have seven of the nine numbers required. We are missing only the 3 and the 9. Looking at the top row, we see that it already contains a 3 (in block 2). Therefore, the 3 must go in the bottom left square of block 3 and (Eureka!) the 9 in the last remaining square. Wow! We've come along way towards solving this puzzle. And on further examination we see that the only number missing in column 7 is the number 2. So we can enter it in block 9. Now you have the basic solving strategy for SuDoku puzzles. Time to try solving some on your own. Here is a selection of easy sudoku puzzles to practice on. As your skill improves, move on to the harder puzzles. Happy puzzling!   The rest of this tutorial is for novices who would like to see the entire solution covered. Looking over the grid we can see that block 6 requires a 2 and since column 8 and row 6 already contain a 2, we can eliminate all the cells in the block except the one in the upper right-hand corner, so enter a 2 there. Now column 9 is missing the 3, 4, 6 and 9. There is already a 9 in block 9 so the 9 must go in the bottom-right cell of block 6. Looking at the bottom cell of column 9, we can eliminate the 3 and 4 as they both appear in row 9, so the 6 must go there. Placing that 6 eliminates all but one cell for the 6 in block 8. Now there's only one cell for the 6 in column 3 and that eliminates all but one cell in block 4 for the 6 (check the columns, rows and blocks). We can also determine that there is only one cell available for the 2 in column 3. Now column 3 is missing only a 9 and placing that 9 eliminates all but one cell for the 9 in block 8. Row 4 is now missing only the 3 and 9 and there is already a 9 in block 6 so it must go in block 4 and the 3 in block 6. So the final cell in block 6 must be a 6. Now let's consider the top-left cell in block 7. By a process of elimination we can dismiss every number except 3 for this cell. (Remember, the 1 and 2 must go in the bottom row.) Entering the 3 in block 7 now allows us to complete block 9. We can enter the 3 and 4 in block 9 and now columns 7, 8 and 9 are complete. Things will unfold quickly from here on in.  There is only one empty cell left in row 7 so we can enter the 1 there. Entering the 1 in row 7 eliminates all other possibilities for the 1 in block 2 so we can enter a 1 in the lower left-hand cell. Entering the 1 in row 3 eliminates one of the possibilities for the 7 in that block so we can enter the 7 and that in turn eliminates one of the two 7s in block 8 and allows us to enter the 7 there. Checking column 4, we need to place the 4 and 9. There's already a 4 in row 2 so the 4 must go in row 5 and the 9 in row 2. In row 5 we are missing the 3 and 9. The 3 has to go in block 4 (there is already a 9 there) and the 9 in block 5. This leaves one empty cell in each of these blocks. So enter the 3 and the 4 in their respective cells. >Now go to row 2. We can place the 2 and 6 in the last two cells in this row (the 6 has to go in block 2). Since we have 2 in the first cell of row 2, that determines where the 1 and 2 go in row 9.