How to Solve Sudoku Puzzles


The SuDoku grid has three main elements. There are 9 columns9 rows and 9 blocks.

sudoku

Using the numbers 1 through 9, the 81 cells in the sudoku grid must be filled so that every columnrow and block contains the numbers 1 through 9. No number can repeat within any columnrow 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. 

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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.

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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

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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.

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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?

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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.

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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.

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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.

As your skill improves, move on to the harder puzzles. Happy puzzling!

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