Always Obvious Placements While Solving
We are going to solve a easy sudoku puzzle, and as we say in the sub header every time we are going to place a digit we can look for an obvious placement and find one.
Image 1 below shows the easy sudoku we will solve during this tutorial.
As you can see the given digits are all in black color.
The digits we will enter while solving it, will be in blue color.
In the first steps we will make the background of the actual row, column or box green.
The row, column or box that can not contain the digit we are going to enter will have a yellow background.
After a few steps you have got more used to this and we can skip the colored backgrounds and place more digits in each step.
Look at the row with the green background in image 2 below. Only the digits 1 and 4 are missing. You can also see that the first (left) empty cell in the column with yellow background can not hold a digit 1 since the column already have a digit 1. So the digit 1 goes in the other empty cell between digit 9 and 3 and digit 4 goes into the first empty cell. You can see the row completed in image 3 below.
The green row in image 3 below has the digits 4 and 9 missing. digit 4 can and must go into the first (left) empty cell on the row since the other empty cell is in the bottom right box which already has a digit 4 in it. So the digit 9 goes into the other empty cell on the row. As you can see it must go there since the first empty cell belongs to a column that already contain the digit 9. You can see the row completed in image 4 below.
The green column in image 4 has the digits 1, 4, 5 and 7 missing. The digit 1 has to go into the empty cell on row 2 from the top. The top row already has a digit 1 and the other empty cells are in boxes that already has a digit 1.
The next obvious placement in the green column is digit 7 which can only go into the empty cell in the bottom box. Top box and middle box both contain the digit 7.
Now we see that there is only one possible placement of digit 4 in the bottom box. It has to go into the empty cell left of the digit 7 we just entered and the digit 4 in the middle box can only be placed in the green empty cell.
The digit 5 in the green column now have only the green empty cell on the top row to go into.
This step gave us five placements an you can see them in image 5.
Now, looking at image 5, we can see three obvious placements in the three bottom boxes.
In column 3 (from left) the digit 8 must go into the empty cell in the bottom box.
After that there is only one empty cell int the left bottom box which will hold the digit 6.
The digit 6 in the right bottom box must go into the empty cell in row 9 from left.
Column 1 (from left) must hold a digit 5 so the only missing digit in column one is 9 which goes into the empty cell in the topbox.
Column three now have two empty cells in the middle box an you can easily see the one in row 4 (from top) must hold the digit 9 and the empty cell below must hold a digit 2.
Column 9, in image 6 below, has three empty cells and digits 2, 3, 8 missing. We can easily see that digit 2 must go into the empty cell in row one and makes the empty cell in row to the only alternative for digit 8. The only empty cell after that is the one in row 4 so the digit 3 goes there.
Both column 7 and 8 have the digit 4 so you can easily see that digit 4 in column 6 must go into the empty cell on row 2.
The top right box has now only one empty cell for digit 3, the only missing digit in that box.
Earlier we had to leave two cells empty in the top left box. Both digit 3 and 6 could go into any of them. Now we see that digit 3 goes into row 1 and 6 gos into row 2.
I assume you by now have noticed how it's done.
The only thing I have to tell about the seven placed digits in image 7 below is in what order they was placed.
In the middle right box I started with digit 5. Then where to place digit 8 became obvious. Digit 2 had only one place to go then.
In the bottom right box the placement of digits 3 and 7 was obvious and lead to the placement of digit 2. Then digit 1 had only one empty cell to go to.
Lets now go for all the rest of the 15 empty cells in image 8 and I just give you the order of entering the digits in each box.
In the middle center box, we enter the digits 3, 4.
In the top center box the digits 4, and 6.
Now we can continue in the middle center box and enter the digits 6, 7 and 8.
In the top middle box we can enter 7 and 5.
Finaly in the bottom center box we can enter 8, 5, 9 and 1.
Congratulations! The sudoku puzzle is solved. If you check each row, column and box in image 9 below, all of them contains the digits 1 to 9.
What we have learned from this, is that in such an easy sudoku puzzle like this one, there is possible to find an obvious placement for every digit we enter.
That is not the case when you solve more difficult sudoku puzzles.
In a medium level sudoku, you may have to think two steps ahead to find an obvious placement for a digit and in a really difficult one you may have to think several steps ahead to find that placement.