Sudoku Mind Exerciser
The following is a step-by-step approach to solving the very
popular game called Sudoku. When doing this game without a worksheet, it became
very apparent that some assistance would be a great aid and as a result the
following worksheet was developed and the method for using it.
The following grid is an example of a Sudoku Grid that is rated
as GOLD or the most difficult. To use the Worksheet available in the following
PDF file proceed as follows:
NOTE: The nomenclature used to describe this grid is as follows:
The major grid is a 3x3 with the minor grid of 3x3 within each major grid cell.
Major grids are known as Row-1, Row-2, and Row-3 with the corresponding Columns
as Column-1, Column-2, and Column3. The minor grid is labeled R-1 to R-9 and C-1
Make a copy of the worksheet. File is a PDF document
From the Sudoku Grid that you wish to solve, using the one
shown here as an example.
Use a red (or any color) ballpoint pen and circle the number
3 on the worksheet that corresponds to the position shown on the original
grid. This is the 3 found in the block of 9 cells in R-1, C-2 on the worksheet.
Proceed to do the same as indicated in step 3 but do this
for the remaining numbers shown on the original grid. When you are done, the
worksheet should have red circles around the numbers 3, 2, 5, 9, and 4 in
the major cell in the top left corner of the worksheet. Do all of the major
cells and check that no errors were made.
Now using an ordinary pencil cover all of the remaining 3's
in the top row (R-1) as they are not allowed in the solution. Do the same for the
vertical column for all 3's in the second column and all remaining 3's in
the major cell in the top left corner as the 3 shown in red is part of the
Do the same as in step 5 for all the rows, columns, and
cells where numbers are circled in red. Check your results carefully to make
sure you have not missed any values as any errors at this stage will give
you a false solution. Example solution
#1. to end of this step.
Look for any minor cell that has all values stroked off with
pencil but only one value remains which indicates the value for that cell is
the number that is not stroked off. Use a black or blue ballpoint to circle
that value as that is part of the solution. Now proceed to remove all
entries in that row, column and major cell that have this number as they are
not allowed in the final solution. Analysis of the sample solution #1
indicates that row two column 1 has only one cell not checked as well as row
nine column two and column three. Choose any of these and process as in step
4-6 shown above.
Systematically work through all remaining rows and columns
using the same approach as indicated in step 7. An example of this problem
is shown in the following image.
As can be seen, the solution is not complete as several cells still require
a solution. This is the reason that this problem is called a GOLD level as
indicated in step 10.
Keep repeating steps 7 and 8 until all cells are either
stroked off or a value is circled to indicate the solution for that cell.
At the GOLD level as one gets near the end, it may
impossible to find any further cells that can be removed and two cells
remain each with the possibility of the same numbers. Here is where one has
to make a judgment as to the solution that will satisfy the requirements for
the Sudoku game. Looking at the solution
to this point, it can be seen that
the major cell at row-2, column-1 has a single value of 8 in the minor cell
at location R-4, C-3, indicating that his must be the required 8 for
this major cell. Once this is selected then it becomes obvious that the same
major cell at location, R-5, C-3 has a one that must be the solution
for this major cell. Continue this process for the other major cell to
determine possible solutions. The major cell at row-1, column-2 shows a
single value of 5 at R-3, C-5 which indicates that this 5 must be the
solution for this cell. If the solution is still not found then one has to
look at each row for the occurrence of a single number that indicates it is
the solution for that value. If such a number is found then circle it and
then remove that number from the row, column, and major cell. Repeat this
for all column and repeat the process that was done for the rows. Continue this process until all cells are process
and the final solution is found.
Sunday, July 26, 2009
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