Solving Sudoku Puzzles

by LESLIE MUTCHLER
(EVERETT, WASHINGTON,USA)

LABELING

Across the top label the large squares A, B, C and down the left side D, E, F. Generally the bottom and right side don't need to be labeled G, H, I, J, K, L and M center, some times a situation will come up to use these labels. The rows and columns for each large square are labeled 1, 2, 3.

EXAMPLES:

B3 would be the third column of square B and E2 would be the center row of square E.

SURE NUMBERS

To find the sure numbers by looking at the missing numbers of the rows , columns and large squares to find one that will only go into a small square. When the sure numbers are found mark them some way. I mark them by putting a slash mark in the top left corner of the small squares with the sure numbers.

TEST NUMBERS

Mark the small squares that test numbers are tried. Work the puzzle until you have a contradiction or the puzzle solves out. I mark the test squares by putting 2 slash marks in the top left corner of the square. When 2 numbers are missing there are 2 possible ways they can be entered in the squares. EXAMPLE: Square B is missing 1 and 6. They can be test by entering 1, 6 or 6, 1.
If there are 2 two numbers missing there are 4 possible way that they can be tested.

EXAMPLE:

Column B3 is missing 1 and 6. and row E2
3 and 4. The possible ways would be

(1)

B3 E2
1, 6 3, 4
1, 6 4, 3
6, 1 3, 4
6, 1 4, 3

When 3 numbers are missing there are six possible way they can be entered.

EXAMPLE:

Column B3 is missing 2, 5, 9. There are six possible way that they can be entered

B3
x 2, 5, 9
x 2, 9, 5
x 5, 2, 9
5, 9, 2
9, 2, 5
x 9, 5, 2

You look at the first position and cross out the numbers that don't fit. In this case 2. Then check the second position for numbers that don't fit. In this case 5. Then check the third position for numbers that don't fit. In this case 9.

This give two test numbers that can be combined with the test numbers hat are missing in row E2 to make four possible test numbers of five digits.

EXAMPLE:

E2 B3
3, 4 5, 9, 2
4, 3 5, 9, 2
3, 4 9, 2, 5
4, 3 9, 2, 5

(2)

To find four digit test numbers a different procedure is used.

EXAMPLE:

Row D3 is missing the numbers 2, 5, 6, 9.
In your mind you label the positions left to right for rows or down for columns A, B, C, D. You write down D3 ( 2, 5, 6, 9)
Check each number with each position put the number in the positions that don't cancel and an X where the number cancels.

D3 ( 2, 5, 6, 9)
A B C D
2 2 2 2 x
5 5 x x 5
6 6 6 x 6
9 x 9 9 x

The numbers 9 and 5 are in two positions , 5 positions A and D and
9 positions B and C.

When 5 is in position A the remaining numbers are 2, 6, 9.
When 5 is in position D the remaining numbers are 2, 6, 9.

List the numbers like this;

D3/5A D3/5D
x2, 6, 9 x 2, 6, 9
2, 9, 6 x2, 9, 6
x6, 2, 9 x 6, 2, 9
x6, 9, 2 x 6, 9, 2
9, 2, 6 9, 2, 6
9, 6, 2 9, 6, 2


Put 5 in position A and check the remaining three numbers crossing out the ones that cancel. Then put 5 in position D and cross out the
ones that cancel.

Example:

This will give five four digit test numbers.
5, 2, 9, 6
5, 9, 2, 6
5, 9, 6, 2
9, 2, 6, 5
9, 6, 2, 5

These numbers can be combined with other test numbers.
When you come to a contradiction with the test numbers erase
the numbers in the squares that that do not have the slash marks in
the top left corners. If you come to a dead end try test numbers
to go with the test numbers. Mark these test number squares with
two slash marks in the lower right corner. By using imagination and ingenuity these puzzles can be conquered. GOOD LUCK!!!!

Leslie Mutchler
03/24/2010