Sudoku Puzzle Notation

SP Notation

Sudoku solutions can be shown step-by-step. Sudoku Puzzle Notation or SP Notation depicts the starting puzzle and each step to solve the puzzle.

Starting Puzzle 

The starting puzzle is represented by 9 zero-padded numbers: a 9-digit number for each row. Zeros represent blank cells and the digits 1 to 9 represent filled cells.  Figure 1 is an example.

Figure 1 

123456000

456000123

000123456

312000978

000978312

978312000

000564897

564897000

897000564

 Step-By-Step Solution

There are 3 types of steps: fill, observation and elimination. The fill step indicates which cell is filled by which number and the reason for it. The observation step is a prelude to an elimination step and it indicates the digit or digits that may fill in a cell or multiple cells. The elimination step indicates the digit that may be eliminated as a candidate for a cell or multiple cells and the reason for elimination.

Cell Numbering                                                                                

The cells are identified by a column letter and a row number, beginning from the upper left corner. In the example on Figure 2, cell A1 is filled by “1”, cells A3, B3, C3 are blank, and cells G1, H1 and I1 are also blank.

Figure 2

	A	B	C	D	E	F	G	H	I
1	1	2	3	4	5	6
2	4	5	6				1	2	3
3				1	2	3	4	5	6
4	3	1	2				9	7	8
5				9	7	8	3	1	2
6	9	7	8	3	1	2
7				5	6	4	8	9	7
8	5	6	4	8	9	7
9	8	9	7				5	6	4

Step Logic

There are 4 possible reasons for filling in a cell or for eliminating a candidate digit from a cell.

1.       (B) – there is only one cell in the 3x3 block where the digit may be placed

2.       (C) – there is only one cell in the column where the digit may be placed

3.       (R) – there is only one cell in the row where the digit may be placed

4.       (N) – there is only one digit that may be placed in the cell

Fill Step

The fill step has the format <cell>=<digit> <reason(s)>. An example of a fill step using Figure 2 is: 

A3=7 BCNR.

There are 4 reasons for filling cell A3 with “7”: B, C, N and R.

• The top-left block has 3 blanks: on columns A3, B3 and C3. Columns B and C already have the digit “7”, therefore “7” can only be placed on A3 in this block (reason B).
• Column A has 3 blanks: on rows 3, 5 and 7. Rows 5 and 7 already have the digit “7”, therefore “7” can only be placed on A3 along column A (reason C).
• Row 3 has 3 blanks: on columns A, B and C. Columns B and C already have the digit “7”, therefore “7” can only be placed on A3 along row 3 (reason R).
• Cell A3 is in a block with the digits 1, 2, 3, 4, 5 and 6 and in column A with the digits 8 and 9. Only “7” can be placed in cell A3 without repeating a digit in the block, column or row (reason N).

Puzzle Difficulty

Sudoku puzzles that are rated as easy to moderate can be solved by fill steps alone. An easy puzzle will have fill steps that have multiple reasons. The moderate puzzles would have some fill steps that have only one reason, which makes it more challenging. The difficult puzzles would have more single-reason steps and may also require elimination steps.

Jammed Puzzles

A jammed puzzle has a fill step that keeps it from being solved. See how quickly you can unjam the following moderate puzzles.

Apple

							1	3
	1			3			8
3	7		1
			2		6	1	3
	3	1				9		6
			3	1		8
6	8	3	5	7	1	2	9	4
			4	8	3	7	6	1
1	4	7				3	5	8

000000013

010030080

370100000

000206130

031000906

000310800

683571294

000483761

147000358

Banana

			5	8			1	4
4				2			5
5				4
	1	5	8		4
7	4				2	5		1
			1		5	4
1			4	5		7	3	2
	5	4	2			1
2	3	7	9	1	8	6	4	5

000580014

400020050

500040000

015804000

740002501

000105400

100450732

054200100

237918645

Cherry

				3			1	2
	2	3	6
	4		2		7		3	6
4	1	6	7	2	3
8	9	2	5			3	7
7	3	5				6	2
2	8		9			1	4	3
			3		2	5
3	5					2

000030012

023600000

040207036

416723000

892500370

735000620

280900143

000302500

350000200