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Difficult Sudoku Group Puzzle
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The small superscript in each undetermined location is the step number at which the location must be fill before all of the locations with subsequent step numbers can be determined. A detailed description of the moves in each step is given below.

Display the puzzle with superscripts showing just the step number for the first few steps in their empty grid locations.

See the puzzle answer grid.

Deductive steps to solve the puzzle

The moves within each step may be done in any order.

All of the moves within a particular step must be done before all of the moves in the subsequent step can be guaranteed to be completed.

Rows are numbered top to bottom, columns from left to right, and rectangles from left to right and then top to bottom. Coordinates are (col, row). Precise details on numbering within each group are specified in the on-line instructions .

Step 1. There are 6 independent moves.

• The only spot left for 6 in the 8th column is at (8, 7).
• The only spot left for 1 in the 9th column is at (9, 7).
• The only spot left for 8 in the 3rd 3x3 square is at (7, 3).
• The only spot left for 6 in the 4th 3x3 square is at (1, 5).
• The only spot left for 5 in the 5th 3x3 square is at (6, 4).
• The only spot left for 8 in the 8th 3x3 square is at (4, 8).

Step 2. There are 2 independent moves.

• The only spot left for 6 in the 4th column is at (4, 2).
• The only spot left for 6 in the 8th 3x3 square is at (5, 8).

Step 3. There are 3 independent moves.

• The only spot left for 2 in the 8th row is at (6, 8).
• The only spot left for 6 in the 3rd 3x3 square is at (7, 1).
• The only spot left for 1 in the 8th 3x3 square is at (5, 9).

Step 4. There are 2 independent moves.

• 7 must be placed at (7, 7) because it is the only value left that is not already in the 7th row, the 7th column or the 9th 3x3 square.
• 3 must be placed at (7, 2) because it is the only value left that is not already in the 2nd row, the 7th column or the 3rd 3x3 square.

Step 5. There are 3 independent moves.

• The only spot left for 7 in the 5th column is at (5, 1).
• The only spot left for 3 in the 6th 3x3 square is at (9, 5).
• The only spot left for 7 in the 8th 3x3 square is at (6, 9).

Step 6. There are 3 independent moves.

• The only spot left for 2 in the 1st row is at (9, 1).
• The only spot left for 4 in the 6th column is at (6, 3).
• The only spot left for 2 in the 2nd 3x3 square is at (4, 3).

Step 7. There are 4 independent moves.

• The only spot left for 9 in the 1st row is at (2, 1).
• The only spot left for 3 in the 2nd 3x3 square is at (6, 1).
• The only spot left for 9 in the 3rd 3x3 square is at (9, 3).
• The only spot left for 5 in the 3rd 3x3 square is at (9, 2).

Step 8. There are 3 independent moves.

• The only spot left for 9 in the 8th row is at (1, 8).
• The only spot left for 5 in the 2nd column is at (2, 5).
• The only spot left for 5 in the 1st 3x3 square is at (3, 1).

Step 9. There are 4 independent moves.

• The only spot left for 7 in the 1st column is at (1, 3).
• The only spot left for 7 in the 4th 3x3 square is at (3, 5).
• The only spot left for 5 in the 6th 3x3 square is at (8, 6).
• The only spot left for 5 in the 7th 3x3 square is at (1, 9).

Step 10. There are 5 independent moves.

• The only spot left for 8 in the 5th row is at (8, 5).
• The only spot left for 8 in the 3rd column is at (3, 7).
• The only spot left for 3 in the 1st 3x3 square is at (2, 3).
• The only spot left for 8 in the 4th 3x3 square is at (2, 4).
• The only spot left for 7 in the 7th 3x3 square is at (2, 8).

Step 11. There are 8 independent moves.

• The only spot left for 2 in the 5th row is at (5, 5).
• The only spot left for 9 in the 5th row is at (4, 5).
• The only spot left for 3 in the 7th row is at (5, 7).
• The only spot left for 1 in the 2nd column is at (2, 2).
• The only spot left for 9 in the 8th column is at (8, 9).
• The only spot left for 9 in the 6th 3x3 square is at (7, 6).
• The only spot left for 3 in the 7th 3x3 square is at (3, 9).
• The only spot left for 1 in the 7th 3x3 square is at (3, 8).

Step 12. There are 11 independent moves.

• The only spot left for 3 in the 4th row is at (1, 4).
• The only spot left for 1 in the 6th row is at (1, 6).
• The only spot left for 4 in the 3rd column is at (3, 6).
• The only spot left for 4 in the 5th column is at (5, 4).
• The only spot left for 2 in the 8th column is at (8, 4).
• The only spot left for 4 in the 1st 3x3 square is at (1, 2).
• The only spot left for 3 in the 5th 3x3 square is at (4, 6).
• The only spot left for 1 in the 6th 3x3 square is at (7, 4).
• The only spot left for 4 in the 7th 3x3 square is at (2, 7).
• The only spot left for 4 in the 8th 3x3 square is at (4, 9).
• The only spot left for 2 in the 9th 3x3 square is at (7, 9).

Monday August 19, 2024   https://www.grouppuzzles.com