Difficult HyperSudoku-X Group Puzzle
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Place each element of the group (1 2 3 4 5 6 7 8 9) exactly once in each row, each column, each 3x3 square, each 3x3 inner square, and each diagonal.

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 8 independent moves.

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

Step 2. There are 3 independent moves.

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

Step 3. There are 3 independent moves.

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

Step 4. There are 2 independent moves.

• The only spot left for 6 in the 4th row is at (9, 4).
• The only spot left for 6 in the 3rd 3x3 inner square is at (3, 6).

Step 5. There is 1 independent move.

• 1 must be placed at (8, 2) because it is the only value left that is not already in the 2nd row, the 8th column, the 3rd 3x3 square, the 2nd 3x3 inner square or the 2nd diagonal.

Step 6. There is 1 independent move.

• The only spot left for 1 in the 2nd 3x3 square is at (4, 3).

Step 7. There is 1 independent move.

• The only spot left for 1 in the 4th row is at (5, 4).

Step 8. There is 1 independent move.

• The only spot left for 8 in the 4th row is at (4, 4).

Step 9. There are 2 independent moves.

• The only spot left for 8 in the 2nd 3x3 square is at (5, 2).
• The only spot left for 8 in the 3rd 3x3 inner square is at (3, 8).

Step 10. There are 4 independent moves.

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

Step 11. There are 6 independent moves.

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

Step 12. There are 10 independent moves.

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

Step 13. There are 12 independent moves.

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

Step 14. There are 6 independent moves.

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

Tuesday November 5, 2024   https://www.grouppuzzles.com