Difficult HyperSudoku-8 Group Puzzle
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Place each element of the group (1 2 3 4 5 6 7 8) exactly once in each row, each column, each 4x2 rectangle, and each 2x4 inner rectangle.

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 4 independent moves.

• The only spot left for 5 in the 2nd 4x2 rectangle is at (6, 2).
• The only spot left for 1 in the 5th 4x2 rectangle is at (4, 5).
• The only spot left for 7 in the 7th 4x2 rectangle is at (2, 8).
• The only spot left for 8 in the 8th 4x2 rectangle is at (5, 7).

Step 2. There are 4 independent moves.

• The only spot left for 1 in the 4th row is at (8, 4).
• The only spot left for 1 in the 2nd column is at (2, 7).
• The only spot left for 1 in the 3rd 4x2 rectangle is at (1, 3).
• The only spot left for 7 in the 1st 2x4 inner rectangle is at (3, 5).

Step 3. There are 4 independent moves.

• The only spot left for 5 in the 1st column is at (1, 6).
• The only spot left for 7 in the 8th column is at (8, 3).
• The only spot left for 5 in the 3rd 4x2 rectangle is at (2, 3).
• The only spot left for 7 in the 6th 4x2 rectangle is at (5, 6).

Step 4. There are 3 independent moves.

• The only spot left for 4 in the 4th 4x2 rectangle is at (5, 3).
• The only spot left for 6 in the 1st 2x4 inner rectangle is at (2, 2).
• The only spot left for 5 in the 2nd 2x4 inner rectangle is at (7, 5).

Step 5. There are 4 independent moves.

• The only spot left for 8 in the 2nd row is at (8, 2).
• The only spot left for 6 in the 3rd row is at (4, 3).
• The only spot left for 3 in the 4th 4x2 rectangle is at (6, 4).
• The only spot left for 8 in the 2nd 2x4 inner rectangle is at (7, 6).

Step 6. There are 6 independent moves.

• The only spot left for 4 in the 2nd row is at (1, 2).
• The only spot left for 8 in the 4th column is at (4, 4).
• The only spot left for 6 in the 6th column is at (6, 8).
• The only spot left for 3 in the 3rd 4x2 rectangle is at (3, 3).
• The only spot left for 8 in the 5th 4x2 rectangle is at (2, 5).
• The only spot left for 6 in the 2nd 2x4 inner rectangle is at (7, 4).

Step 7. There are 5 independent moves.

• The only spot left for 2 in the 2nd row is at (5, 2).
• The only spot left for 4 in the 3rd column is at (3, 6).
• The only spot left for 8 in the 1st 4x2 rectangle is at (3, 1).
• The only spot left for 6 in the 2nd 4x2 rectangle is at (5, 1).
• The only spot left for 2 in the 1st 2x4 inner rectangle is at (3, 4).

Step 8. There are 2 independent moves.

• The only spot left for 1 in the 5th column is at (5, 8).
• The only spot left for 1 in the 2nd 4x2 rectangle is at (7, 1).

Step 9. There are 4 independent moves.

• The only spot left for 3 in the 5th column is at (5, 5).
• The only spot left for 4 in the 7th column is at (7, 8).
• The only spot left for 4 in the 2nd 4x2 rectangle is at (8, 1).
• The only spot left for 3 in the 8th 4x2 rectangle is at (8, 8).

Step 10. There are 5 independent moves.

• The only spot left for 2 in the 8th row is at (4, 8).
• The only spot left for 2 in the 8th column is at (8, 5).
• The only spot left for 4 in the 7th 4x2 rectangle is at (4, 7).
• The only spot left for 2 in the 8th 4x2 rectangle is at (6, 7).
• The only spot left for 4 in the 2nd 2x4 inner rectangle is at (6, 5).

Step 11. There are 4 independent moves.

• The only spot left for 2 in the 1st column is at (1, 1).
• The only spot left for 3 in the 4th column is at (4, 6).
• The only spot left for 2 in the 5th 4x2 rectangle is at (2, 6).
• The only spot left for 3 in the 7th 4x2 rectangle is at (1, 7).

Step 12. There is 1 independent move.

• The only spot left for 3 in the 1st 4x2 rectangle is at (2, 1).

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