Challenging HyperSudoku-Xtreme Group Puzzle
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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 20 independent moves.

• The only spot left for 8 in the 1st 3x3 square in the upper left puzzle is at (1, 2).
• The only spot left for 8 in the 5th 3x3 square in the upper left puzzle is at (5, 6).
• The only spot left for 8 in the 9th 3x3 square in the upper left puzzle is at (9, 9).
• The only spot left for 3 in the 9th 3x3 square in the upper left puzzle is at (7, 8).
• The only spot left for 2 in the 1st diagonal in the upper left puzzle is at (1, 1).
• The only spot left for 1 in the 3rd column in the upper right puzzle is at (15, 8).
• The only spot left for 2 in the 3rd column in the upper right puzzle is at (15, 3).
• The only spot left for 1 in the 2nd 3x3 square in the upper right puzzle is at (18, 3).
• The only spot left for 1 in the 4th 3x3 square in the upper right puzzle is at (14, 6).
• The only spot left for 1 in the 7th row in the center puzzle is at (11, 13).
• The only spot left for 5 in the 7th 3x3 square in the center puzzle is at (7, 14).
• The only spot left for 4 in the 7th 3x3 square in the center puzzle is at (8, 13).
• The only spot left for 9 in the 9th 3x3 square in the center puzzle is at (15, 13).
• The only spot left for 2 in the 2nd 3x3 inner square in the center puzzle is at (13, 8).
• The only spot left for 3 in the 8th column in the lower left puzzle is at (8, 16).
• The only spot left for 6 in the 1st 3x3 square in the lower left puzzle is at (1, 14).
• The only spot left for 4 in the 7th 3x3 square in the lower left puzzle is at (2, 21).
• The only spot left for 4 in the 2nd diagonal in the lower left puzzle is at (6, 16).
• The only spot left for 3 in the 6th 3x3 square in the lower right puzzle is at (21, 18).
• The only spot left for 3 in the 7th 3x3 square in the lower right puzzle is at (15, 20).

Step 2. There are 11 independent moves.

• The only spot left for 8 in the 6th 3x3 square in the upper left puzzle is at (8, 5).
• The only spot left for 7 in the 9th 3x3 square in the upper left puzzle is at (8, 9).
• The only spot left for 7 in the 1st diagonal in the upper left puzzle is at (2, 2).
• The only spot left for 2 in the 4th column in the upper right puzzle is at (16, 1).
• The only spot left for 2 in the 9th 3x3 square in the upper right puzzle is at (21, 7).
• The only spot left for 8 in the 4th column in the center puzzle is at (10, 11).
• The only spot left for 8 in the 2nd 3x3 square in the center puzzle is at (12, 8).
• The only spot left for 4 in the 7th column in the lower left puzzle is at (7, 18).
• The only spot left for 9 in the 1st 3x3 square in the lower left puzzle is at (1, 13).
• The only spot left for 4 in the 9th 3x3 square in the lower left puzzle is at (9, 19).
• The only spot left for 3 in the 2nd row in the lower right puzzle is at (18, 14).

Step 3. There are 8 independent moves.

• The only spot left for 3 in the 6th 3x3 square in the upper left puzzle is at (8, 6).
• The only spot left for 5 in the 1st diagonal in the upper left puzzle is at (8, 8).
• The only spot left for 7 in the 9th row in the upper right puzzle is at (17, 9).
• The only spot left for 7 in the 2nd row in the center puzzle is at (11, 8).
• The only spot left for 4 in the 4th column in the center puzzle is at (10, 15).
• The only spot left for 5 in the 9th 3x3 square in the lower left puzzle is at (9, 20).
• The only spot left for 9 in the 2nd diagonal in the lower left puzzle is at (7, 15).
• The only spot left for 9 in the 2nd 3x3 square in the lower right puzzle is at (17, 14).

Step 4. There are 12 independent moves.

• The only spot left for 2 in the 8th column in the upper left puzzle is at (8, 3).
• The only spot left for 6 in the 1st diagonal in the upper left puzzle is at (5, 5).
• The only spot left for 3 in the 2nd diagonal in the upper left puzzle is at (6, 4).
• The only spot left for 7 in the 1st row in the upper right puzzle is at (14, 1).
• The only spot left for 7 in the 2nd 3x3 square in the upper right puzzle is at (18, 2).
• The only spot left for 5 in the 2nd 3x3 square in the center puzzle is at (11, 7).
• The only spot left for 5 in the 4th 3x3 square in the center puzzle is at (9, 11).
• The only spot left for 9 in the 4th row in the lower left puzzle is at (5, 16).
• The only spot left for 5 in the 2nd column in the lower left puzzle is at (2, 16).
• The only spot left for 9 in the 6th 3x3 square in the lower left puzzle is at (9, 17).
• The only spot left for 5 in the 2nd diagonal in the lower left puzzle is at (3, 19).
• The only spot left for 9 in the 6th row in the lower right puzzle is at (14, 18).

Step 5. There are 10 independent moves.

• The only spot left for 6 in the 8th column in the upper left puzzle is at (8, 7).
• The only spot left for 3 in the 2nd 3x3 square in the upper left puzzle is at (4, 1).
• The only spot left for 1 in the 1st diagonal in the upper left puzzle is at (7, 7).
• The only spot left for 7 in the 7th column in the upper right puzzle is at (19, 4).
• The only spot left for 7 in the 3rd 3x3 square in the upper right puzzle is at (21, 3).
• The only spot left for 7 in the 7th 3x3 square in the upper right puzzle is at (13, 7).
• The only spot left for 7 in the 4th row in the lower left puzzle is at (3, 16).
• The only spot left for 9 in the 2nd 3x3 square in the lower left puzzle is at (6, 14).
• The only spot left for 5 in the 8th 3x3 square in the lower left puzzle is at (5, 21).
• The only spot left for 8 in the 4th 3x3 square in the lower right puzzle is at (15, 18).

Step 6. There are 9 independent moves.

• The only spot left for 7 in the 1st row in the upper left puzzle is at (6, 1).
• The only spot left for 9 in the 9th 3x3 square in the upper left puzzle is at (9, 7).
• The only spot left for 2 in the 4th row in the upper right puzzle is at (17, 4).
• The only spot left for 7 in the 4th 3x3 square in the upper right puzzle is at (15, 5).
• The only spot left for 2 in the 6th 3x3 square in the upper right puzzle is at (19, 6).
• The only spot left for 6 in the 7th 3x3 square in the upper right puzzle is at (14, 8).
• The only spot left for 1 in the 5th row in the center puzzle is at (14, 11).
• The only spot left for 9 in the 2nd column in the center puzzle is at (8, 12).
• The only spot left for 7 in the 1st column in the lower right puzzle is at (13, 17).

Step 7. There are 8 independent moves.

• The only spot left for 9 in the 2nd diagonal in the upper left puzzle is at (8, 2).
• The only spot left for 4 in the 5th column in the upper right puzzle is at (17, 7).
• The only spot left for 9 in the 2nd diagonal in the upper right puzzle is at (19, 3).
• The only spot left for 9 in the 2nd row in the center puzzle is at (10, 8).
• The only spot left for 1 in the 2nd column in the center puzzle is at (8, 15).
• The only spot left for 1 in the 9th 3x3 square in the center puzzle is at (13, 14).
• The only spot left for 9 in the 2nd 3x3 inner square in the center puzzle is at (14, 9).
• The only spot left for 1 in the 1st diagonal in the lower right puzzle is at (20, 20).

Step 8. There are 8 independent moves.

• The only spot left for 1 in the 8th column in the upper left puzzle is at (8, 1).
• The only spot left for 9 in the 2nd 3x3 square in the upper left puzzle is at (5, 1).
• The only spot left for 4 in the 8th row in the upper right puzzle is at (19, 8).
• The only spot left for 9 in the 1st diagonal in the upper right puzzle is at (18, 6).
• The only spot left for 9 in the 5th 3x3 square in the center puzzle is at (11, 10).
• The only spot left for 4 in the 9th 3x3 square in the center puzzle is at (14, 14).
• The only spot left for 4 in the 2nd 3x3 inner square in the center puzzle is at (13, 9).
• The only spot left for 9 in the 8th column in the lower right puzzle is at (20, 21).

Step 9. There are 12 independent moves.

• The only spot left for 4 in the 1st row in the upper left puzzle is at (3, 1).
• The only spot left for 4 in the 5th column in the upper left puzzle is at (5, 3).
• The only spot left for 4 in the 5th row in the upper right puzzle is at (16, 5).
• The only spot left for 8 in the 6th row in the upper right puzzle is at (13, 6).
• The only spot left for 9 in the 5th column in the upper right puzzle is at (17, 2).
• The only spot left for 4 in the 3rd 3x3 square in the upper right puzzle is at (20, 3).
• The only spot left for 8 in the 5th 3x3 square in the upper right puzzle is at (18, 4).
• The only spot left for 4 in the 4th row in the center puzzle is at (7, 10).
• The only spot left for 2 in the 8th row in the center puzzle is at (9, 14).
• The only spot left for 4 in the 5th 3x3 square in the center puzzle is at (11, 11).
• The only spot left for 9 in the 6th column in the lower right puzzle is at (18, 20).
• The only spot left for 9 in the 1st diagonal in the lower right puzzle is at (16, 16).

Step 10. There are 18 independent moves.

• The only spot left for 5 in the 5th column in the upper left puzzle is at (5, 4).
• The only spot left for 4 in the 3rd 3x3 square in the upper left puzzle is at (7, 2).
• The only spot left for 4 in the 2nd diagonal in the upper left puzzle is at (1, 9).
• The only spot left for 8 in the 1st row in the upper right puzzle is at (20, 1).
• The only spot left for 6 in the 3rd row in the upper right puzzle is at (13, 3).
• The only spot left for 3 in the 6th row in the upper right puzzle is at (20, 6).
• The only spot left for 8 in the 3rd column in the upper right puzzle is at (15, 2).
• The only spot left for 6 in the 5th column in the upper right puzzle is at (17, 1).
• The only spot left for 5 in the 4th 3x3 square in the upper right puzzle is at (13, 5).
• The only spot left for 8 in the 7th 3x3 square in the upper right puzzle is at (14, 7).
• The only spot left for 4 in the 1st diagonal in the upper right puzzle is at (14, 2).
• The only spot left for 5 in the 2nd diagonal in the upper right puzzle is at (21, 1).
• The only spot left for 6 in the 5th row in the center puzzle is at (12, 11).
• The only spot left for 8 in the 9th column in the center puzzle is at (15, 10).
• The only spot left for 8 in the 4th 3x3 square in the center puzzle is at (7, 12).
• The only spot left for 7 in the 2nd row in the lower left puzzle is at (5, 14).
• The only spot left for 2 in the 6th 3x3 square in the lower left puzzle is at (7, 17).
• The only spot left for 9 in the 6th 3x3 square in the lower right puzzle is at (21, 17).

Step 11. There are 23 independent moves.

• The only spot left for 1 in the 5th column in the upper left puzzle is at (5, 8).
• The only spot left for 6 in the 3rd 3x3 square in the upper left puzzle is at (9, 3).
• The only spot left for 4 in the 4th 3x3 square in the upper left puzzle is at (2, 5).
• The only spot left for 4 in the 8th 3x3 square in the upper left puzzle is at (4, 7).
• The only spot left for 1 in the 2nd diagonal in the upper left puzzle is at (4, 6).
• The only spot left for 3 in the 5th row in the upper right puzzle is at (18, 5).
• The only spot left for 3 in the 2nd column in the upper right puzzle is at (14, 4).
• The only spot left for 5 in the 5th column in the upper right puzzle is at (17, 6).
• The only spot left for 5 in the 7th column in the upper right puzzle is at (19, 7).
• The only spot left for 3 in the 1st 3x3 square in the upper right puzzle is at (13, 1).
• The only spot left for 5 in the 2nd 3x3 square in the upper right puzzle is at (16, 2).
• The only spot left for 6 in the 3rd 3x3 square in the upper right puzzle is at (21, 2).
• The only spot left for 4 in the 4th 3x3 square in the upper right puzzle is at (15, 4).
• The only spot left for 5 in the 6th 3x3 square in the upper right puzzle is at (20, 4).
• The only spot left for 3 in the 7th 3x3 square in the upper right puzzle is at (15, 7).
• The only spot left for 8 in the 1st diagonal in the upper right puzzle is at (21, 9).
• The only spot left for 6 in the 1st diagonal in the upper right puzzle is at (16, 4).
• The only spot left for 6 in the 4th row in the center puzzle is at (9, 10).
• The only spot left for 7 in the 1st column in the center puzzle is at (7, 11).
• The only spot left for 8 in the 9th 3x3 square in the center puzzle is at (13, 13).
• The only spot left for 6 in the 4th 3x3 inner square in the center puzzle is at (13, 12).
• The only spot left for 3 in the 2nd row in the lower left puzzle is at (2, 14).
• The only spot left for 2 in the 1st diagonal in the lower left puzzle is at (8, 20).

Step 12. There are 23 independent moves.

• The only spot left for 3 in the 2nd column in the upper left puzzle is at (2, 7).
• The only spot left for 3 in the 4th 3x3 square in the upper left puzzle is at (1, 5).
• The only spot left for 7 in the 5th 3x3 square in the upper left puzzle is at (4, 5).
• The only spot left for 1 in the 7th 3x3 square in the upper left puzzle is at (2, 9).
• The only spot left for 2 in the 2nd diagonal in the upper left puzzle is at (3, 7).
• The only spot left for 7 in the 2nd diagonal in the upper left puzzle is at (7, 3).
• The only spot left for 3 in the 9th row in the upper right puzzle is at (16, 9).
• The only spot left for 3 in the 3rd 3x3 square in the upper right puzzle is at (19, 2).
• The only spot left for 6 in the 6th 3x3 square in the upper right puzzle is at (20, 5).
• The only spot left for 5 in the 8th 3x3 square in the upper right puzzle is at (18, 8).
• The only spot left for 6 in the 8th 3x3 square in the upper right puzzle is at (18, 7).
• The only spot left for 3 in the 9th 3x3 square in the upper right puzzle is at (21, 8).
• The only spot left for 3 in the 7th column in the center puzzle is at (13, 10).
• The only spot left for 6 in the 2nd 3x3 square in the center puzzle is at (11, 9).
• The only spot left for 1 in the 4th 3x3 square in the center puzzle is at (9, 12).
• The only spot left for 1 in the 1st 3x3 inner square in the center puzzle is at (10, 10).
• The only spot left for 6 in the 3rd 3x3 inner square in the center puzzle is at (10, 14).
• The only spot left for 2 in the 7th 3x3 square in the lower left puzzle is at (3, 21).
• The only spot left for 6 in the 9th 3x3 square in the lower left puzzle is at (8, 21).
• The only spot left for 6 in the 1st diagonal in the lower left puzzle is at (5, 17).
• The only spot left for 2 in the 2nd diagonal in the lower left puzzle is at (4, 18).
• The only spot left for 6 in the 3rd row in the lower right puzzle is at (15, 15).
• The only spot left for 8 in the 2nd diagonal in the lower right puzzle is at (14, 20).

Step 13. There are 29 independent moves.

• The only spot left for 1 in the 3rd row in the upper left puzzle is at (6, 3).
• The only spot left for 7 in the 4th row in the upper left puzzle is at (9, 4).
• The only spot left for 9 in the 9th row in the upper left puzzle is at (6, 9).
• The only spot left for 1 in the 1st column in the upper left puzzle is at (1, 4).
• The only spot left for 9 in the 2nd column in the upper left puzzle is at (2, 6).
• The only spot left for 2 in the 4th column in the upper left puzzle is at (4, 8).
• The only spot left for 1 in the 1st 3x3 square in the upper left puzzle is at (3, 2).
• The only spot left for 7 in the 4th 3x3 square in the upper left puzzle is at (3, 6).
• The only spot left for 2 in the 5th 3x3 square in the upper left puzzle is at (6, 5).
• The only spot left for 9 in the 7th 3x3 square in the upper left puzzle is at (3, 8).
• The only spot left for 5 in the 7th 3x3 square in the upper left puzzle is at (1, 7).
• The only spot left for 9 in the 8th row in the upper right puzzle is at (16, 8).
• The only spot left for 1 in the 9th row in the upper right puzzle is at (20, 9).
• The only spot left for 9 in the 6th 3x3 square in the upper right puzzle is at (21, 5).
• The only spot left for 1 in the 8th 3x3 square in the upper right puzzle is at (16, 7).
• The only spot left for 9 in the 9th 3x3 square in the upper right puzzle is at (20, 7).
• The only spot left for 7 in the 4th column in the center puzzle is at (10, 12).
• The only spot left for 3 in the 5th column in the center puzzle is at (11, 14).
• The only spot left for 5 in the 7th column in the center puzzle is at (13, 15).
• The only spot left for 7 in the 9th 3x3 square in the center puzzle is at (15, 14).
• The only spot left for 3 in the 1st 3x3 inner square in the center puzzle is at (10, 9).
• The only spot left for 9 in the 9th row in the lower left puzzle is at (4, 21).
• The only spot left for 6 in the 4th 3x3 square in the lower left puzzle is at (3, 18).
• The only spot left for 9 in the 9th 3x3 square in the lower left puzzle is at (8, 19).
• The only spot left for 3 in the 2nd diagonal in the lower left puzzle is at (9, 13).
• The only spot left for 6 in the 5th row in the lower right puzzle is at (14, 17).
• The only spot left for 8 in the 7th column in the lower right puzzle is at (19, 14).
• The only spot left for 8 in the 9th 3x3 square in the lower right puzzle is at (21, 19).
• The only spot left for 7 in the 1st diagonal in the lower right puzzle is at (21, 21).

Step 14. There are 27 independent moves.

• The only spot left for 6 in the 4th row in the upper left puzzle is at (7, 4).
• The only spot left for 5 in the 6th row in the upper left puzzle is at (7, 6).
• The only spot left for 6 in the 4th column in the upper left puzzle is at (4, 2).
• The only spot left for 5 in the 6th column in the upper left puzzle is at (6, 2).
• The only spot left for 5 in the 1st 3x3 square in the upper left puzzle is at (2, 3).
• The only spot left for 6 in the 4th 3x3 square in the upper left puzzle is at (1, 6).
• The only spot left for 5 in the 4th 3x3 square in the upper left puzzle is at (3, 5).
• The only spot left for 2 in the 4th 3x3 square in the upper left puzzle is at (2, 4).
• The only spot left for 2 in the 6th 3x3 square in the upper left puzzle is at (9, 6).
• The only spot left for 1 in the 6th 3x3 square in the upper left puzzle is at (9, 5).
• The only spot left for 9 in the 6th 3x3 square in the upper left puzzle is at (7, 5).
• The only spot left for 5 in the 8th 3x3 square in the upper left puzzle is at (4, 9).
• The only spot left for 6 in the 8th 3x3 square in the upper left puzzle is at (6, 8).
• The only spot left for 7 in the 7th 3x3 square in the center puzzle is at (9, 15).
• The only spot left for 3 in the 9th 3x3 square in the center puzzle is at (14, 15).
• The only spot left for 7 in the 2nd 3x3 inner square in the center puzzle is at (14, 10).
• The only spot left for 7 in the 4th 3x3 inner square in the center puzzle is at (12, 13).
• The only spot left for 3 in the 4th 3x3 inner square in the center puzzle is at (12, 12).
• The only spot left for 7 in the 1st row in the lower left puzzle is at (2, 13).
• The only spot left for 3 in the 3rd column in the lower left puzzle is at (3, 17).
• The only spot left for 3 in the 1st row in the lower right puzzle is at (20, 13).
• The only spot left for 1 in the 2nd column in the lower right puzzle is at (14, 21).
• The only spot left for 6 in the 7th column in the lower right puzzle is at (19, 20).
• The only spot left for 6 in the 3rd 3x3 square in the lower right puzzle is at (21, 14).
• The only spot left for 1 in the 4th 3x3 square in the lower right puzzle is at (15, 17).
• The only spot left for 7 in the 6th 3x3 square in the lower right puzzle is at (19, 18).
• The only spot left for 2 in the 1st diagonal in the lower right puzzle is at (19, 19).

Step 15. There are 23 independent moves.

• The only spot left for 2 in the 8th 3x3 square in the center puzzle is at (12, 15).
• The only spot left for 2 in the 9th 3x3 square in the center puzzle is at (14, 13).
• The only spot left for 5 in the 2nd 3x3 inner square in the center puzzle is at (12, 10).
• The only spot left for 5 in the 4th 3x3 inner square in the center puzzle is at (14, 12).
• The only spot left for 2 in the 1st row in the lower left puzzle is at (5, 13).
• The only spot left for 8 in the 3rd column in the lower left puzzle is at (3, 13).
• The only spot left for 2 in the 1st 3x3 square in the lower left puzzle is at (2, 15).
• The only spot left for 3 in the 5th 3x3 square in the lower left puzzle is at (5, 18).
• The only spot left for 7 in the 2nd diagonal in the lower left puzzle is at (1, 21).
• The only spot left for 7 in the 1st row in the lower right puzzle is at (17, 13).
• The only spot left for 2 in the 2nd row in the lower right puzzle is at (20, 14).
• The only spot left for 2 in the 5th row in the lower right puzzle is at (16, 17).
• The only spot left for 5 in the 2nd column in the lower right puzzle is at (14, 16).
• The only spot left for 5 in the 7th column in the lower right puzzle is at (19, 13).
• The only spot left for 7 in the 3rd 3x3 square in the lower right puzzle is at (20, 15).
• The only spot left for 4 in the 4th 3x3 square in the lower right puzzle is at (15, 16).
• The only spot left for 2 in the 6th 3x3 square in the lower right puzzle is at (21, 16).
• The only spot left for 2 in the 7th 3x3 square in the lower right puzzle is at (15, 21).
• The only spot left for 6 in the 7th 3x3 square in the lower right puzzle is at (13, 21).
• The only spot left for 1 in the 8th 3x3 square in the lower right puzzle is at (17, 19).
• The only spot left for 5 in the 9th 3x3 square in the lower right puzzle is at (21, 20).
• The only spot left for 1 in the 2nd diagonal in the lower right puzzle is at (16, 18).
• The only spot left for 7 in the 2nd diagonal in the lower right puzzle is at (18, 16).

Step 16. There are 17 independent moves.

• The only spot left for 1 in the 9th row in the lower left puzzle is at (9, 21).
• The only spot left for 8 in the 2nd column in the lower left puzzle is at (2, 17).
• The only spot left for 1 in the 5th column in the lower left puzzle is at (5, 19).
• The only spot left for 2 in the 8th 3x3 square in the lower left puzzle is at (6, 19).
• The only spot left for 1 in the 2nd diagonal in the lower left puzzle is at (2, 20).
• The only spot left for 2 in the 6th column in the lower right puzzle is at (18, 15).
• The only spot left for 4 in the 5th 3x3 square in the lower right puzzle is at (17, 18).
• The only spot left for 6 in the 5th 3x3 square in the lower right puzzle is at (17, 16).
• The only spot left for 4 in the 6th 3x3 square in the lower right puzzle is at (19, 17).
• The only spot left for 4 in the 7th 3x3 square in the lower right puzzle is at (13, 20).
• The only spot left for 5 in the 8th 3x3 square in the lower right puzzle is at (17, 21).
• The only spot left for 2 in the 8th 3x3 square in the lower right puzzle is at (17, 20).
• The only spot left for 7 in the 8th 3x3 square in the lower right puzzle is at (16, 20).
• The only spot left for 6 in the 8th 3x3 square in the lower right puzzle is at (18, 19).
• The only spot left for 4 in the 9th 3x3 square in the lower right puzzle is at (20, 19).
• The only spot left for 5 in the 2nd diagonal in the lower right puzzle is at (15, 19).
• The only spot left for 4 in the 2nd diagonal in the lower right puzzle is at (21, 13).

Step 17. There are 12 independent moves.

• The only spot left for 8 in the 9th row in the lower left puzzle is at (6, 21).
• The only spot left for 8 in the 5th column in the lower left puzzle is at (5, 15).
• The only spot left for 8 in the 9th column in the lower left puzzle is at (9, 18).
• The only spot left for 1 in the 4th 3x3 square in the lower left puzzle is at (1, 18).
• The only spot left for 1 in the 5th 3x3 square in the lower left puzzle is at (4, 17).
• The only spot left for 1 in the 6th 3x3 square in the lower left puzzle is at (7, 16).
• The only spot left for 8 in the 9th 3x3 square in the lower left puzzle is at (7, 20).
• The only spot left for 8 in the 1st diagonal in the lower left puzzle is at (4, 16).
• The only spot left for 8 in the 5th column in the lower right puzzle is at (17, 15).
• The only spot left for 4 in the 6th column in the lower right puzzle is at (18, 21).
• The only spot left for 4 in the 2nd 3x3 square in the lower right puzzle is at (16, 15).
• The only spot left for 8 in the 8th 3x3 square in the lower right puzzle is at (16, 21).

Step 18. There are 3 independent moves.

• The only spot left for 7 in the 4th column in the lower left puzzle is at (4, 20).
• The only spot left for 7 in the 5th 3x3 square in the lower left puzzle is at (6, 17).
• The only spot left for 8 in the 7th 3x3 square in the lower left puzzle is at (1, 19).

Step 19. There are 4 independent moves.

• The only spot left for 3 in the 7th row in the lower left puzzle is at (4, 19).
• The only spot left for 6 in the 4th column in the lower left puzzle is at (4, 15).
• The only spot left for 3 in the 7th 3x3 square in the lower left puzzle is at (1, 20).
• The only spot left for 6 in the 8th 3x3 square in the lower left puzzle is at (6, 20).

Step 20. There is 1 independent move.

• The only spot left for 3 in the 2nd 3x3 square in the lower left puzzle is at (6, 15).

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