Difficult Nonlatin-6up-UR-D Group Puzzle | ||
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Place each element of the group (1 2 3 4 5 6) exactly once in each column, each 2x3 rectangle, the upper right corners of each rectangle, and the diagonal elements.
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 3 in the 2nd 2x3 rectangle is at (3, 1).
- The only spot left for 5 in the 3rd 2x3 rectangle is at (5, 3).
- The only spot left for 2 in the 5th 2x3 rectangle is at (4, 6).
- The only spot left for 5 in the diagonal elements is at (1, 1).
Step 2. There are 2 independent moves.
- The only spot left for 6 in the 3rd column is at (3, 6).
- The only spot left for 4 in the 5th 2x3 rectangle is at (4, 4).
Step 3. There are 2 independent moves.
- The only spot left for 4 in the 1st 2x3 rectangle is at (2, 3).
- The only spot left for 4 in the 6th 2x3 rectangle is at (6, 5).
Step 4. There is 1 independent move.
- The only spot left for 1 in the 6th 2x3 rectangle is at (6, 6).
Step 5. There are 2 independent moves.
- The only spot left for 1 in the 1st 2x3 rectangle is at (2, 1).
- The only spot left for 6 in the diagonal elements is at (5, 5).
Step 6. There are 5 independent moves.
- The only spot left for 2 in the 1st 2x3 rectangle is at (1, 3).
- The only spot left for 1 in the 2nd 2x3 rectangle is at (4, 2).
- The only spot left for 3 in the 6th 2x3 rectangle is at (5, 4).
- The only spot left for 2 in the upper right corners of each rectangle is at (2, 4).
- The only spot left for 3 in the diagonal elements is at (2, 2).
Step 7. There are 4 independent moves.
- The only spot left for 6 in the 2nd 2x3 rectangle is at (4, 1).
- The only spot left for 6 in the 4th 2x3 rectangle is at (2, 5).
- The only spot left for 3 in the 4th 2x3 rectangle is at (1, 5).
- The only spot left for 3 in the upper right corners of each rectangle is at (6, 1).
Step 8. There is 1 independent move.
- The only spot left for 6 in the 3rd 2x3 rectangle is at (6, 3).