| Puzzle · 3-steps · | Printable Puzzle or with all steps listed. | |
Difficult Renato 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.
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 3 independent moves.
- The only spot left for N in the 4th row is at (6, 4).
- The only spot left for E in the 2nd 3x2 rectangle is at (4, 2).
- The only spot left for O in the 4th 3x2 rectangle is at (4, 3).
Step 2. There are 3 independent moves.
- The only spot left for T in the 6th column is at (6, 6).
- The only spot left for R in the 2nd 3x2 rectangle is at (6, 2).
- The only spot left for T in the 4th 3x2 rectangle is at (4, 4).
Step 3. There are 3 independent moves.
- The only spot left for R in the 4th column is at (4, 5).
- The only spot left for A in the 6th column is at (6, 3).
- The only spot left for A in the 6th 3x2 rectangle is at (5, 5).
Step 4. There are 2 independent moves.
- E must be placed at (1, 6) because it is the only value left that is not already in the 6th row, the 1st column or the 5th 3x2 rectangle.
- O must be placed at (3, 5) because it is the only value left that is not already in the 5th row, the 3rd column or the 5th 3x2 rectangle.
Step 5. There are 3 independent moves.
- The only spot left for E in the 3rd row is at (5, 3).
- The only spot left for O in the 1st 3x2 rectangle is at (1, 2).
- The only spot left for E in the 3rd 3x2 rectangle is at (3, 4).
Step 6. There are 5 independent moves.
- The only spot left for T in the 1st column is at (1, 5).
- The only spot left for R in the 3rd column is at (3, 6).
- The only spot left for T in the 1st 3x2 rectangle is at (2, 2).
- The only spot left for R in the 3rd 3x2 rectangle is at (2, 3).
- The only spot left for R in the 4th 3x2 rectangle is at (5, 4).
Step 7. There are 4 independent moves.
- The only spot left for A in the 1st 3x2 rectangle is at (3, 2).
- The only spot left for N in the 3rd 3x2 rectangle is at (1, 3).
- The only spot left for A in the 5th 3x2 rectangle is at (2, 6).
- The only spot left for N in the 5th 3x2 rectangle is at (2, 5).