TECHNIQUES FOR SOLVING TATAMI PUZZLES

For a description of TATAMI puzzles, refer to  Building Tatami Puzzles 

The process of solving TATAMI puzzles makes use of "pencil mark" digits in the unsolved cells of the puzzle. The rules which apply to solving the puzzle are used to remove certain of these "pencil marks" until there is only one left, at which point it becomes the solution for that cell. The following graphic shows a TATAMI puzzle with all "pencil marks" in place.


Strategy 1:- Cast out digits based on adjacent cells.

 
The left had graphic shows the situation after relevant "pencil marks" have been removed from all cells which are adjacent to numbered cells. There are three cells in which only a single "pencil mark" remains, so these three cells can be solved immediately. This has been done in the right hand graphic, and adjacent cell "pencil marks" have been removed. No new opportunities are available, so we must turn to strategy 2.

Strategy 2:- Cast out digits based on occupied tile cells.

 
This strategy is based on the rule that a tile must not contain two cells having the same digit. This allows more "pencil marks" to be cast out as shown in the left hand graphic above. This has revealed two new cells containing a single "pencil mark" and these have been converted to solved cells in the right hand graphic. Strategies 1 and 2 should be repeated until no more progress can be made.

Strategy 3:- Cast out digits based on the Row and Column rules.

 
In this puzzle, each row and column must have exactly two of each of the digits 1 to 3. Note that in row 6 and column 6, there are already two 3s, and so any "pencil mark" threes can be removed from that row and column. This is shown in the right hand graphic where it is seen that another cell can be solved. From this point, repeated application of the above three strategies will quickly lead to a complete solution.