Let's move to Fitting In technique, in Medium level. You may wondering where is the Fitting In Easy level, well, in Sudoku Rules and Terminology, see the examples that eight of the numbers nicely fitted in a unit? The last number goes to the last empty cell, that Easy level of Fitting In, too obvious to have a separate blog for it. But it gives the idea what Fitting In technique is: when when eight numbers can fit in a unit, the last number goes to the last empty cell.
See the board below, look at box 3, there are 3 empty cells 31, 34 and 37 and 3 missing numbers 3, 6 and 7. There is a 3 in 23 that can point out 3 from 31 but leaves two empty cells 34 and 37, there is a 7 in 11 that can point out 7 from 31 but leaves two empty cells 34 and 37, so Pointing Out technique cannot apply here.
See the board below, look at box 3, there are 3 empty cells 31, 34 and 37 and 3 missing numbers 3, 6 and 7. There is a 3 in 23 that can point out 3 from 31 but leaves two empty cells 34 and 37, there is a 7 in 11 that can point out 7 from 31 but leaves two empty cells 34 and 37, so Pointing Out technique cannot apply here.
But think from the other side, if 31 cannot be 3 then 3 must in either 34 or 37, if 31 cannot be 7 the 7 must be in either 34 or 37, so 3 and 7 can nicely fit into 34 and 37, we don't know which number in which cell but the point is, eight numbers are now fitting in box 3, leaving the last number 6 go to the last empty cell 31! Click the board to see the animations.
Another example of fitting in a box, like an orchid centerpiece.
More examples, fitting in a column:
Fitting in a row:
Fitting In technique is harder to spot than the same level of Pointing Out, especially when more than three empty cells in a unit, you need to scan three or more numbers in three adjacent units. The same solution may come from different unit depending which unit you choose to be the target. The same solution in previous board, which was four numbers fitting in row 3, could be different four numbers fitting in column 7:
Or could be other five numbers fitting in box 3:
Of course Touch Sudoku will always give you the simplest of the solutions.
With the 3 techniques so for, you can solve all the Medium level Sudoku puzzles.
With the 3 techniques so for, you can solve all the Medium level Sudoku puzzles.
Sudoku Rules and Terminologies
Technique No.1 Pointing Out - Easy Level
Technique No.2 Pointing Out - Medium Level
Technique No.3 Fitting In - Medium Level
Technique No.4 Fitting In - Hard Level
Technique No.5 Pointing Out - Hard Level
Technique No.6 Pointing Out - Expert Level
Technique No.7 Fitting In - Expert Level
The puzzles in this post are from http://school.maths.uwa.edu.au/~gordon/sudokumin.php The work is licensed under a Creative Commons Attribution 2.5 License. Attribution goes to Gordon Royle and The University of Western Australia.
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