You may have guessed from the hint in my last post, the Pointing Out technique Hard level is fitting in then pointing out.
More often than not, you find less than eight number that can fit into a unit, so still more than one empty cells left, wait, we can apply Pointing Out on these empty cells! See the board below, look at box 1, there are five empty cells it, notice that 3 in 27 and 9 in 37 can fit in 15 and 16 in box 1, but that still leaves three cells 17, 18 and 19 empty, and three numbers 1, 2 and 4 missing.
More often than not, you find less than eight number that can fit into a unit, so still more than one empty cells left, wait, we can apply Pointing Out on these empty cells! See the board below, look at box 1, there are five empty cells it, notice that 3 in 27 and 9 in 37 can fit in 15 and 16 in box 1, but that still leaves three cells 17, 18 and 19 empty, and three numbers 1, 2 and 4 missing.
Among the three missing numbers, see there are two 1s in 44 and 72? They are ready to bean their lights, click the board to see the animations. 44 points out 17 and 72 points out 18, leaving 19 the only cell left for 1, solution: 191.
That was the simplest case of fitting in then pointing out, let's see a bit more complicated example in the board below. Look at box 5, 6 and 7 can fit in 56 and 59 of box 5 because the two 6s in 41 and 82, and two 7s in 61 and 85, after their fitting in, the 3 in 22 points out cell 52, 55 and 58, leaving 53 the only cell left for 3, solution: 533.
The same deal when columns and rows are target units, from a simple case:
To a complicated one:
To a more complicated one:
The complexity does not stop there, you know, units that have fitted in cells can in turn be fitters to adjacent unit. In the board below, as 7 in 24 and 8 in 51 fit in 85 and 86 in box 8, cell 86 is also in target unit column 6, so we know 86 can only be 7 or 8, any missing number in column 6 that is other than 7 or 8, can beam light to column 6. In this case 5 in 32 points out 23, 5 in 52 points out 56 and 59, leaving 29 the only cell empty, solution: 295.
In this case box 8 is a unit fitter for column 6. And unit fitters, again, relay. I will leave more complicated examples to another post.
Now you know 5 powerful techniques, hey, they are really just 2 techniques: Pointing Out and Fitting In, applying to the target unit interactively and repeatedly. Practice them, and go solve all the Hard level puzzles.
Difficulty levels are defined differently among newspapers, websites. Hard level in Touch Sudoku is the same as the highest level (Fiendish, Expert, whatever they call it) in most newspapers, and it's the same as the highest level (called Evil) in Web Sudoku.
Yet there is a higher level in Touch Sudoku: Expert, the real expert level, including puzzles being considered diabolical. Stay tuned for more exiting techniques to solve them.
Now you know 5 powerful techniques, hey, they are really just 2 techniques: Pointing Out and Fitting In, applying to the target unit interactively and repeatedly. Practice them, and go solve all the Hard level puzzles.
Difficulty levels are defined differently among newspapers, websites. Hard level in Touch Sudoku is the same as the highest level (Fiendish, Expert, whatever they call it) in most newspapers, and it's the same as the highest level (called Evil) in Web Sudoku.
Yet there is a higher level in Touch Sudoku: Expert, the real expert level, including puzzles being considered diabolical. Stay tuned for more exiting techniques to solve them.
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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