All tips involve merely applying the rules of Sudoku. The easiest puzzles are solved
using these rules with a "one pass" approach. One merely needs to scan the grid
to find where a candidate cannot be placed, and if there is only one location for a particular
candidate in any row column or box (large containers), then that cell is solved.
In a similar fashion, if a cell cannot be all but one of the candidates, that it must equal
the one remaining candidate. Find below some simple examples of this technique.
On puzzle pages at Sudoku.com.au, this tip is shown on the right as solving
techniques 1 and 2. In proofs that are commonly presented at sudoku.com.au, this process of finding
singletons in a large container, or a small container (cell), is labeled as
"Unique Possibilities" or "UP".
Above, note that at the inception of the tough puzzle from 11/30/06, three eights were given.
These are highlighted in green at cells a2, f6, g3. The cells highlighted in blue are the cells
that cannot now be eight because of the rules preventing two eights in any large container.
Thus in box e2, only d1 and e1 could be 8. Since e1 is already 4, the cell highlighted in pink,
d1, must be 8. In the same fashion, consider column e. Because of the three given 8's, only
e1,e7,e8,e9 could be 8. But since e1=4, e8=5, e9=3 are givens, the only remaining location for
8 in row e is e7, highlighted in orange-yellow.
Above, note the cells highlighted in blue. They are one of each of the numbers:
1,2,3,4,5,6,7,9 - but not 8. They intersect at the cell highlighted in yellow. This cell
must be 8. In this case, one could say that cell b2=8 because it cannot be 369 because column b
already contains 369. B2 cannot be 1245 because row 2 already contains 1245. Finally, b2 cannot
be 3457 becauase box b2 already contains 3457. Combining these three ideas, b2<>12345679. Thus, b2=8.
Use of only these techniques will not solve "hard" or "tough" puzzles, but generally will solve
"easy" and most "medium" puzzles.
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