How to Solve Sudoku for Beginners - Unique Possibilities

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.

Unique Possibilities

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".


solve some eights

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.


solve a cell

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.

2 Comments
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This page is part of the base towards eventually getting to the more complex tips.

Hopefully, the tips will progress rapidly towards the more interesting.

For beginners, though... I remember that the first puzzles that I tackled were completed using only 'Unique Possibilities'. I More...
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06/Jun/07 8:51 PM
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