Basic Elimination, also called Unit Elimination or Group Elimination, is the most commonly used technique in Direct Elimination Techniques. If properly used, it can help you to solve puzzles of moderate difficulty level.
The aim to use Basic Elimination is to find the only position for a number in a unit (column, row or block), in other words, to eliminate all unassigned cells until only one is left. It corresponds to Hidden Single Technique of Candidates Elimination Techniques.
How to eliminate all impossible cells? The answer to this question is based on sudoku rules too, that is
To understand these rules more clearly, an example is given below. It shows how Basic Elimination works in a block, which is the most common case in practice.
In the Block at [D1], there are totally six blank cells. Hardly can we place any number into this block if we don't use Basic Elimination Technique.
Observe the positions of all 9s assigned already in the puzzle. They appear at cells [A4], [B2], [C7], [D8], [H9] and [I1]. Among these positions, only [B2], [D8] and [I1] have direct connections with the Block at [D1]. Since [I1] = 9, all other cells in Column 1, where [I1] lies, cannot be assigned with 9 again. So we can eliminate the possibility of assigning value 9 to [D1] or [F1] of Column 1. Similarly, since [B2] = 9, [D2] and [E2] of Column 2 cannot be placed with 9 either. And for Row D: [D8] = 9, so [D3] must not be 9. Now, all possible cells left for value 9 is [E3] only. Set [E3] = 9.
Here is another example:
In the puzzle above, we will try to find which cell in Row H can hold value 4. Although there are totally five blank cells in Row H, value 4 at [C3] helps to exclude [H3], which is also in Column 3, from holding value 4. [I4] helps exclude all other cells in Block at [G4], including [H4] and [H6]. While [E8] removes the possibility of [H8] for being assigned of value 4. Therefore, the only possible position for value 4 in Row H is [H9].
Of course, Basic Elimination Technique can also be used in columns:
The figure itself clearly illustrates how Basic Elimination Technique works, so that we don't waste time on explaining it.
Through studying of the above examples, we can find that if we want to use Basic Elimination Technique against a block, we have to read carefully the rows and columns which intersect the block to find if existing values can help exclude some blank cells in that block; if we want to use this technique against a row, we have to focus on the blocks and columns that intersect the row; and similarly, if we try to use this technique against a column, we should observe those blocks and rows which intersect that column.
Basic Elimination Technique is the very basic technique in Direct Elimination Techniques. To explain this technique clearly, the examples above are marked with distinct colors. In practice, however, the relationship among the columns, rows and blocks is not easily observed. Only through frequent practice can this technique be mastered and become a most useful skill for you.
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