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Sudoku Linear Elimination
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Linear elimination based on the remaining numerals left available within the zone. Because the numerals 1 through 8 are already used, the remaining numeral in the zone must be 9. |
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Another version of linear elimination across multiple zones. Because the numerals 1 through 8 are already used in the same row, the only remaining possible numeral that can be in the cirle is 9. |
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Similar to the example above, this version of linear elimination is vertically oriented. Across multiple zones, the numerals 1 through 8 are used and the only remaining numeral that will work in the sequence is 9. |
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Sudoku Row Elimination |
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Horizonal Row Elimination Because the 4 appears in the second and third row, the only possible remaining location is in the first row. |
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Vertical Row Elimination Similar to the example above, the 4 is placed in the first and third column and the only possible location left is in the second column. |
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Zone and Linear Elimination The 4 in the second row cancels out all the remaining locations in the last zone so the only possible location left is on the third level. |
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Another Version of Zone and Linear Elimination The 4 in the second row cancels out one of the two spaces left in the linear sequence so the 4 must appear in the remaining square. |
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Another Version of Zone and Linear Elimination Because there is a 4 in the second zone, it cancels out three possiblities in the linear sequence and the 4 must appear in the remaining box. |
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50/50 Elimination
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| The 4 in the second row is canceling out three of the five possible remaining locations. This implies that there is a 50/50 chance that either of the two remaining locations is correct. |  |
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| I usually write a small notation in one of the corners to denote the fact that there is only two remaining locations for the 4. This helps to speed up the solution and to helps me remember. |  |
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| While there is only a 50/50 chance that it will appear in either of those two boxes, there is a 100% certainty that it will appear on that row. Therefore, combined with the other information available, the 4 must go in the denoted location. |  |
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| Because the 4 and the 5 both have a 50/50 chance that they will appear on the third row, there is a 100% certainty that no other number can occupy those spaces. Therefore, the last number left in the linear sequence must go in the space on the second row (9). |  |
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| Similar to the example above, because the 4 and the 5 both have a 50/50 chance the will appear in the second and third column, the last remaining number in the linear sequence must go in the first column (6). |  |
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| Similar in concept, there is a 50/50 chance that 4 will appear in the middle or right zone on the first or second row, then there is definately a 100% that it will appear on the either the first or second row and therefore 4 must appear on the third row in the left zone. |  |
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| Looking at the 8 in the top right and bottom right zones, there is a 50/50 chance where the 8 will appear in the third column in the middle right zone. However, the only two locations left for the 4 and 5 occupy the third row. Therefore, it is impossible for the 8 to be in the third row and the only available location left is in the second row. |  |
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| Though it is impossible to determine where exactly the 4, 5, and 6 appear on the third row, they form an interdependance and no other numerals can fit in the third row. There is a 50/50 chance that the 8 can be in either the second or third row but because of the interdependance of the 4, 5, and 6, the 8 must go on the second row. |  |
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| Sometimes if I am stuck and there are a lot of 50/50 possibilities, I will circle one of my notations and assume that it is the correct chose. Then, I will underline the other notations that would be correct assuming the circled notation is correct until I find a conflict. Then, I will go back to the circled 50/50 notation and fill in the other option which must be correct. | ||||
| I hope this little tutorial was helpful and if you have any suggests, my email is dangdatkat at gmail dot com. Also, feel free to check out my website, ExpertAdWords.com | ||||
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