Three missing numbers, whether from a row, column or square are found quite easily, by looking for two of them in a combination of either row, column or square. Example1 shows 3 squares (top-right, middle-left, middle-right) with 3 missing numbers each.
Starting with the top-right square, 4-6-8 are needed. 8 is found in the 2nd row, 4 is found in the 9th column, therefore the cell in the intersection is 6. Now we have 8 & 6 in the 2nd row, with a missing number, which is the missing number from the original three numbers, it is 4. The remaining cell is filled with the 8.
Next the middle-left needs 2-7-8. The 2nd column has a 2 and the 4th row has a 7, so the intersection is filled with the 8. We now have 7 & 8 in the 4th row, so we fill the cell beside the 8 with 2, and the remaining cell fills with 7.
The middle-right square needs 3-6-9. The 5th row has 6 & 9, so fill the cell in that row with 3. The missing cells in that square do not have 3, 6 or 9 in their respective rows or columns, so we have to wait until some other cells have been filled in to determine where the 6 and the 9 go.
The 6th row now has 3 missing numbers, 6-8-9. At this stage we can merely determine that 8 does not go in the 8th column, since there is already an 8 in the middle-right square. Let's pass and come back when we have more information.
The 1st column needs two numbers, 6-7.
The 8th row contains a 6, so the cell in the 1st column 8th row gets 7, leaving the 3rd row to get 6.
Now the top-left and bottom-left squares are missing 3 numbers each, as well as the 3rd row.
The top-left square needs 1-3-7, the 2nd row has 7, the 2nd column has both 3 & 7, so the cell in the 2nd column 2nd row gets the number 1. 1 & 7 are now in the 2nd row, so fill the cell with 3, and the remaining cell with 7.
The bottom-left square needs 1-4-9. Column 2 has 1 & 9, row 9 has 1 & 4, so fill column 2's cell with 4, and row 9's cell with 9, the remaining cell in column 3 row 7 gets the 1.
Row 9 now is missing 3 numbers 5-6-7.
Column 7 has 5 & 7 so it gets the 6. Column 8 and the bottom-right square both contain 5, so its cell gets 7, and column 5 gets the 5. Now there's enough information to fill the remainder of the middle-right square.
There is a 6 in the 7th and 9th columns, so the 6 goes into the 8th column, the remaining cell in the square gets the 9.
Notice we have no 6s in the 3 center columns, it makes it more difficult to determine with certainty where specific numbers go with situations like that. We can determine where the remaining 1 goes, so let's place it. There is a 1 in the 4th and the 5th columns so it goes in the 6th column, and there is a 1 in the 1st row, so we put the 1 in the 3rd row 6th column.
The top-center square has 3 missing numbers now, 5-6-8. Row 3 contains 6 & 8, so fill with the 5. Column 6 has an 8 and the square now has 5, so 6 goes into column 6.
Row 6 needs 8 & 9. Column 5 has an 8, so 8 goes into column 4, making column 5 fill with 9.
Column 4 needs 4-6-9. Row 4 has 4 & 9, so gets filled with 6. Column 4 row 7 is inline with the 6 just placed, and 4 in the row, so it fills with 9, leaving only the 4 for row 8's cell in the column.
Column 5 needs 2-3-6. Row 4 has 2 & 6, so it gets 3. Row 7 has 2 & 3, so it fills with 6. The remaining cell in the column gets the 2.
There are only single missing numbers in two of the squares, and two in the bottom-right square. I'll leave those to you to determine.
Labels: Sudoku
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