Find the Lone Number

In the following example, all the options for region 5 have been penciled in. At first there appear to be three places for the number 1 to go, but look between the 8 and the 3. There is a lone number 1. It was not otherwise obvious that the only cell for the number 1 was row 6, column 5, as there is no number 1 in the immediate vicinity. Checking the adjacent regions and relevant row and column would not provide an immediate answer either – but no other number can go in that region.

While the example uses pencil marks to illustrate the rule, more experienced solvers are quite capable of doing this in their head. Remember that this principle is true for regions, rows, and columns: If there is only one place for a number to go, then it is true for that region, and also the row and column it is in. You can eliminate all the other pencilled 1’s in the region, row, and column and get the grid shown to the left. This immediately solves the 7 in row 5, coloumn 6 and with the 7 in place, there is only one cell available to the 2. Can you see why?

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