A rule of thumb that I use is after solving a box or 5 numbers (you make up the rule) I go back and run the four basic rules again in every row and column. That includes 1-9 in every row, 1-9 in every column and 1-9 in every box.
Today, three solved numbers come from those rules.
First, let's look at [A2]. Notice we have a 4 in column 1 [E1] and a 4 in column 3 [H3] so the remaining 4 must be in column 2. We know it is not in box 4 or 7, so that leaves column 2, box 1. Only one space available, [A2].
Next, using the same rules, let's look at [H7]. We see there is already a 7 in row G and in row J, and in box 7 and box 8 leaving the remaining 7 in row H, box 9. Only 1 space for that 7, [H7].
Finally, a look at [G7]. There is already a 4 in row H and row J and in box 7 and box 8 leaving row G box 9. Two spaces are available, but look at [F9], it's a 4, meaning our 4 belongs in [G7].
Now, to solve our next number, let's take a look at the central column (rows 4-6). Notice that lonely 3 in [A5] and notice the (now infamous) column of three solved numbers in column 4, box 8. There is no 3 in that set. Heavy logic coming. If there is a 3 in column 5 already [A5] (box 2) and there cannot be a 3 in column 4 box 8, then we have ruled out column 4 and column 5 for solving the 3 in box 8. That means the 3 has to be in column 6. There are two choices there [G6] and [H6], but look at the 3 in [H2] ! That allows us to solve the 3 in [G6]. Whew...
So, after today's major brain load, our board looks like this.
BONUS: Tomorrow, the first move will be putting an 3 in [B7]. Why ?
Keep on truckin...
The (Sudoku) Doctor.
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