Sudoku - Day 5

Good afternoon.

Yesterday I left you hanging with the 3 in [B7]. This introduces a new concept called virtual solving. I developed this technique while studying from the Sudoku Masters.

Let's focus on box column set 3 (Columns 7,8,9). Notice the 8 in [H8]. That 8 prevents us from solving [G9] or [J9] as 8. Also notice that [D9, E9, F9] are already solved, along with [A9]. Now using the basic rules, there must be an 8 in every column. So if we cannot put an 8 in [D9 - J9] or [A9] the 8 must go in [B9] or [C9]. We don't know which one yet, but we know that the 8 in box 3 is in column 9. Since the 8 is already in column 8 in box 9, then we also know that the 8 for column 7 must be in box 6. This is called virtual column solving, and it will greatly assist us in solving this puzzle.

So using this new technique, we know that the 8 for box 3 is in column 9 [B9 or C9]. Well, if we look a little harder, at column 9, we see we have three open spaces. And we need the 8,7 and 1. But look at the 1 in [B8] and [G3]. This solves [J9] as 1. So write the 1 in [J9]. Now we are left with resolving the 7 and 8 for column 9 and we know they go in [B9] and [C9].

This is excellent information, so let's focus in on killing box 3. We have a 6,9,1 and 5 solved. So we need 2,3,4,7 and 8. We can eliminate [B9] and [C9] as we already know what they are (7,8). So let's set our sights on the 4 for box 3. The 4's in [A2], [G7] and [F9] solve the 4 for [C8]. Kill [C8] with a 4.

Now we have 2 spaces remaining. (because we already know what [B9] and [C9] are. We need the 2 and the 3 and they go in either [A8] or [B7]. Notice the 3 in [A5] which solves the 2 for box 3 in [A8] and the 3 in [B7].

So without knowing what spaces the 7 and 8 go in in box 3, we solved all the rest of the numbers because of the virtual solution of knowing what column the 7 and 8 were in.

Whoa... That was the heaviest logic yet. We will use it again to solve this puzzle in box set 1 (columns 1-3). So there you have it, today's 4 numbers.

Your board should now look like this.

Strangers in my pants....

Dr. Sudoku.