Sudoku Lesson IX - Bifurcation
Now, pick a marked box having only two numbers marked in it. Try not to pick a coupled pair -- they won't get you very far. Make some indication of this starting box, perhaps by drawing an outline around the box. I picked (4,9):
Slash one of the dots indicating a marked number. Pretend like that number is in the box. If that number is in the box, use all of the techniques that I taught you in the previous lessons to solve another box. Slash the dot indicating the solution for that box. Continue onward until you find that you can't solve anymore boxes, or you find a conflict. In my example, I slashed the 9 dot. That led me to slash the following dots in the succeeding boxes:
7 in (4,3); 2 in (4,6); 7 in (5,6); 5 in (4,8); 4 in (1,8); 5 in (1,7); 6 in (7,8); 4 in (9,9); 2 in (6,8); 6 in (5,9); 4 in (7,6); 6 in (8,6); and 8 in (4,2). The puzzle now looks like this:
A conflict is where you have slashed the same dot for two boxes in any row, column or square. If you find a conflict, then go back to the starting box and write in the unslashed number. For example, I continue to slash dots in the above puzzle, in the following order: 4 in (8,2); 2 in (6,2). But I note that there is already a 2 marked in (6,8), thus creating a conflict:
So now, since picking a 9 in (4,9) lead to a conflict, I must pick the non-slashed dot, starting with the box (4,9), and then continue to fill in numbers as I go. I filled in 4 in (4,9); 6 in (9,9); 4 in (7,8); 9 in (5,9); 5 in (1,8); 4 in (1,7); 5 in (4,7); 4 in (8,6); 6 in (7,6); 2 in (4,8); and 6 in (6,8). The puzzle now looks like this:
If you are just stuck, go back to the starting box and put a backslash (or some other tick mark of your own choosing) on the other dot. Then repeat this process, using the other indicator, until you reach a conflict, or get stuck. If you reach a conflict, write in the slash dot number in the starting box. This did not happen for our example, the rest of the numbers followed, and the puzzle was easily completed:
If you are not so lucky, don't give up. You tried both ways, and neither path reached a conflict. Go back and mark the remaining squares, then try to solve more /s and \s to find a conflict for either branch. Mark the whole puzzle if you must.