Learn to Solve Sudoku the Dreamagic Way is a Dream Machine Site The Dream Machine --- The Imagination of the World Wide Web

This puzzle, though quite difficult, starts out with a bunch of cherries to pick. So, do those first. There are so many of them, it appears that you can completely solve this puzzle, as you did those in the previous exercises, with nothing but singletons. This turns out not to be true. If you are confident of your ability to recognize singletons, simply turn on the F1 function and fill them all in as quickly as possible. If you are a little less confident, turn on the F2 function instead. This will put up singletons...one at a time...until there are no more. Before you fill in each one, make certain you understand why it IS a singleton. Since the computer can "see" much more of the board than you and I, some its choices might be quite difficult to comprehend, since it may depend upon other squares...also singletons...being filled in to lead to it. If you can't figure it out, skip that one...by turning the F2 function off and back on. It will probably be more obvious the second time it comes up. In any case, make sure you have got them all before proceeding to the main point of this exercise, looking ahead or simply making an educated guess.

Make sure you turn on the F3 function as well at some point. By the time you have filled all the singletons, the F3 function will show you that there are still a lot of 2's, 7's and 8's left to fill in this puzzle.

Now turn on the F6 function to locate all the doubletons. By that, we mean those squares where only one of exactly two possible numbers fit. This function can also be duplicate in the paper-and-pencil case, but it leads to messy...crowded...puzzles. The author has gotten in the habit of making a duplicate of the puzzle at the point where all singletons have been located and then proceeding to mark this duplicate up, in order to keep the original puzzle cleaner. If nothing else, it will give you a lot of practice drawing straight lines.

The idea at this point is to choose one of a pair that you think will most likely lead to either a full solution of the puzzle or a dead end. By "dead end" we mean a point where some square in the puzzle will allow no number whatsoever. The program will notify you of this situation and allow you to back up to where you made the choice. Furthermore, you now KNOW for a fact...if you haven't made any errors...that the other choice MUST lead...sooner or later to a solution. So, you have progressed.

The most expedient...and often best choice...is to pick the number that seems to lead to the most new singletons. The author has discovered that this most often is the "wrong" choice, since it will lead to a dead end. Does that mean you should always pick the other one? No it doesn't. The reason is subtle but obvious, once you think about it. The "lesser" choice is most likely to lead to another choice point...rather than the desired solution, which means that you now have at least two MORE paths to investigate. The "expedient" choice is more likely to actually lead to a dead end, which give you CERTAIN knowledge of how to proceed.

In any case, once you make a choice of one of the possibilities in a doubleton, the computer will set a "breakpoint." Later, if you wish to return to this point since you have either reached a dead end or simply want to try the other path, hitting the backslash key the one with a "\" character on it, will take you there, erasing all the numbers you filled in. By the way, if you haven't encountered a breakpoint...the computer notifies you when it sets one...the backslash key will take you all the way back to the start of the puzzle, just like the delete key.

If you have forgotten which square was the breakpoint, the F11 function, when turned on, will show all the breakpoints that have been set. If you have tried only one of the numbers, then it will be highlit in green. If you have already chosen both, it will be shown in red. When the backslash key returns you to one of them, you can then choose the other number. If you have already tried both paths from the breakpoint, it will return you to the previous breakpoint, etc. This process is called back-tracking. This particular puzzle should involve no more few of these, and all of them well past the halfway point to the solution. Indeed, at some point, the remaining squares may be so few that you can actually try them out in your head to eliminate one of the possibilities.

By the way, if the F11 function is turned on when the backslash key is struck, it will actually fill in the second choice for you so you won't have to remember. which one you chose first. The computerized breakpoints are an enormous help solving difficult puzzles. The F1 function...displaying all available singletons...can also be very useful...when frequently backtracking.

If you have only a single breakpoint and both paths lead to dead ends, then you have made an error somewhere and should begin the puzzle over. Sad but true. Hey, it WILL be easier the second time around and...it will teach you to be more careful. LOL