Chapter 10: Solving a Diabolical Puzzle

In its structure there is no difference between a tough Sudoku and a diabolical puzzle. The grading is only increased because in a diabolical puzzle there are more places where clues can run out and more apparent dead ends. You can find diabolical puzzles in a variety of places including puzzle books and on the Internet. If you buy a puzzle book you will find difficult and diabolical Sudoku puzzles after the easy to moderate puzzles. Always keep in mind that diabolical puzzles will take a bit more time to solve than easy to moderate puzzles. In fact, as you start to learn how to solve Sudoku puzzles it may take you over an hour to solve a difficult puzzle!

In the above example, ignore the pencil marks on the grid except for the first pair: at 1,5 you have either a 6 or a 9. There is at least one other pair that you could have chosen on the grid, but this was the first, so let’s be logical and use that. If you choose to try the 6 first, the following grid shows the numbers that you will be able to complete using this number.

Pencil the now obvious numbers into the cells so that you bring the puzzle closer to a solution. You can always take a back step and find your back to where you started if you hit a dead end. Solving Sudoku puzzles is all about trying to follow the maze through to the end even though there may be many road blocks along the way.

But with just two cells to fill, look at what we have: at 4,8 the region needs a 4 to complete it, but there is already a 4 in that row at 4,6. Similarly, at 5,4 that region needs a 6, but one already exists in that row at 5,7. No second guess was needed to prove that at 1,5 the 6 was incorrect.

So now you need to return to 1,5 and try the 9. Now you are able to prove the 9 at 2,1 but nothing else is obvious; every cell is left with options. In this case you could leave both 9’s because you have proved without doubt that the 6 at 1,5 could not be correct, but if the 6 had simply left you without sufficient clues, as the 9 did, you wouldn’t know which was true. Rather than start a new, uncertain path it is better to return to the situation you were in before you chose at 1,5 and find another cell to try from. This is a base that you know to be true.

In the following grid you can see that you need to look at cell 1,7 , where the choice is between a 3 and a 6. When you choose the 3 you find yourself on a path that takes you to just two more to go but then you discover that a 2 is required to complete region 7. There is already a 2 in that row at 9,5. In region 9 you need an 8, but there is already an 8 in row 8 already. You now need to wind the thread to get back to 1,7 where 3 was chosen last time. Trying 6 here will lead you to the solution.