DJ Ape .Net – The Home of Perfect Sudoku

This could well be the most difficult puzzle I’ve ever created. Yet, unlike some previous ones which were intentionally created to require trial&error, this one can surely be solved without guessing.

This is a Zero Killer Sudoku puzzle in a Clueless format. Once more I want to thank Ruud for inventing the “Clueless” arrangement of puzzles.

For those who are new to the Clueless concept, I would first suggest to try and solve some earlier puzzles of this sort. Here is a link to Clueless Sudoku X and here is a link to Clueless Killer Sudoku.

Rules: There are 9 Sudoku puzzles with no overlapping regions! Solve them according to the rules of Sudoku and use the given cages as clues. Small numbers shown in each cage indicate the sum of cells that constitute that cage. Numbers cannot be repeated in a cage! If you only look at the 9 sub-puzzles, you won’t be able to solve the whole lot! Why? Because there is the 10th sub-puzzle hidden! Here is where the “clueless” part comes in: in all 9 puzzles, the center nonet is completely empty. As you plug in your numbers, center nonets (shaded in grey) start filling up. The trick is that those 9 center nonets, put together, also constitute a valid Sudoku puzzle. So, when you run out of ideas, start working on the 10th puzzle and it will give you enough information to solve the whole lot. Those 10 puzzles together have, of course, a single solution.

Clueless Zero Killer Sudoku for Thursday, August 30, 2007 – this is the only place you can find this kind of Sudoku puzzles!

Download the puzzle by clicking on this thumbnail:

solution – final

Previously I said that you should not attempt to solve these puzzles because they’re too difficult. This time I’d like to here from you what you think!

A few visitors to my forum have been creating these puzzles for quite some time. Well, here is one from me.

Rules: Everything is exactly the same as in your ordinary Killer Sudoku puzzles, except that there are even fewer clues given to you to start with. Some cells are not joined in any cages, so you don’t have any starting information about them.

IMPORTANT: I will start posting these Zero Killer Sudoku puzzles every Sunday on the Daily Killer page. They will usually be fairly difficult. Also, as of tomorrow, Monday, August 27, there will be a change on the Daily Sudoku page. After a few months of (non)consecutive puzzles, I will now start posting Jigsaw Sudoku (irregular nonets) and Hyper Sudoku (Windoku) puzzles.

Zero Killer Sudoku for Sunday, August 26, 2007. – Difficulty: IQ

Download the puzzle by clicking on this thumbnail:

Text file to import into Perfect Sudoku. Important: PS v0.4 will report there are 0 solutions for this one because it is unable to solve “Zero” Killer puzzles!

solution – final

Enjoy!

I promised to explain this technique, which applies to Jigsaw (aka irregular blocks) puzzles, a while ago, so it’s time to keep the promise. You can find the same technique explained on various other sites, too.

This technique is somewhat similar to innies/outies which is used for solving Killer Sudoku puzzles, but there is no math involved and, again, it applies to Jigsaw Sudokus (and variations thereof).

First, I’ll explain some terminology that will be used:

LOL can be applied to any number of either rows or columns. How many rows you will use, it’s up to you (depending on the puzzle you are solving). The rows you are using must be adjacent to each other and they can start from the middle. In other words, they can, but don’t have to, be aligned to the edge of the puzzle. The adjacent rows (columns) that you choose to apply LOL, we will call AREA.

Some jigsaw nonets will be completely outside your chosen area, some will be completely inside it and some will have cells both inside and outside your area. Focus on nonets that have cells both inside and outside the area. We’ll call them BROKEN NONETS.

INNIES are cells that are within the area and belong to broken nonets which have fewer cells inside the area than outside of it.

OUTIES are cells that are outside the area and belong to broken nonets which have fewers cells outside the area than inside it.

Ok, this sounds quite confusing. So here is a sample puzzle to make it clear:

By using the common Sudoku solving techniques, you should reach this position:

Now what? Look at the first 3 columns. This will be your area. It is outlined in red in this picture:

If you are paying attention, you will already know why are some cells outlined in green. They are innies and outies. If you are not sure why, read the definition of innies and outies again!

IMPORTANT: The number of innies must always be equal to the number of outies. If your number of innies doesn’t match to your outies, you’ve done something wrong. Go back and look at it again!

Finally, it is time to state The Law of Leftovers:

The set of numbers in innies must be the same as the set of numbers in outies.

Why? Because in your area, which consists of “N” rows, there must be precisely “N” occurences of each digit (1-9 in normal Sudoku case). This is always the case in any Sudoku puzzle. Also, any “N” nonets contain precisely “N” times each digit (1-9). Now, jigsaw nonets that are broken by this area, “borrow” (or “lend”, depends how you look at it) some of their numbers from the rest of the puzzle. Those are innies and outies. In order to keep the puzzle consistent, those numbers that are borrowed must be the same as the numbers that are lent.

Anyway, lets apply LOL to our sample puzzle. Our 3 innies have these candidate numbers (some of them are naked singles, but it doesn’t matter): 7, 2 and 3|9. Our 3 outies can be: 2|8|9, 2|8 and 7. So, number 3 is a candidate in innies, but it’s not a candidate in outies. According to the Law of Leftovers, this cannot be! Therefore, we can eliminate 3 from the list of candidates in innies. Accordingly, we can eliminate 8 from outies (because it does not appear in the list of candidates for innies). There you go! We have solved two cells: R3C4=2 and R8C3=9.

From here, this puzzle can be solved by using the usual techniques. Here is the final solution.

Obviously, LOL can be applied to Jigsaw overlapping puzzles (Samurai, TwoDoku and any other) as well, using the same approach.

Hello everyone, I’m back!

After a few weeks of no updates and some problems with the site, it’s time to get back to usual daily and weekly routines.

The Washington Post Samurai Sudoku solutions have been updated. The Weekly Samurai X puzzles is now also in place. On Tuesday, there will be a new one.

Hopefully, those problems won’t occur again.

Anyhow, here is a new puzzle for you. Since I’m in the mood for creating Jigsaw Sudoku puzzles, this is another addition to my collection.

Jigsaw TwoDoku for Saturday, August 18, 2007 – Difficulty: THINKER

Rules: Solve the puzzle so that every row, column and jigsaw nonet contain all numbers from 1 to 9. There are no 3×3 square nonets as in ordinary Sudoku puzzles!

Download the puzzle by clicking on this thumbnail:

HINT: You need to use the Law of Leftovers to solve this puzzle.

solution – final