Samurai SuDoku, Killer Sudoku and more

Solving Hitori puzzles is about recognizing patterns. I will show you some examples of those patterns. They can be split into two groups, one of those that depend solely on the initial positioning of numbers, and another group of patterns that depend on the black and white cells which have been painted in the solving process.

One trivial advice that you should always keep in mind: if a cell cannot be black, it must be white! And vice versa. From this comes one simple solving technique: when you conclude that a cell must be painted, circle the numbers in all four adjacent cells to indicate that they must be left unpainted. Now, back to the patterns:

Corners

Check the corners first. Here is an example:

When you have 2 same numbers adjacent to each other in a corner, you can circle at least one other number. Why? It is easy to see that the 1 cannot be black, because one of the 4s must be black. If the leftmost 4 were black, the 1 would be adjacent to it. If the rightmost 4 were black, the 1 couldn’t be black because those two black cells would isolate the other 4 in the corner, which is against the 2nd rule of Hitori. Got it?


Here are some other similar patterns that occur in corners:
        


And here are some other examples for you to practice:
            

Squeezed in the middle

This is probably the most common pattern in Hitori puzzles.

A number squeezed between two same numbers must be white! If it were black, it would eventually cause two black cells to be adjacent, which is not allowed.
Oh, and don’t be put off by three same numbers adjacent in a row or column. The same rule applies.

Elimination

By the way, once you’ve circled a number, make sure to eliminate all other occurrences of the same number in the same row and column:

No room for three
Another very common pattern is when two same numbers are adjacent to each other and there is another one in the same row/column. Obviously, one of the adjacent 3s will have to be white (they can’t both be black). Whichever one it is, the 3rd 3 in the same column will have to be black, as you can’t have two 3s in one column.

Those were the basics. That’s how you start solving any given puzzle. In a few days, I will post some more complex patterns that are used in the more difficult of puzzles.

Here is an explanation of a Hidato solving technique that some people might find obvious and they use it without even thinking of it as a special technique. But, for those who still struggle with the more difficult puzzles, here is a quick guide of the technique that I call “cornering“.

It can be used when a cell has only one “neighbor” that is an empty cell. In such a case, that cell (with only one empty neighbor), must contain a number that is consecutive to (at least) one of the already filled in neighbors.

Look at the upper left corner. Number 33 could in theory go into any of the 4 cells that are neighbors to both 32 and 34. However, it must actually go into R1C1 (row 1, column 1). Why? Because R1C1 has only one empty neighbor and according to the rule I stated above, in such a case that cell must be consecutive to (at least) one of the existing neighbors.
Why? Because each cell (other than 1 and the largest number) must have both a “+1” and a “-1” neighbor. So, the only options for R1C1 are 31 or 33 or 35. If you put any number other than one of those in R1C1, it would have only one of the “+1”, “-1” neighbors, because there is only room for one number next to it. That is why I also call this technique “dead-end”. But 31 would be too far from 29; and 35 would be too far from 39. Therefore R1C1=33!

Now, look at R1C7 (it’s circled). See if you can figure out why the number in that cell MUST BE 5.

Some of you may have already started playing “the new Sudoku” puzzles that appear in The Times (UK). We call them CalcuDoku or “Square Wisdom“.

It’s an interesting concept, quite similar to Killer Sudoku, but with all four basic arithmetic operations involved. Another change is that repeats within a cage are allowed if possible.

To help out those of you who are starting to like this game, I have prepared a tool that shows you which combinations of numbers can go into a certain cage. All you need to do is plugin the numbers, click “Calculate” and voila!, you get the list of possible options.

Obviously, this same calculator can also be used for Killer Sudoku and Kakuro puzzles.

Here is the calculator:

Cage Value
Operation	+	*	-	/	no op

Number of cells

2

3

4

5

6

7

8

9

Maximum repeats?

No repeats

1

2

3

4

5

6

7

8

Allowed numbers

1

2

3

4

5

6

7

8

9

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 Sudoku variant puzzles (Samurai, TwoDoku and any other) as well, using the same approach.

A while ago I explained the X-Wing solving technique.
Recently I shown my explanation of other basic, Classic Sudoku solving techniques.

The only remaining solving method that I don’t consider trial and error is Swordfish. So, to complete the list of Sudoku solving tips, here is an example of a Sudoku puzzle that can be solved using Swordfish.

Here is the puzzle:

This is how far you can get without using Swordfish: (more…)