![]() Pretty cool, huh? The great thing about Unique Rectangle is it is easy to spot - and because of that, you actually see it quite often! They just can't possibly be candidates if this is a true Sudoku puzzle. See the four cells that make up the corners of the blue box? Notice how three of them have only 3 & 5 in them? Well, using our new knowledge, we can safely remove the 3 & 5 from the fourth cell. How can I be so sure? Because they print the answers as well, and you never see more than one answer!Įven if you didn't really follow everything written above, here is all you really need to know:Īny time you see a rectangle of four unsolved cells, where three of the four cells have the exact same two pencil marks in them, you can remove those pencil marks from the fourth cell completely. So how can we use this information to solve a real Sudoku? Well, if we can assume the puzzle we are working on had been previously deemed "unique" (which is a pretty safe assumption), then we can also assume there will never be four cells - falling into exactly two rows, two columns, and two blocks - with the same two pencil marks.Īlthough I'm only guessing, probably well over 99% of the Sudoku puzzles published in books, magazines, and newspapers have one unique answer. This is how they are able to interchange 3s and 7s - two different numbers being transposed in two different rows, for example, does not upset the balance. Notice that the four unsolved cells share exactly two of each kind of "house." That is, they fall in exactly two different rows, exactly two different columns, and exactly two different blocks. Ironically, this invalid puzzle is a perfect way for me to illustrate the "Unique Rectangle" principle to you. Either way would work, making this puzzle, by most current definitions, invalid. But, you could also put an 7 in the upper left and solve it as well. But which ones are 3s and which ones are 7s? You could put a 3 in the upper left cell and solve it from there. There are only four cells yet to be filled in. Take a look at this example of an invalid puzzle: Let me first show you how Unique Rectangle works. The good news is that there is just about a 100% chance the puzzle you are working on does have only one unique answer, but more on that in a minute. ![]() Most people today agree that a puzzle has to be unique to truly be a Sudoku. It is true that early Sudoku puzzles were created by hand, and without being tested by computers it was sometimes hard to tell if the puzzle had only one answer. While most modern definitions state that a Sudoku puzzle has to have only one answer, a few people claim that a single unique solution is not a requirement. There is a bit of a disagreement in the Sudoku community on this. My own personal experience is that it is not common to find that you need this technique to solve a puzzle.This method is actually a bit controversial, because the logic it uses assumes the fact that the Sudoku puzzle you are working on has only one unique answer. Net result: any "5" along a red line that's not in a blue line can be removed (all the 5s in the pink cells can be erased).Īpparently, some examples of this technique create a pattern that resembles the actual fish it's named after. We don't know which blue line we just know it's at a blue line. The result is each red line's 5 is going to be where a blue line crosses it. ![]() Why is this important? Well, it isn't - unless the red lines have other 5s in them somewhere! You see, each of the three blue rows is going to have a 5, and since the possible locations are limited, each row will end up having a 5 in one of the red lines. Let me say that a different way: The blue lines only have 5s where the red lines cross. ![]() Here is the same puzzle, but with some markings added for illustration:Īs you can see, the three rows marked by the blue lines all have their possible locations for a 5 confined to the same three columns (marked by the red lines). There are three rows where all the possible 5s appear in the same three columns. The puzzle above has a Swordfish on the number 5. It is not super complex to understand - it's just very hard to spot one.īut, in the interest of being complete, I will cover it. I must confess - this is probably my least favorite technique. Even if you know it's there, it can take some time to find. Just as the X-Wing involves two candidates in two columns or rows, the Swordfish involves three candidates in three columns or rows. ![]()
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