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. Please visit my channel and check out my other uploads such as 'How to solve a Sudoku puzzle - A. Either way would work, making this puzzle, by most current definitions, invalid. RFC963 5.7K subscribers Subscribe 1.9M views 6 years ago Master these strategies and be an expert. But, you could also put an 7 in the upper left and solve it as well. Once you’ve mastered some of the basic Sudoku techniques, if you’re looking for a more advanced. Solving Sudoku puzzles is a fun mental challenge because this seemingly simple game of nine numbers and 81 spaces is actually filled with nearly infinite complexity. 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. Intermediate Sudoku Solving Techniques Part 1: Looking for Number Pairs. 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. I find this mistake (saying the above A, B should be "locked pairs") in the book "Extreme Sudoku for Dummies" by Andrew Heron & Andrew Stuart, so I check here, I hope this helps the discussion to go clear.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. As a result, (B5, E2) could be (C, non-C), (non-C), or (C, C), and in all scenarios, C should be eliminated from cell E5. Similarly, the two A's in cells B2 & E2 are not a "locked pair" either, there could be other A's in column 2. Note that: the two B's in cells B2 & B5 are not a "locked pair", in other words, there could be other B's in row B.
The statement "So whatever happens, C is certain in one of those two cells marked C.", which implies C in one of the two cells, actually C can also be in both cells. The definition of "see" is "two cells within the same element (row, column, box)" (the two cells see each other) 1 to explain this.Ĭell B2 with AB (bi-value), the pivot, which connects (sees) B5 and E2Ĭell E5, the target cell to eliminate C, if any, which "sees" both B5 and E2 There's a small mistake about Y-wing in the logic of proof:
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