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Most Sudoku puzzles published have only one solution. If there is more than one solution, it is probably a mistake. That said, puzzles with incomplete clues can have multiple solutions. In the extreme case, a puzzle with no clues has 6,670,903,752,021,072,936,960 solutions according to Wikipedia. I don't know if it's possible to have exactly 3 solutions, ...


The solution is: or, in text form: Explanation (not the fastest way, I realized some improvements while writing it):


You will be forced to backtrack more quickly if you proceed line-by-line, because the sudoku constraints are enforced line by line (and column by column and in each sub-square). If you fill in cells in a random order, you will have to fill in many cells before you ever get a conflict in a line, or in a column, or in a 3-by-3 sub-square. Specifically, if ...


Here are two proper, irreducible sudoku with the same solution as each other and disjoint sets of clues (24 & 25 clues, respectively). 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 ·-------·-------·-------· ·-------·-------·-------· A| · · · | 4 · · | 7 · · | A| 1 2 3 | 4 5 6 | 7 8 9 | B| · · 6 | · 8 · | 1 · · | B| 4 5 6 | 7 8 9 |...


For the sake of completeness, there are actually 3 possible solutions. Using process of elimination and deduction can get you to this point: One solution is given by Sid already: But two more are: and:


Building off of Kevin's answer, I can get it to 33: ###|.#.|.#. ###|...|... ###|...|... ---+---+--- .#.|###|.#. ...|###|... ...|###|... ---+---+--- .#.|.#.|### ...|...|### ...|...|### Keeping his assumption "that a completely empty 3x3 box can always be solved as long as there are four completely full 3x3 boxes in the same major row or column." and we can ...


The completed dish The reasons why The ultimate message Follow the directions My answer


Here's the solution: I will provide the explanations within the next 24 hours because now I have to go to bed.


The next part of this puzzle can be found at: How I got this: So, what to do next:


I have seen two dissenting opinions on this subject (and in my opinion, the first option is right): By definition, a Sudoku has only one solution. Anything else is just a grid of numbers. Sometimes, there are errors in a publication, and a starting grid has multiple solutions, but, then the starting grid was not a Sudoku! From Wikipedia: The number of ...


Final solution Step-by-step explanation In each of the 2x2 boxes with determinant 0, we have four numbers $a,b,c,d$ between 1 and 9 such that $ad=bc,a\neq b\neq d\neq c\neq a$. This leaves surprisingly few possibilities: The only possibilities for the pairs $\{a,d\},\{b,c\}$ (unordered in all ways; these are just two pairs with equal products) are: {1,9},...


I'll just state some sudoku solving strategies in general, so not for the sudoku posted by you in particular. (NOTE: You probably know the first few, but I just state all of them for completeness.) 1. Naked Single Probably the easiest one that everyone knows: When there is only one candidate available, you can simply fill it in. For example: We can only ...


The poem is ...   The completed sudoku puzzle looks like this - hopefully no errors made in the transcription from the original text version Original text version solution - this is what I used to solve it: Uppercase are letters that were supplied; lower-case were added while solving. It should be noted that the sudoku is not fully constrained; I ...


The solution is The crossword was first solved by @NeilW, and @Sconibulus solved the alphametic and the maze (go upvote them!). For the Sudoku: For the Anagram: For the Logic puzzle: Back to the Sudoku: Finally to the Maze:


EDIT : wrote the complete answer. Take a look at the grid submitted by OP. There's also those intriguing blue squares. We can move on. I'm struggling with the 'spoiler' blocks. Here comes my original work (I feel like a fraud ^^) and the hint of OP This made me think of Fiddling with the versions, one was right on it. So to your question "who am i ...


The filled grid looks like this: Several of the clues have only a single possibility considering that we know the number of digits and that all digits have to be unique. The second clue especially gives a little of information. Starting with around half of the clues entered into the grid and solving with the sudoku rules we can slowly decipher the other ...


I believe Spencerkatty's solution is maximal... Any net may be constructed by choosing which of the 81 cells to mask. There are $\sum_{k=0}^{81}{81\choose k}=2^{81}$ ways to construct a net. Rather than attempt to search this vast space we can attempt to partition the space in a way that will allow us to find out where we may need to look in more detail. ...


If I didn't make any mistakes, this should do: Insights into the solving process:


If F1 is a 2, then On the other hand, if F1 is not a 2, then Therefore,


There is a unique solution to the following The solution is Proof of uniqueness


Guessing single values in a depth-first search is sub-optimal. So, here is a reasoning chain based on a breadth-first hypothesis/disproof method (which my stepson reluctantly calls "educated guessing"). Just following the chain including contradictions requires to solve 23 variants of the sudoku, so it's best used with a computer aided solver. However, it ...


I got: The steps I took to get there were:


For a standard $9 \times 9$ sudoku, the minimum is $17$ squares. It had long been known that at least $16$ were required and that $17$ was sufficient. This article closes the gap.


Final solution Detailed explanation Right at the beginning, we can tell that certain sets of cells must all contain the same number. Starting from the extreme bottom right cell, we can find a sequence of equal numbers (say this number is A) by considering each bold-framed area in turn starting from the bottom left and working to the right. This gives us a ...


Finally found some more time and solved the crossword. Some initial thoughts: The solutions to the crossword are: Now Finally the crossword looks like this: To be continued...


Others have already said this, but I'll try to put it in as clear words as possible: When solving Sudoku puzzles, you don't put the numbers where they might be, you only put them where they must certainly be. Deduce, eliminate possibilities, find restrictions on options, but only when you are certain, put the number in. Or even more clearly: You never have ...


The solution is at the bottom, but note: Step 1 Step 2: Step 3: Step 4: Step 5: Step 6: Step 7: Step 8: Step 9: Step 10: Step 11

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