# Tag Info

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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, ...

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Partial solution

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I'd like to add a simple, direct proof:

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

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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 |...

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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 ...

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This seems to fit: The initial step was to replace all 1's (red) with a 2 (black) and all 9's with an 8: Then, whenever a red number was +/- 1 of a black number which was on the same row, column or box, the red number was changed to its other possible value. E.g. if a red 6 was on the same row as a black 5, the red 6 was changed to a black 7 as it couldn't ...

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Final solution Step by step deduction Firstly, note that MASTERING is a full nine-letter word so it takes up a whole row, and EMIGRANT is an eight-letter word so the column is either EMIGRANTS or SEMIGRANT. Also note that ARTEMIS must begin from either the 1st or 3rd place in its row, because otherwise the A will clash with MASTERING; and the remaining ...

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I have been asked by a couple of people to show the creation process for this puzzle, so here we go: Also if people want to see more of these strange, Sudoku mash ups then I'll be more than happy to combine some new types :) Wrap-up: The Making Of This Samurai Pseudoku This is not a solution to the puzzle, but provides notes from its poster. This type of ...

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

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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:

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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 ...

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

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

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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 ...

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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},...

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This puzzle is certainly not Solving the crossword: The clues: Then solving as a 'Wordoku': (Not posted logical path as it is quite straightforward, but can if needed)

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You're

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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 ...

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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 ...

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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 ...

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

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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:

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

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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 ...

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It is not possible. Any solution to this puzzle must also be a solution to the 9x9 Queens puzzle. Luckily, that is a well-known puzzle. It has 352 solutions, but due to symmetry, those 352 solutions can be reduced to 46 solutions. After that, it is just a matter of checking against those 46 solutions. I found a page showing the solutions at: http://stamm-...

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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. ...

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The Needs to be upgraded! Quick explanation of how to solve (lots of pictures for step by step solutions): Solution to the nonogram: Steps: 1: 2: 3: The riddle: Now Solving the new sudoku: Steps: 1: 2: 3: 4: 5: 6: 7: And from there we can fill in the rest as a normal sudoku: Reading off the yellow letters gives The initials are also ...

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