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This was a very tricky puzzle, but in the end I believe the solved grid should look like this: In the step-by-step diagrams that follow I have used three different colours in the small pencil marks: Red in the bottom-right corner indicates an impossible value; Green in the top-right corner indicates the only possible values; Grey in the top-right corner ...

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This is a very nice puzzle made by: This is the solve process: The next step is to:

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First step (some simple logical deduction): Now, if we focus on this highlighted 2x3 grid: That leads to: Let's clean this up: Now, using some more logic, we can place: Let's clean up again: From the information given by the rules we can conclude that: We now replace the letters with the corresponding numbers and get the full grid:

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7x7 solution 8x8 solution

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Can we remove the magic? This is the path I took to make a magic square into the grid: First, let's take the magic square given: We need to make it to: Notice So with that, After that, That helps out a ton, as the rest is pretty trivial: Then, Lastly, Well, say goodbye to the magic in the 3 by 3 magic square, and say hello to a normal 3 by 3 square!

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Here's a partial answer explaining (in detail) what I believe to be the first few steps of the puzzle's solution. However, beyond that point I am as yet unsure how to proceed... First off, consider the schematic in 3 and the image in 5 together. We can combine these... It then makes sense to consider clues 1 and 2 together with what we have found. Solving ...

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The answer is The first step was The next step was Moving along, Moving up And finally Nice puzzle! If there is an easier method, I'd love to hear it.

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In the puzzle you generated, there is

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First we notice that: Then we realize that In response, I anagram the solution:

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solving yin-yang:

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Partial answer - Curve Data and Tapa solved, stuck on Yin-Yang Curve Data Note that Now look at the section Yin-Yang (unsolved) Some important lemmas for Yin-Yang that it is good to know: So, let's think about this puzzle in a different way. And now we can start getting somewhere! ...and this is where I'm stuck. Tapa To start,

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Here's another step forward

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The unique solutions to the 3 puzzles have all been found by @Deusovi (Curve Data & Tapa) and @Retudin (Yin-Yang) - here's how to extract the final message... (See their answers for explanations of the puzzles' individual solutions...) Overall then, the answer to "What should I do to avoid this from happening again?" is:

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(Thanks to Stiv and M Oehm in chat and the partial answer, I just came in the end) First-Trichain Second-Slitherlink Interpreting Don't let that trick you, though! Last Steps Using this revelation to our advantage, Finally, Final thoughts

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There are many websites with online sudoku solvers that show you which technique can be used next. For example this one. It came up with a Y-wing configuration here:

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Question one can be solved with Question two can be solved with Getting Started First, let's assign a letter to each transformable sub-section of the grid; in this case I'll simply use $L$ and $R$ to represent the left and right sides respectively. Next, we begin by analyzing the letters available for plausible solutions. These are: Identified by @Morris' ...

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The maximum is 1 2 2 3 3 . 4 4 5 5 1 1 2 3 6 6 . 4 5 7 8 8 . 9 6 10 10 . 7 7 8 11 12 9 9 10 13 14 15 15 11 11 12 12 . 13 13 14 14 15 16 16 17 17 18 19 20 20 21 21 22 16 17 18 18 19 19 20 21 23 22 22 . 24 24 25 25 . 23 23 26 26 27 28 24 25 29 30 31 31 26 27 27 28 28 29 29 30 30 31 I obtained this solution via ...

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Partial answer (it feels like I have understood almost everything here that there is to understand, except that apparently I'm supposed to extract a word from the answer and I don't see how to do that): This puzzle is really about In this puzzle we'll We find So Some other relevant features of the puzzle: However,

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Converting a Disconnect Four puzzle to a SAT instance is very easy. Based on this

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Like so? The "1" region is a given, and the white splotch at the bottom left consists entirely of squares in numbered regions. There are only so many ways (two, to be exact) to split that splotch, and one of them immediately leads to problems (r5c1 can only connect to white areas that won't be able to house the required white group). The ...

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I tried to solve the puzzle from the newspaper without using the hints, only the numbers and the village positions. It allows multiple solutions. One ambiguity is in the top left, the other is in the middle at the right edge. You need to use 2 hints to solve the puzzle. The two hints at the villages are not needed. I could solve it up to the ambiguities ...

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[I previously deleted this answer, as the method was flawed, so the conclusion was not sound. I believe the bugs in my program are now fixed] Following the removal of the tag no-computers from this puzzle, this answer initially treats it as a computer-puzzle. In summary (TL;DR), my current answer to the question "Can you reactivate this 4x4 magic square?...

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My apologies for not knowing the correct terms, but my first thought is that

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First one is Second one looks like but I'm not sure about that...

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I came up with the same answer as @Dr Xorile: This one was actually pretty easy to do by hand in a spreadsheet. However it took enough steps that I couldn't undo all the way back to the beginning, so the first few steps are just going to be what I remember doing. I'll try to recreate the first part later when I have some time: As soon as that was no longer ...

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Per OP's request, here is a full solution with logical steps (except the very end, because it's too trivial to bother writing out). "Steps" uppercase-"S" are broken semi-arbitrarily at when all of a letter had been placed. Pictures are clickable to show a less-compressed version. I use the standard coordinate system. B/R/C indicators are ...

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To kickstart, But as we are given 7 empty squares, Which gives a total of

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I have solved all but #9 which currently eludes me... Grid 1: NB For tidiness and ease of explanation, for all subsequent explanatory diagrams I have merely circled the starting initials of the words in the hidden set. Readers should at least now be able to spot the hidden words by inspecting the starting letters of the word lists given below, without the ...

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Overview To be completely honest, solving this puzzle was mostly trial and error for me. I initially focused on the top left corner and throughout the entirety of the solution path I focused primarily on testing how the diagonal relationships impacted the surrounding areas. The Top Row I spent a fair amount of time here, initially focused on the top left ...

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