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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 ...


Here is the finished tiling: To get started: Next step: Looking at the left pear: With those chokepoints: For the next step I took a guess: From there, I just looked at the pieces I had left and found something that worked.


5 numbers are certainly enough to make it unsolvable. This is a simple example : You can never put one in the bottom left corner. Maybe someone has an optimization?


Completed grid (tapa clues in red, pata clues in blue): Solution: The bottom right: Continuing in the middle: Coming around left: Let's look in the upper left: Hopefully finishing:


OP here (hi!). I have awarded the green checkmark to @MOehm's answer for being the most complete (the LITS solved state is presented, the hidden connecting wall is identified, and the final one-word answer has been found). I also highly commend the answer by @Sconibulus for verbalising a logical path through the LITS grid deduction process and being first to ...


I thought I'd try my hand at writing a program for Mobius sudoku. I used the Z3 SMT solver (Python wrapper) for this. There isn't much of a "solution path" to describe: most of the constraints translate fairly directly, even the wrapping around of the columns. The main difficulty was The other constraint which required some care was: Here's the ...


First, build a spreadsheet. This has links surrounding it so that I can see where things will be relative to each other. Then


In general, with logic puzzles it's important to mark not only the parts of the solution, but also things you know can't be part of the solution. Here, that means you should mark segments that you aren't allowed to draw, because there would be no way of completing the puzzle if you did. For example, there can't be a connection between F1 and F2, because F1 ...


Using the SAT solver from Google's ORTools:


The topical word is: The LITS solution is: The next step: First level: Second level Third and last level: Remarks:


This puzzle is a reference to the The Nurikabe has multiple solutions, and I'm not sure how it's relevant:


Partial answer, stuck near the last step. LITS solution: Diagram (apologies for messiness): Pulling the words out, we get these lists: These look a little like they might be Connect Walls... and I've maybe got these categories? L I T S


I am thinking of a number X. Find Y such that the square of Y is X. What if I tell you there is only one such Y?


Partial answer for the LITS, I believed I have encountered an error. The big aha moment (putting it early to not waste time): And now, Some more logic: A very nice little step here: And now I think I have reached a contradiction. And this is the problem: For the other genre: EDIT: I would fix this today, but it's getting late where I'm from, so ...


Vanilla? Perhaps. Easy? No. The resolved grid should look like this: The logical break-in I found was the following: This now enables us to shade some more spaces around the other two 7's: Now, we just need to ask ourselves which one of the two remaining spaces to the left of the 2-4 clue needs to be shaded.


EDIT: I realise now that the example given doesn't require uniqueness to solve the puzzle, but I'll leave the example below for those interested. I can give an example of a Sudoku where you can use uniqueness logic to get to a solution. However, uniqueness is not the only way to get to that solution, so this is probably not pertinent to your question. The ...


Completed grid: Logic: Let's look at the bottom row first. Continuing in the bottom row: Hoping this is the breakout: Picking a winner: The road goes ever onward:


I have an answer. I have not proved uniqueness. My start is very similar to Ankit's. Put in all the possible numbers. Start reducing at the red squares. However, what really helped was


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


The original claim that any "hourglass" contains the same pair of digits is true. Proof: Image taken from https://nicksnels.gumroad.com/l/wrusE


Solution How I solved it Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9


Completed grid Step by step solution Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 Step 15

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