In which I solve an EXTREME SUDOKU for Twitter

I'm Scott Strosahl, and today I'm solving a sudoku that was requested by Kia7 on twitter.

[kupler]

I haven’t played much sudoku, I know how it works and thought it was pretty straightforward until he started speaking a foreign language going at light speed

[elkilik]

That 1 and 5 pair would kill me if i tried this

[bencejoful]

Clever puzzle and nice solving, very enjoyable to see the logic presented so clearly, and at about 10x faster than I would get it.

[kurzackd]

anyone else find it weird that Scott's thought is much quicker with a harder puzzle like Sudoku than it is with easier puzzles like Wordle/variants ?

[lioneddy]

I have recently started playing sudoku, the way you deduced 1, 5 pair is simply awesome, had to watch multiple times just to understand, brilliant.

[wilfredocasinojr.]

After watching the video, I average 11 minutes in extreme now. Thank you so much! Nice methods and app/website.

[paulakeay]

I used the slot machine technique on the 1s and 5s which essentially worked the same in figuring out box 5. Good puzzle and very interesting to see your approach, thanks

[vanderwilhelm]

This video taught me so many strategies so fast, thanks!

[ryanager]

16:29. I noticed 1 and 5 had the classic markers for a swordfish (3 digits in different boxes that share no columns or rows) while not a swordfish, realising there was definitely something funky going on there, with a little logical inference got me going pretty quick.

[JikeWimblik]

P Vs NP paper.


Imagine you have a giant Sudoku puzzle, but instead of numbers, it uses weird symbols you don't understand. Luckily, you have a special magnifying glass.

This magnifying glass is amazing! If you point it at a symbol, it can tell you if that symbol is definitely wrong based on the symbols you've already placed. It doesn't tell you the right answer, just if that one is wrong.

Now, here's the trick:

 * Symbol Search: You start by looking at every single spot on the puzzle and trying out every possible symbol with your magnifying glass.

 * "Wrong!" Because there's only one solution to the puzzle, your magnifying glass will always find at least one wrong symbol for each spot.

 * Cross It Off:  You cross off that wrong symbol.  It can't be there!

 * Repeat: You keep doing this, checking every spot and every symbol over and over. Each time, you find at least one more wrong symbol and cross it off.

Why does this work quickly?

 * Limited Space: Even though the puzzle is huge, there are only so many spots and so many symbols.

 * Steady Progress: Every time you use the magnifying glass, you eliminate at least one wrong symbol, so you're always making progress.

 * No Wasted Time: You never waste time trying symbols that you've already crossed off.

Think of it like a sculptor chipping away at a block of stone. Each time they chisel, they remove a bit that doesn't belong, slowly revealing the statue hidden inside. Your magnifying glass is like the chisel, removing wrong symbols and revealing the correct solution.

The key is that you're not randomly guessing. You're systematically eliminating wrong answers, and because you always find at least one wrong answer each time, you're guaranteed to find the solution in a reasonable amount of time.

That's why this method works in "polynomial time" – it's a fancy way of saying that the time it takes to solve the puzzle doesn't explode out of control even when the puzzle gets bigger. It's like a steady walk to the finish line, not a frantic scramble!

Theorem: The proposed Sudoku solving algorithm, which utilizes a 45-grid encoding and a 2-SAT solver to iteratively identify and eliminate invalid '1' placements, has a polynomial-time complexity.
Proof:
* Sudoku Encoding:
* The Sudoku puzzle is encoded using 45 grids, where each grid corresponds to a specific number (1-9) and a specific position within a 3x3 subgrid.
* Each grid contains '1's representing the presence of that number in the corresponding cells and '2's representing its absence.
* Each grid must have exactly two '1's, ensuring the Sudoku constraints are satisfied.
* Algorithm Description:
a) Initialization: All possible '1' placements across all 45 grids are considered.
b) Iteration:
i. 2-SAT Solver: For each grid, a 2-SAT instance is constructed based on the current '1' placements and the Sudoku constraints (row, column, and subgrid). The 2-SAT solver is used to identify at least one invalid '1' placement within that grid.
ii. Elimination: The identified invalid '1' placement is marked, permanently eliminating that possibility.
iii. Constraint Propagation: The information from the invalid placement is propagated to other grids, potentially identifying more invalid placements.
c) Termination: The algorithm terminates when a valid solution is found, which occurs when each grid contains exactly two '1's that satisfy all Sudoku constraints.
* Complexity Analysis:
* Constant Grid Size: Each grid has a constant size (9 cells).
* Guaranteed Invalid Placement: In each iteration, at least one invalid '1' placement is guaranteed to be found in one of the grids (as long as the puzzle is solvable).
* Limited Iterations: The total number of iterations is limited by the total number of possible '1' placements across all grids (45 grids * 9 cells/grid = 405).
* Polynomial Time per Iteration: Each iteration involves:
* Constructing a 2-SAT instance, which takes polynomial time.
* Running the 2-SAT solver, which also takes polynomial time.
* Marking the invalid placement and propagating constraints, which takes constant time.
* Overall Complexity:
* Since the number of iterations is limited by a constant (405), and each iteration takes polynomial time, the overall complexity of the algorithm is polynomial.
Conclusion:
The proposed Sudoku solving algorithm, which utilizes a 45-grid encoding and a 2-SAT solver to iteratively identify and eliminate invalid placements, has been proven to have a polynomial-time complexity. This result demonstrates that Sudoku, when encoded and solved using this method, can be solved efficiently.
Further Considerations:
* Optimizations: The algorithm can be further optimized by using heuristics to prioritize certain '1' placements or by employing more sophisticated constraint propagation techniques.
* Generalization: While this proof focuses on Sudoku, the underlying principle of encoding a problem and using a constraint solver to iteratively eliminate invalid possibilities might be applicable to other NP-complete problems. This warrants further investigation and could have implications for the P vs. NP question.

[jesus_saves_]

8:59 I was like, "sir there can't be 2 there so it's 7 sir look sir " lol 😂

[therocknrollmillennial]

Just over the video length (14:59) for me! My hope faded quickly, I didn't spot anything that I probably should've to get me to a quicker time, I sort of just did it in my head like I do with classics, and I got stumped for about 45 seconds trying to disambiguate a string that I mistakenly added a number to that shouldn't have been there! Whoops. This was a cool puzzle and thank you, Scott, for the reminder that I need to work on my classic sudoku technique! :)

[windchwang]

Solved in 14:01. I marked all the cells that could be a 5, by trying all three possibilities in block 3, we can know in all three scenario, R3C5 is not a 5 => pointing pair in block 2, R6C4 also not a 5. For 1, also marked in color, then we can see that if R2C5 is 1, then no place to put a 1 in block 5.=>R1C4=1 R6C4=7 R3C4=5, then the puzzle will fall apart.
Many thanks for introducing this puzzle to us😊

[JesterCakes]

I was stuck at that same exact part for at least 3 day. I looked at it with all candidates, no candidates, everything. I eventually started messing with the 5 candidates in box 7 and discovered the 5 must go in cell 2F and that pretty much broke the puzzle. This has to be the hardest sudoku ive ever tried.

[carlosmujun]

What app are you using for these puzzles, these pencil marks and colors look great

[kav-t]

Love your videos! Always helps me with different strategies I can use for wordles :D Love from India..

[mifthaakbie]

I love extreem sudoku. Thats hurt my brain sometimes but make me addict 😂 good for calming down my stress time.

[nhutang]

18:52 for me, I struggled with the phistomephel ring for 10 mins straight to find where the 1s go lol.

[stegra]

Took me 10 minutes longer but I did it notation free. I found that once the 68 and 9 were identified in box 8, either position for 1 in row 7 put 1 in r1c4. I won't say it was easy after that but it certainly pushed things along a bit.

[sudokuandme]

So glad I found your channel. :) I just started playing again - after not playing for many years. I decided I wanted to avoid doing dishes today.