Re: The World's Hardest Sudoku (June 2012)
Alright, so I finally solved this damn thing. Have a look at my solution path if you're interested/stuck/bored. By bored I mean VERY bored.
Warning: contains spoilers.
Step 0: Why this puzzle is really not that hard. (you can skip this bit)
So over the last few years, it turns out that developments have been made to facilitate manual solving of ultra hard puzzles that don't rely on chain based methods. I'm still reading up on three years worth of material so don't take my words 100% for granted, but this'll do. These are called "exotic patterns". The idea behind this is that when people start doing sudokus they look for patterns in the candidate grid that will instantly give eliminations, for instance, when you see a naked pair, you'll think "oh that's going to kill all the other candidates that see the cells in the pair" and eliminate them without thinking. When you run out of patterns you start doing this whole chain business where you assume this number is true and see where it goes from there, which is human intuitive and USUALLY the best way to go about doing these things. The idea behind exotic patterns is to go back to the more "global" ideas of spotting big patterns and abandon the "local" chain-based approach. That's fine if you're a computer, but if you're a carbon-based lifeform it's hard to see big patterns, so we reduce everything to a bunch of patterns that a human player could reasonably find. We haven't found everything yet - this is still cutting edge stuff.
It turns out that at the highest level (SE rating) ~80-85% of puzzles have some big pattern that makes them easier to human players (this % goes down as the rating goes down). The thing is, we have no bloody idea what the hell to do with the ones that don't. Maybe there's some pattern that hasn't yet been found, or maybe they're just hard. Either way, throwing toilet paper at a tree is a more productive use of your time than doing them.
This puzzle does have such a pattern, whereas Arto Inkala's other 7-year-old Escargot, surprisingly, does not. This guy should stick to things he's good at, unlike publishing hard sudokus - that are easier than the ones he published 7 years ago, haha.
Step 1: the "multi-fish" pattern
This puzzle contains a pattern known as a "multi-fish" (I think) or a "big rank-0 logic". The idea is to look for the base/cover sector approach I outlined in my other post and you might like to look over that, or not, if you like to live dangerously. Have a look at the clue grid
See how the numbers 2, 4, 5, 7, 9 all line themselves up in nice neat columns and rows? And the other numbers 1, 3, 6, 8 do the same in the other columns/rows? If you've actually tried your hand at this puzzle you probably have. I'm pretty sure that is, in fact, a coincidence - it turns out that loads of hard puzzles have this property and we can exploit it. I don't know why they do though!
Have a look at the columns where the 2, 4, 5, 7, 9 numbers are, and look in particular at where the other numbers 1, 3, 6, 8 appear as pencilmarks in these columns.
... as expected, the numbers all line up nicely(ish) within these rows! So if we took the numbers 1, 3, 6, 8 in these columns to use as our base sectors, we'd get 4 numbers in each of 4 columns, that's 16 sectors. Let's try to find 16 cover sectors:
voila!
By the principle of base/cover elimination (apparently nobody calls them base or cover sectors anymore except me but I don't care), that means we can kill everything in the cover except for the numbers in the table!
So all of these are lies:
6r1c3 3r1c4 1r1c9 3r1c9 6r1c9 1r2c1 8r2c8 1r2c9 4r3c6 2r4c5 9r4c7 2r5c2 6r6c1 6r6c3 6r6c9 3r7c1 3r7c4 3r8c1 6r8c1 3r8c9 2r9c5 7r9c5 2r9c6
and our candidate grid looks a lot less intimidating!
Ok I admit, I did need a bit of external assistance to find this thing, but it's certainly visible with some patience especially if you know it's there, then the pattern should come naturally. The rest of this solution is my own doing.
Step 2: some easy moves
Step 3: an elimination that gets a few more numbers
Step 4: another chain thingy
Step 5: This puzzle is surprisingly resilient to being broken apart
You're such a liar.
Yep, it's still pretty hard now. If I could have found a faster way to throw it open, I would, but this is putting up a lot of resistance. There are loads of cells with 2 values but no obvious starting point of attack. Eventually I got 2 out of r2c2:
Assume r2c2=2. Then r2c6=8, then r6c5=8, which locks the 2 in block 8 in column 5, which then makes r7c4=9 and r7c6=4.
Then in block 6, r6c6=9, which means r6c7=5, and then r7c7=3.
The 3 and the 4 make r7c2 a 2, which means r2c2 isn't 2, contradiction.
We get r2c2=4 and a box-line of 4 in block 7 and column 1.
Step 6: Fun with almost-locked sets
This step isn't that critical in the path but I liked the feel of it so I left it in while writing up. The idea behind almost-locked-set theory is that an almost-locked set has N+1 candidates in N cells and if you have 2 of these things interacting in various ways they can do stuff.
Here the almost-locked sets are 236 in r78c2 and 23567r9c1389, marked A and B. They are doubly-linked to each other by 3 and 6, in that both of them have 3s and 6s in them, and all the 3s see each other and all the 6s see each other.
They also have a 2 in both of them. Now get this: because of this interaction, we can kill any other common candidate (in this case 2) from any cell that sees one of the almost-locked sets. Work it out yourself if you don't trust me. (Why wouldn't you trust me?)
r6c2, r789c1, r9c34 aren't 2. Then there's a line-box: 2 in row 9 and block 9. So r8c9 isn't 2.
Step 7: This puzzle STILL doesn't die!
It's actually getting annoying now how damn resilient this sudoku is. Sometimes they're like that, you've got to do a slog. I guess Arto Inkala did that on purpose, heh. Well, that's the way things are.
Chain to get rid of 9 from r6c7:
if r6c7=9, then r6c9=5, then r6c3=4, then r9c3=7, then r8c9=7, then the 9 in block 9 is locked to column 7, then r6c7 isn't 9, a contradiction. This chain doesn't backtrack so it's straightforward. It gives you a bunch of numbers.
This thing STILL needs work... ugh.
Step 8: This puzzle is REALLY IRRITATING NOW
Here's an XY-chain, which means that the only thing you care about at each step is that the cell you're going to has 2 numbers in it. Pretty easy to follow.
Start at r9c3 and follow the starred cells round: r9c3, r9c1, r7c2, r7c4, r7c7, r8c7, r8c6. You have that 6 must be true at one end or the other of the chain.
Result: r8c2 and r9c6 aren't 6.
Singles and locked candidates and pairs get you to the ... oh wait.
AAAAGHGHGHRGHGHRGHGHGHGHFDKJGSKLHSDFKH
Step 9: WHY WON'T THIS GODDAMN SUDOKU JUST FUCKING DIE. OH MY GOD. SERIOUSLY.
6-cell XY-chain. Follow the starred cells: r2c1, r6c1, r6c6, r4c5, r1c5, r1c9. 9 must be the solution at either end. r1c3 and r2c9 aren't 9.
FUCKING FINALLY.
Step 10: mash some FFR songs
That's it. Thread over. You can all go home now.
Alright, so I finally solved this damn thing. Have a look at my solution path if you're interested/stuck/bored. By bored I mean VERY bored.
Warning: contains spoilers.
Step 0: Why this puzzle is really not that hard. (you can skip this bit)
So over the last few years, it turns out that developments have been made to facilitate manual solving of ultra hard puzzles that don't rely on chain based methods. I'm still reading up on three years worth of material so don't take my words 100% for granted, but this'll do. These are called "exotic patterns". The idea behind this is that when people start doing sudokus they look for patterns in the candidate grid that will instantly give eliminations, for instance, when you see a naked pair, you'll think "oh that's going to kill all the other candidates that see the cells in the pair" and eliminate them without thinking. When you run out of patterns you start doing this whole chain business where you assume this number is true and see where it goes from there, which is human intuitive and USUALLY the best way to go about doing these things. The idea behind exotic patterns is to go back to the more "global" ideas of spotting big patterns and abandon the "local" chain-based approach. That's fine if you're a computer, but if you're a carbon-based lifeform it's hard to see big patterns, so we reduce everything to a bunch of patterns that a human player could reasonably find. We haven't found everything yet - this is still cutting edge stuff.
It turns out that at the highest level (SE rating) ~80-85% of puzzles have some big pattern that makes them easier to human players (this % goes down as the rating goes down). The thing is, we have no bloody idea what the hell to do with the ones that don't. Maybe there's some pattern that hasn't yet been found, or maybe they're just hard. Either way, throwing toilet paper at a tree is a more productive use of your time than doing them.
This puzzle does have such a pattern, whereas Arto Inkala's other 7-year-old Escargot, surprisingly, does not. This guy should stick to things he's good at, unlike publishing hard sudokus - that are easier than the ones he published 7 years ago, haha.
Step 1: the "multi-fish" pattern
Code:
8 1246 24569 |2347 12357 1234 |13569 4579 1345679 12459 124 3 |6 12578 1248 |1589 45789 14579 1456 7 456 |348 9 1348 |2 458 13456 -------------------+-------------------+------------------- 123469 5 2469 |2389 2368 7 |1689 2489 12469 12369 12368 269 |2389 4 5 |7 289 1269 24679 2468 24679 |1 268 2689 |5689 3 24569 -------------------+-------------------+------------------- 23457 234 1 |23479 237 2349 |359 6 8 23467 2346 8 |5 2367 23469 |39 1 2379 23567 9 2567 |2378 123678 12368 |4 257 2357
See how the numbers 2, 4, 5, 7, 9 all line themselves up in nice neat columns and rows? And the other numbers 1, 3, 6, 8 do the same in the other columns/rows? If you've actually tried your hand at this puzzle you probably have. I'm pretty sure that is, in fact, a coincidence - it turns out that loads of hard puzzles have this property and we can exploit it. I don't know why they do though!
Have a look at the columns where the 2, 4, 5, 7, 9 numbers are, and look in particular at where the other numbers 1, 3, 6, 8 appear as pencilmarks in these columns.
Code:
column 2 5 6 7 -------------------------- row 1 16 13 13 136 row 2 1 18 18 18 row 3 138 row 4 368 168 row 5 1368 row 6 68 68 68 68 row 7 3 3 3 3 row 8 36 36 36 3 row 9 1368 1368
Code:
column 2 5 6 7 cover
--------------------------
row 1 16 13 13 136 < 136 in row (3)
row 2 1 18 18 18 < 18 in row (2)
row 3 138 < this cell (1)
row 4 368 168 < these two cells (2)
row 5 1368 < this cell (1)
row 6 68 68 68 68 < 68 in row (2)
row 7 3 3 3 3 < 3 in row (1)
row 8 36 36 36 3 < 36 in row (2)
row 9 1368 1368 < these two cells (2)
total: 16
By the principle of base/cover elimination (apparently nobody calls them base or cover sectors anymore except me but I don't care), that means we can kill everything in the cover except for the numbers in the table!
So all of these are lies:
6r1c3 3r1c4 1r1c9 3r1c9 6r1c9 1r2c1 8r2c8 1r2c9 4r3c6 2r4c5 9r4c7 2r5c2 6r6c1 6r6c3 6r6c9 3r7c1 3r7c4 3r8c1 6r8c1 3r8c9 2r9c5 7r9c5 2r9c6
and our candidate grid looks a lot less intimidating!
Code:
8 1246 2459 |247 12357 1234 |13569 4579 4579 2459 124 3 |6 12578 1248 |1589 4579 4579 1456 7 456 |348 9 138 |2 458 13456 -------------------+-------------------+------------------- 123469 5 2469 |2389 368 7 |168 2489 12469 12369 1368 269 |2389 4 5 |7 289 1269 2479 2468 2479 |1 268 2689 |5689 3 2459 -------------------+-------------------+------------------- 2457 234 1 |2479 237 2349 |359 6 8 247 2346 8 |5 2367 23469 |39 1 279 23567 9 2567 |2378 1368 1368 |4 257 2357
Step 2: some easy moves
Now we can make progress:
hidden pair 36 in block 3
singles --> r2c7=1, r3c8=8
line-box 5 in row 3 and block 1
naked triple 249 in block 1
single --> r3c4=4
We also get another easy-ish step: a short loop that gets you r4c7:
if r4c7=6, then r6c7=8, then r5c2=8, then r1c2=1, then r1c7=6, then r4c7=/=6, contradiction
So r4c7=8. This chain doesn't backtrack anywhere on itself, so it's pretty simple to follow.
Code:
8 1246 2459 |247 12357 1234 |13569 4579 4579 2459 124 3 |6 12578 1248 |1589 4579 4579 1456 7 456 |348 9 138 |2 458 13456 -------------------+-------------------+------------------- 123469 5 2469 |2389 368 7 |168 2489 12469 12369 1368 269 |2389 4 5 |7 289 1269 2479 2468 2479 |1 268 2689 |5689 3 2459 -------------------+-------------------+------------------- 2457 234 1 |2479 237 2349 |359 6 8 247 2346 8 |5 2367 23469 |39 1 279 23567 9 2567 |2378 1368 1368 |4 257 2357
singles --> r2c7=1, r3c8=8
line-box 5 in row 3 and block 1
naked triple 249 in block 1
single --> r3c4=4
Code:
8 16 249 |27 12357 123 |36 4579 4579 249 24 3 |6 2578 28 |1 4579 4579 156 7 56 |4 9 13 |2 8 36 -------------------+-------------------+------------------- 123469 5 2469 |2389 368 7 |68 249 12469 12369 1368 269 |2389 4 5 |7 29 1269 2479 2468 2479 |1 268 2689 |5689 3 2459 -------------------+-------------------+------------------- 2457 234 1 |279 237 2349 |359 6 8 247 2346 8 |5 2367 23469 |39 1 279 23567 9 2567 |2378 1368 1368 |4 257 2357
if r4c7=6, then r6c7=8, then r5c2=8, then r1c2=1, then r1c7=6, then r4c7=/=6, contradiction
So r4c7=8. This chain doesn't backtrack anywhere on itself, so it's pretty simple to follow.
Code:
8 16 249 |27 12357 123 |36 4579 4579 249 24 3 |6 2578 28 |1 4579 4579 156 7 56 |4 9 13 |2 8 36 -------------------+-------------------+------------------- 123469 5 2469 |239 36 7 |8 249 12469 12369 1368 269 |2389 4 5 |7 29 1269 2479 2468 2479 |1 268 2689 |569 3 2459 -------------------+-------------------+------------------- 2457 234 1 |279 237 2349 |359 6 8 247 2346 8 |5 2367 23469 |39 1 279 23567 9 2567 |2378 1368 1368 |4 257 2357
Step 3: an elimination that gets a few more numbers
The multi-fish is actually the least useful one of the known "exotic patterns" in that it tells you nothing about what to do after you've found it. You're left on your own. This puzzle is still hard, but attackable with chain-based "local" approaches without too much hassle.
It's not hard to resolve the 36 pair in block 3, like this
Assume r3c9=6 and r1c7=3.
Then in column 7, r6c7=6 and r7c7=5.
In block 1, r3c3=5, r3c1=1 and r1c2=6.
The two 5s mean that 5 in block 7 must be in r9c1, and then the 6 must be in r9c3.
So in row 5, r5c1=6, which gives you a 38 pair in r5c24, but then you can't put a 1 in block 4...
... contradiction. So r1c7=6 and r3c9=3. We get to put a few more numbers in! We have r1c2=1, r9c5=1, r3c6=1, and a hidden pair of 16 in block 6. Not that hard after all :P
Code:
8 16 249 |27 12357 123 |36 4579 4579 249 24 3 |6 2578 28 |1 4579 4579 156 7 56 |4 9 13 |2 8 36 -------------------+-------------------+------------------- 123469 5 2469 |239 36 7 |8 249 12469 12369 1368 269 |2389 4 5 |7 29 1269 2479 2468 2479 |1 268 2689 |569 3 2459 -------------------+-------------------+------------------- 2457 234 1 |279 237 2349 |359 6 8 247 2346 8 |5 2367 23469 |39 1 279 23567 9 2567 |2378 1368 1368 |4 257 2357
Assume r3c9=6 and r1c7=3.
Then in column 7, r6c7=6 and r7c7=5.
In block 1, r3c3=5, r3c1=1 and r1c2=6.
The two 5s mean that 5 in block 7 must be in r9c1, and then the 6 must be in r9c3.
So in row 5, r5c1=6, which gives you a 38 pair in r5c24, but then you can't put a 1 in block 4...
... contradiction. So r1c7=6 and r3c9=3. We get to put a few more numbers in! We have r1c2=1, r9c5=1, r3c6=1, and a hidden pair of 16 in block 6. Not that hard after all :P
Code:
8 1 249 |27 2357 23 |6 4579 4579 249 24 3 |6 2578 28 |1 4579 4579 56 7 56 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 123469 5 2469 |239 36 7 |8 249 16 12369 1368 269 |2389 4 5 |7 29 16 2479 2468 2479 |1 268 2689 |59 3 2459 -------------------+-------------------+------------------- 2457 234 1 |279 237 2349 |359 6 8 247 2346 8 |5 2367 23469 |39 1 279 23567 9 2567 |2378 1 368 |4 257 257
Step 4: another chain thingy
In fact this puzzle is still pretty hard and I've got nothing to do apart from throw chain-based things at it, so I might as well.
Suppose r2c6=8.
Then r6c5=8 (in column 5), so r9c4=8 (in column 4). That locks the 3 in column 4 of block 5, so r4c5=6.
Then r6c2=6 (in row 6), so r8c6=6 (in row 8). That leaves 3 as the only value for r9c6, so r1c6=2.
That's not a contradiction, but it tells us that r1c6 or r2c6 must be 2. So we can kill 2 from elsewhere in the column and block.
Also if you put the last cell (r1c6) in the chain at the beginning and do the same thing, you get that r1c6 or r9c6 must be 3, so kill 3 from elsewhere in column 6.
Another number done: r1c4=7.
Code:
8 1 249 |27 2357 23 |6 4579 4579 249 24 3 |6 2578 28 |1 4579 4579 56 7 56 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 123469 5 2469 |239 36 7 |8 249 16 12369 1368 269 |2389 4 5 |7 29 16 2479 2468 2479 |1 268 2689 |59 3 2459 -------------------+-------------------+------------------- 2457 234 1 |279 237 2349 |359 6 8 247 2346 8 |5 2367 23469 |39 1 279 23567 9 2567 |2378 1 368 |4 257 257
Then r6c5=8 (in column 5), so r9c4=8 (in column 4). That locks the 3 in column 4 of block 5, so r4c5=6.
Then r6c2=6 (in row 6), so r8c6=6 (in row 8). That leaves 3 as the only value for r9c6, so r1c6=2.
That's not a contradiction, but it tells us that r1c6 or r2c6 must be 2. So we can kill 2 from elsewhere in the column and block.
Also if you put the last cell (r1c6) in the chain at the beginning and do the same thing, you get that r1c6 or r9c6 must be 3, so kill 3 from elsewhere in column 6.
Another number done: r1c4=7.
Code:
8 1 249 |7 35 23 |6 459 459 249 24 3 |6 58 28 |1 4579 4579 56 7 56 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 123469 5 2469 |239 36 7 |8 249 16 12369 1368 269 |2389 4 5 |7 29 16 2479 2468 2479 |1 268 689 |59 3 2459 -------------------+-------------------+------------------- 2457 234 1 |29 237 49 |359 6 8 247 2346 8 |5 2367 469 |39 1 279 23567 9 2567 |238 1 368 |4 257 257
Step 5: This puzzle is surprisingly resilient to being broken apart
Code:
8 1 249 |7 35 23 |6 459 459 249 24 3 |6 58 28 |1 4579 4579 56 7 56 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 123469 5 2469 |239 36 7 |8 249 16 12369 1368 269 |2389 4 5 |7 29 16 2479 2468 2479 |1 268 689 |59 3 2459 -------------------+-------------------+------------------- 2457 234 1 |29 237 49 |359 6 8 247 2346 8 |5 2367 469 |39 1 279 23567 9 2567 |238 1 368 |4 257 257
Yep, it's still pretty hard now. If I could have found a faster way to throw it open, I would, but this is putting up a lot of resistance. There are loads of cells with 2 values but no obvious starting point of attack. Eventually I got 2 out of r2c2:
Assume r2c2=2. Then r2c6=8, then r6c5=8, which locks the 2 in block 8 in column 5, which then makes r7c4=9 and r7c6=4.
Then in block 6, r6c6=9, which means r6c7=5, and then r7c7=3.
The 3 and the 4 make r7c2 a 2, which means r2c2 isn't 2, contradiction.
We get r2c2=4 and a box-line of 4 in block 7 and column 1.
Code:
8 1 29 |7 35 23 |6 459 459 29 4 3 |6 58 28 |1 579 579 56 7 56 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 12369 5 2469 |239 36 7 |8 249 16 12369 1368 269 |2389 4 5 |7 29 16 279 268 2479 |1 268 689 |59 3 2459 -------------------+-------------------+------------------- 2457 23 1 |29 237 49 |359 6 8 247 236 8 |5 2367 469 |39 1 279 23567 9 2567 |238 1 368 |4 257 257
Step 6: Fun with almost-locked sets
Code:
8 1 29 |7 35 23 |6 459 459 29 4 3 |6 58 28 |1 579 579 56 7 56 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 12369 5 2469 |239 36 7 |8 249 16 12369 1368 269 |2389 4 5 |7 29 16 279 268 2479 |1 268 689 |59 3 2459 -------------------+-------------------+------------------- 2457 23A 1 |29 237 49 |359 6 8 247 236A 8 |5 2367 469 |39 1 279 23567B 9 2567B |238 1 368 |4 257B 257B
Here the almost-locked sets are 236 in r78c2 and 23567r9c1389, marked A and B. They are doubly-linked to each other by 3 and 6, in that both of them have 3s and 6s in them, and all the 3s see each other and all the 6s see each other.
They also have a 2 in both of them. Now get this: because of this interaction, we can kill any other common candidate (in this case 2) from any cell that sees one of the almost-locked sets. Work it out yourself if you don't trust me. (Why wouldn't you trust me?)
r6c2, r789c1, r9c34 aren't 2. Then there's a line-box: 2 in row 9 and block 9. So r8c9 isn't 2.
Code:
8 1 29 |7 35 23 |6 459 459 29 4 3 |6 58 28 |1 579 579 56 7 56 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 12369 5 2469 |239 36 7 |8 249 16 12369 1368 269 |2389 4 5 |7 29 16 279 68 2479 |1 268 689 |59 3 2459 -------------------+-------------------+------------------- 457 23 1 |29 237 49 |359 6 8 47 236 8 |5 2367 469 |39 1 79 3567 9 567 |38 1 368 |4 257 257
Step 7: This puzzle STILL doesn't die!
Code:
8 1 29 |7 35 23 |6 459 459 29 4 3 |6 58 28 |1 579 579 56 7 56 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 12369 5 2469 |239 36 7 |8 249 16 12369 1368 269 |2389 4 5 |7 29 16 279 68 2479 |1 268 689 |59 3 2459 -------------------+-------------------+------------------- 457 23 1 |29 237 49 |359 6 8 47 236 8 |5 2367 469 |39 1 79 3567 9 567 |38 1 368 |4 257 257
It's actually getting annoying now how damn resilient this sudoku is. Sometimes they're like that, you've got to do a slog. I guess Arto Inkala did that on purpose, heh. Well, that's the way things are.
Chain to get rid of 9 from r6c7:
if r6c7=9, then r6c9=5, then r6c3=4, then r9c3=7, then r8c9=7, then the 9 in block 9 is locked to column 7, then r6c7 isn't 9, a contradiction. This chain doesn't backtrack so it's straightforward. It gives you a bunch of numbers.
Code:
8 1 29 |7 35 23 |6 459 459 29 4 3 |6 58 28 |1 579 579 6 7 5 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 1239 5 2469 |239 36 7 |8 249 16 1239 1368 269 |2389 4 5 |7 29 16 279 68 2479 |1 268 689 |5 3 249 -------------------+-------------------+------------------- 5 23 1 |29 7 4 |39 6 8 4 236 8 |5 236 69 |39 1 7 37 9 67 |38 1 368 |4 25 25
Step 8: This puzzle is REALLY IRRITATING NOW
Code:
8 1 29 |7 35 23 |6 459 459 29 4 3 |6 58 28 |1 579 579 6 7 5 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 1239 5 2469 |239 36 7 |8 249 16 1239 1368 269 |2389 4 5 |7 29 16 279 68 2479 |1 268 689 |5 3 249 -------------------+-------------------+------------------- 5 23* 1 |29* 7 4 |39* 6 8 4 236 8 |5 236 69* |39* 1 7 37* 9 67* |38 1 368 |4 25 25
Start at r9c3 and follow the starred cells round: r9c3, r9c1, r7c2, r7c4, r7c7, r8c7, r8c6. You have that 6 must be true at one end or the other of the chain.
Result: r8c2 and r9c6 aren't 6.
Singles and locked candidates and pairs get you to the ... oh wait.
Code:
8 1 29 |7 35 23 |6 4 59 29 4 3 |6 58 28 |1 7 59 6 7 5 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 13 5 4 |29 36 7 |8 29 16 13 68 29 |38 4 5 |7 29 16 29 68 7 |1 268 69 |5 3 4 -------------------+-------------------+------------------- 5 23 1 |29 7 4 |39 6 8 4 23 8 |5 26 69 |39 1 7 7 9 6 |38 1 38 |4 5 2
Step 9: WHY WON'T THIS GODDAMN SUDOKU JUST FUCKING DIE. OH MY GOD. SERIOUSLY.
Code:
8 1 29 |7 35* 23 |6 4 59* 29* 4 3 |6 58 28 |1 7 59 6 7 5 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 13 5 4 |29 36* 7 |8 29 16 13 68 29 |38 4 5 |7 29 16 29* 68 7 |1 268 69* |5 3 4 -------------------+-------------------+------------------- 5 23 1 |29 7 4 |39 6 8 4 23 8 |5 26 69 |39 1 7 7 9 6 |38 1 38 |4 5 2
Code:
8 1 2 |7 5 3 |6 4 9 9 4 3 |6 8 2 |1 7 5 6 7 5 |4 9 1 |2 8 3 -------------------+-------------------+------------------- 1 5 4 |2 3 7 |8 9 6 3 6 9 |8 4 5 |7 2 1 2 8 7 |1 6 9 |5 3 4 -------------------+-------------------+------------------- 5 2 1 |9 7 4 |3 6 8 4 3 8 |5 2 6 |9 1 7 7 9 6 |3 1 8 |4 5 2
Step 10: mash some FFR songs
200th mashed FC get!
That's it. Thread over. You can all go home now.
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