No GUESSING Is Necessary In The Sudoku Fog

Рет қаралды 64,821

Күн бұрын

** STREAMING TONIGHT **
Just a reminder, we're streaming more Dungeons & Diagrams tonight at 10pm UK time. You can watch at the following link:
kzfaq.infov-HZKdVvnoQ
** TODAY'S PUZZLE **
We love Fog-Of-War sudokus and today we get to try Oddlyeven's Foggy Nonsense, a lovely example of the form in which we need to use the digits 0-8! Don't forget, the constructor will have designed the puzzle such that guessing is not required or intended so try to solve it by logic alone!
Play the puzzle at the link below:
sudokupad.app/lvxh3flv0i
Rules:
Place the digits 0 to 8 once each in every row, column and 3x3 box. One cell in every row, column and box is a “doubler”. This cell counts as double its value for the rules below. Each of the digits 0 to 8 appears exactly once in a doubler cell. Values on an X sum to 10. Values on a V sum to 5. Digits in a cage may not repeat. Values in a cage sum to the total in the top-left most corner of the cage. The grid is partially covered in fog. Placing correct digits will clear the fog from surrounding cells. Guessing is not necessary.
Jane Street's Bug Bytes puzzle is available here:
www.janestreet.com/bug-byte/
(Simon's solve of this puzzle is on Patreon.)
** NEW SUDOKU HUNT ON PATREON **
We're delighted to share with you a brand new sudoku hunt themed around snake egg puzzles by Glum Hippo. If you've never tried snake egg logic puzzles before, prepare for serious fun - these sudokus are outstanding! Finish by May 20 to enter the competition!
Other treats on Patreon include:
- the Sumgeons & Diagrams sudoku by sunnyjum;
- Simon's latest forays into the world of Islands Of Insight;
- Mark's video looking at the new OneUp puzzle from Rodolfo Kurchan;
- his solve of Region Geometry by Emre Kolotoğlu (3hr 36min long...!);
- and Mark's latest solve of The Times Club Monthly cryptic crossword
/ crackingthecryptic
** GET OUR FOG KICKSTARTER DELUXE & OUR BOOKS **
Check out this link for the kickstarter books and Fog Novella we've created over the years:
coffeebean.games/product-cate...
▶ SUDOKU PAD - Use Our Software For Your Puzzles ◀
You can input classic sudoku puzzles into our software and help support Sven, the programmer responsible for the wonderful user interface we all use to play these puzzles everyday. The app also comes with 12 handmade puzzles from us:
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ALSO on Amazon: Search for “SudokuPad”
▶ Contents Of This Video ◀
0:00 Theme music & puzzle intro
1:35 Our New Fog App SOON
1:56 Dungeons & Diagrams Stream
2:20 Patreon
3:06 John's Tattoo
3:54 Victoria's Fan Art
4:54 Happy Birthdays
6:46 Rules
8:32 Start of Solve: Let's Get Cracking
▶ Contact Us ◀
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Simon Anthony & Mark Goodliffe
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(Please note to use our real names rather than 'Cracking The Cryptic'.)
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Пікірлер: 223

@oddlyeven8775 Ай бұрын

Thank you very much for solving my puzzle! I am blown away by the response to this puzzle considering I made it as a fun exercise using left over ideas from a couple of my other puzzles!

@sambiman Ай бұрын

Based

@gavindeane3670 Ай бұрын

Thank you for creating it. It was a lot of fun. Fog of War and lots of arithmetic (doublers, V and X pairs) - a nice combination of rules, and approachable. I only got bogged down due to my own ability to miss obvious next steps.

@puritan7473 Ай бұрын

What a wonderful puzzle, I absolutely loved the flow of the solve, thank you!!

@longwaytotipperary Ай бұрын

Lovely puzzle!

@r0bbiegill Ай бұрын

Really enjoyed this puzzle! Did it a few days ago and have been hoping it’d be featured here because it was so good.

@GregJonson Ай бұрын

I'd just like to report that within three hours of this video's release, the puzzle's solve count has jumped up by TWO THOUSAND. That's what I like to see!

@WeaselOnaStick Ай бұрын

I'm proud to have solved it before the video's release all by myself 🙃

@gandalf_le_rouge Ай бұрын

@@WeaselOnaStickSo did I thanks to James Sinclair's newsletter!

@TaleraxDeAvon Ай бұрын

25:42 Classic Simon as always. Using 3 different logics to rule out doubled 3,4,5 when there is a 345 looking at it.

@dustpan5356 Ай бұрын

He does something similar later with the V in box 7, not seeing that the doublers were used in Columns 2&3 already.

@charlesgaskell5899 Ай бұрын

33:16 😀

@stangerrits6712 Ай бұрын

@@dustpan5356If only he actually colored all cells that couldn’t be doublers, when he was trying to do so a bit earlier in the solve…

@katiekawaii Ай бұрын

And I hope he never changes 😄

@cptn_n3m012 Ай бұрын

98:10 for me. Usually I just watch Simon works his magic, but I don't know why this time I felt like trying myself ! Took me a lot longer than expected, but the feeling after placing that last digit is fantastic ! Will definitely try again with other puzzles ^^

@steeevealbright Ай бұрын

Congrats!! The more complicated ones start to come into reach as you do more and more puzzles.

@want-diversecontent3887 Ай бұрын

Similar amount of time here, 91:36, I've tried two before but I think this is the one that's going to actually get me into variant sudoku puzzles.

@hanness8536 Ай бұрын

46:38 "i liked this bit here, where we could see that the cage couldn't go anywhere. it reminded me of me" so deep out of nowhere. although we might feel limited from time to time we should not let our thoughts restrict us. Lots of love to everyone here!

@TheClawNinja Ай бұрын

Love the fogs with the doubler rule like this puzzle. Nothing insane like that thing you did yesterday, just a very workable puzzle that's not terribly simple. Perfect!

@Vic-hy2ml Ай бұрын

same, I love a puzzle that takes some time to solve and you really have to think, but it's not waaay too difficult, so you're never really stuck

@Gonzalo_Garcia_ Ай бұрын

Oh, I just solved this one like 30 minutes ago. Great and approachable puzzle, I’d really encourage everyone to give it a go.

@supucr2526 Ай бұрын

That's the first puzzle I tried out myself. I struggle a bit here and there but i got it in 70 Mins and really enjoyed the journey

@longwaytotipperary Ай бұрын

👏🏻👏🏻👏🏻👏🏻👏🏻

@shellmichael9665 Ай бұрын

I liked how in box 9, you ended up with Double 0, 7. I thought for sure you’d call out the James Bond reference.

@nataloves Ай бұрын

Lovely crochet Victoria! I'm thinking of making a quilt myself! Awesome!

@longwaytotipperary Ай бұрын

Yes, it IS lovely!!

@CrankyOtter Ай бұрын

Whenever I see a particularly pleasing sudoku solve I save it as a screenshot in my quilt folder. I only have patience to quilt squares, so sudoku boards are ideal.

@longwaytotipperary Ай бұрын

@@CrankyOtter 😃

@nicocost33 Ай бұрын

46.11 for me. I love fog sudoku's. Compliments for this and really all the setters. Solving this beauties is like eating a wonderful meal. The time spend eating is a fraction of the energy putting into the creation. Well done Oddlyeven.

@chocolateboy300 Ай бұрын

I finished in 41 minutes. This puzzle was incredible. One of my favorites. It's kind of crazy how changing it from the standard Sudoku digits to 0-8 has a completely different feel. I quite like like that. This was an incredible collection of rulesets constructed to perfection. Also, for me to be on par with Simon's time is a great additional feeling. Great Puzzle!

@brianarsuaga5008 Ай бұрын

I really loved this puzzle! I suspect it would have been too hard for me, without the hand-holding of the fog, which is what I love about fog puzzles! I especially liked how you could sort of see in advance that you'd need to use the unique doubler rule in a few places, only to ricochet back and forth to get there.

@SteveHuffMedia 6 күн бұрын

I truly enjoy watching how your mind works. One small request. Please refrain from negative or critical comments about yourself. You really shine in the world of logic and puzzles. Thanks for what you do.

@emilywilliams3237 Ай бұрын

I knew I had to come back to this one, even though I did not have time to watch it the day it was posted. It was a lovely puzzle, and just might be within my ability. I am going to put it on my maybe list (and I will feel free to refer to the video). Thanks, Simon!

@TheUndeadKid Ай бұрын

I loved this puzzle! This is the first Variant Sudoku puzzle that I did before Simon and I got super excited to see him solve it. I remember saying that this puzzle really was nonsense! My time was 251 minutes but at least I'm getting more confident at Variant Sudokus now. Thanks CtC!

@steeevealbright Ай бұрын

This puzzle was great! I solved it in 100 minutes, and loved every minute of it. Why is that arrangement of 3 numbers called a chocolate teapot?

@longwaytotipperary Ай бұрын

A chocolate teapot is useless (as a teapot - as it would melt before boiling water).

@ronjohnson6916 Ай бұрын

Loved it. A puzzle right up my alley since it nearly always left only one way forward and with limited options on that one way.

@jerzeyvermont Ай бұрын

I take that time to have a go at every puzzle…by the time Simon gets cracking I have usually reached a decision to pursue a solve or to sit back and enjoy the logic unfolding. This was the first time I got a full box done in that time. (Sans guessing ofc) Exciting! Thank you for the videos.

@davidrattner9 Ай бұрын

Great solve from you Simon!!! Continue to solve with such joy and enthusiasm. Your passion is just extraordinary!!!

@chris5619 Ай бұрын

One thing that I've noticed more and more in the past (well, probably many) months, is that I will do something very similar to the way I then see Simon or Mark did when I watch their solve. Even if it's not integral to the solving. For instance in this puzzle, when I got to the point of resolving the 13 cage in box 3, I removed the green that I had shaded to double check/ensure the cells in row 3 were already cleared of fog, and the cage had to be within the top right corner of the box. Simon did the same thing. There was something very similar in yesterday's Simon video that we both did as well. This is absolutely a result of me watching both of them solve these puzzles almost daily for over 4 years now. And at the beginning, I wasn't even attempting to solve them. And over time, I was able to do more and more work on them, and now I'm at the point where I can pretty much solve every puzzle on this channel, sometimes quicker than them (not that often though). For whatever reason though, I'm always very happy when I do something like I did today and then see they did the exact same thing.

@longwaytotipperary Ай бұрын

Congratulations on progressing to master solver!😁

@chris5619 Ай бұрын

@longwaytotipperary Haha, I wouldn't say that. But I will say to anyone relatively new or who feels like these are impossible, if you watch enough and just try to solve as much as you can, you will absolutely get better at it!

@longwaytotipperary Ай бұрын

@@chris5619 if you can solve “pretty much every puzzle on this channel “ - I think you deserve the title of Master Solver!!!

@shinsoujuuzou8423 Ай бұрын

32:01 Simon using big brain moves to resolve squares while the simple sudoku option is there will never not amuse me

@shinsoujuuzou8423 Ай бұрын

Oo one more time at 44:34

@janeflett4971 28 күн бұрын

Really enjoyed this puzzle, love fog of war and this made great use of the doublers

@VeritasUnae Ай бұрын

A lovely walk through the fog on this one, great fun for sure. The interplay between the cages, XV constraints and the doublers was a real delight. Thanks for sharing, Simon, and kudos to Oddlyeven for the setting! (I think I took over 40 minutes, but my timer now seems to say less than 40, so it is a mystery…)

@frankjiang1857 Ай бұрын

Finished in 17:34. Pretty straightforward approachable fog of war sudoku. Fun puzzle!

@sascharuler Ай бұрын

I'm not a big sudoku nerd, I usually use these videos to fall asleep- But!! As a huge Kakuro fan/player, I found myself using my Kakuro experience to follow along with the sudoku logic! I'll never be an expert in either of those fields but it is so nice to see some overlap X]

@novemberdag1127 Ай бұрын

I love how at 44:37 you found the naked single in R8C9 because you were convinced there was nothing else so you took the ling way round again instead of using the 6 you just placed in R2C8 to place 6 in box 9. what a wonderful mind you have. I would have a blast conversing with you at parties Simon.

@Daymickey Ай бұрын

Very much enjoyed this puzzle! Did have to reference the video a couple of times but otherwise flowed well. I love fog puzzles

@ayannababii Ай бұрын

What a magnificent puzzle. I kept forgetting zeros existed. It slowed me down 😭

@r0bbiegill Ай бұрын

I did this puzzle the other day when it was published on LMG. I stared at it for like 12 minutes confused because I didn’t read the instructions fully and completely missed the part about doublers. I was soooooo very confused. I’m glad this is getting featured. It was a very fun solve!

@boydegg Ай бұрын

37:01 ... I can't believe I managed to solve this AND beat Simon's time. I'm blown away. It's such a lovely puzzle and very clever the way it unfolds giving just enough information to remove each new section of fog. Love it!!! Amazing setting, OddlyEven.

@chelseac4553 Ай бұрын

Wow! What a fun puzzle! It was totally refreshing having to rethink the XV rules.

@MattYDdraig Ай бұрын

18:38 This was a gorgeous puzzle, particularly the step into box 4 when it looked like there was nothing. Particularly clever use of the doivler subset to provide information across the board too. ❤

@MRafas-ie9zh Ай бұрын

19:39 Simon explaining that we can't have 4x2+2, but missing on the possibility of 3x2+4 (even if its obviously repeats 3 in a column)

@RichSmith77 Ай бұрын

Seems he got his wires slightly crossed when ruling out options. He'd noted that the Y of 2X+Y=10 also had to be even, and then saw that 2 and 6 were already used in the column, leaving 0,4,8 as the options for Y. But instead of ruling out Y=4 from that list, he ruled out X=4, as it would need a repeated 2. As you say, if he'd checked Y=4, as he meant to, he would have quickly seen it needed X=3, repeating 3. Small slip.

@praematura Ай бұрын

Tried this a few days ago and didn't get anywhere, but decided to give it a shot again! My solve felt very sloppy and I kept mis-marking cells, but was able to finish in 30:47 (conflict checker off). Really wonderful puzzle from OddlyEven, many thanks to him!

@JPgreekgaming Ай бұрын

Such a beautiful and smooth solve!

@jadeEpeace 26 күн бұрын

Loved this puzzle :) and thanks for the solve video simon :)

@Orenotter Ай бұрын

You have filled my puzzling need. Forgive me a small bit of greed. I cannot let you rest So I find you solve best At one point five times playback speed.

@longwaytotipperary Ай бұрын

I ❤ foggy puzzles!!!

@davidrattner9 Ай бұрын

They continue to always be magical and wonderful. 💜🩵

@evetheeevee2977 Ай бұрын

44:20! Wonderful puzzle, I really enjoyed it! For some reason I really enjoyed the steps with the 12 cage and also the 11 cage lol

@RealMooMan Ай бұрын

i'd love to try out puzzles like this one it was very interesting to watch and figure out along with the video

@gibbbon Ай бұрын

i first closed the game when i read "doublers" but then i saw the video title and decided to give it another chance, and i'm glad i did, as doublers go, this one is on the simpler side, even i managed to finish it

@harrilewis2617 Ай бұрын

At 10:28 is there a reason why R1C1/R3C2 couldn’t be doubled 1 with an 8?

@geoff544 Ай бұрын

Not in isolation but it would break the other Vs. Double 1 would need a 3 across the V which breaks the other V.

@0Taneb Ай бұрын

I tried following along with Simon on this one, and had some success! There were a few digits I got sooner than Simon, although I'd misunderstood the start completely

@eddieharwood7788 Ай бұрын

As always I loved the fog. Hard but not too difficult.

@warren_r Ай бұрын

33 minutes for me. Took me a little while to clue into the use of "process of elimination" with the doubler digits. Beautifully constructed puzzle, as always from Oddlyeven.

@evgeniaferber Ай бұрын

33:49 for me. i'm not usually good with doublers, but decided to give this one a try - and i'm glad i did!

@piarittersporn Ай бұрын

Brilliant and exciting puzzle.

@GianniBergandi Ай бұрын

32:44, amazing puzzle !

@BRBTheFireball Ай бұрын

I was busy with my wife and children for my birthday last night so I didn't get to watch this video until today, but thank you for the birthday shoutout. And, by the way, I have 15 tattoos, so John has only 14 more to go. ;-) --Russ

@grahamania Ай бұрын

00:29:11 for me. Loved the puzzle! Nice and smooth logic, start to finish. Doublers and fog always seem to work well together. Kind comment.

@dangrene617 Ай бұрын

18:05 solve time. What a joy! Love me a good fog puzzle!

@penningmeestercgkdelft9159 Ай бұрын

47:29 for me. :-) Solved many fog of war puzzles before, but this was my first one with doublers!

@Kirbyfan87827 Ай бұрын

Finished in 36:20. Almost thought I wouldn't be able to work with the doubler rule, but I did it!

@jdyerjdyer Ай бұрын

Not a bad puzzle at all! Just over 40 minutes for me!

@markp7262 Ай бұрын

22:50 finish. Another fun puzzle using math, helping to keep this old brain active. Excellent!

@57thorns Ай бұрын

33 minutes for me with a false start before I realized the doubler constraint. A bunch of wild nines appeared as well, but I think I got most of it logically after all. Can't resist a good fog puzzle.

@tamaspolyak5564 Ай бұрын

When someone else is solving the puzzle, and they don't see at once what I see, just because they didn't follow through the clues is quite maddening. But then it took me over an hour to solve Lightly Buried Treasure, because I stared at the puzzle for over 30 minutes not seeing that only one of the digits on the Dutch whisper was 4 apart. Only one. And that one unraveled the whole puzzle. Over 30 minutes, lol. So yeah. It's much easier to find errors in others, lol.

@coldheat7373 Ай бұрын

This was a very enjoyable puzzle!

@anaayoung9142 Ай бұрын

Amazing! I tried and I did it!! Yey! And did not find that hard too! 😀

@redstonekid2222 Ай бұрын

Awesome puzzle! First 9x9 fog of war clear, in 68:44, and it was very enjoyable to solve!

@josephbentley7780 Ай бұрын

46:38 for me. I didn't see the V in the fog in the bottom left box for a long time. As soon as I saw it, the entire puzzle followed through quickly from my previous deductions with the double 6 and double 8 positions.

@RichSmith77 Ай бұрын

There's a very small slip made at 19:40. You're trying to find which even digit can be the natural digit in the pair summing to 10, when the other digit is a doubler. You know it's 0, 4 or 8, since 2 and 6 already appear in the column. You correctly rule out 0, as needing a doubled 5, unavailable. But then you rule out 4 being a doubled digit (requires a repeated 2) and not 4 being a natural digit. A natural 4 requires a doubled 3, also not available. It's a trivial step to rule out, but you overlooked it because you ruled out doubled 4 rather than a natural 4.

@RichSmith77 Ай бұрын

You even continue with the crossed thinking when you enter the 1-8 pair as you call it "double 8, 1" when entering it, instead of double 1, 8.

@themuffin437 Ай бұрын

27:43, always love solving fog of war puzzles, even when I mess up

@k.c.8658 Ай бұрын

My favorite segments are when Simon has to solve sudoko while fending off insects, as he did at 18:05 with a Grendel-like fly. Anyone can solve sudoku arthropod-free. 😊

@TurquoizeGoldscraper Ай бұрын

26:25 for me - what a fun trip through the fog.

@tawilk Ай бұрын

looking forward to the fog of war app. have all of your apps and getting close to finishing them all. need more!!

@luketurner314 Ай бұрын

At 33:20 no, it can't involve a doubler because both columns already have doublers

@enericm Ай бұрын

I was able to work though quit a bit of this one only needing to get a few hints from watching the video to solve it. That's 2 doublers in a row where I was able to mostly do the puzzle on my own. Although on the previous doubler, I don't think I would have ever spotted the logic needed in 2 places on my own.

@f.b.jeffers0n Ай бұрын

I needed a bit of help, but this is the first Doubler puzzle!

@heres.someart Ай бұрын

I attempted to actually try and solve this puzzle today, got about 5 minutes into it, couldnt figure out how to get a single digit, and then decided this might not be the best puzzle to try and solve for the first time solving a complicated sudoku

@artursruseckis4242 Ай бұрын

Simon: Uses coloring and custom rule to eliminate one possible value and detects a naked single in specific cell Everyone else: With eight 6-es in the puzzle set, where the last 6 goes?

@CoreyCota 4 күн бұрын

Outrageous indeed that we're made to do sudoku in these sudoku puzzles 🙄🙄 16:36

@MMN-pt8il Ай бұрын

Wow, for some reason, I found this one easier than the one Mark has solved today.

@awilliams1701 Ай бұрын

"I'm getting a tattoo" turns into I've count of my tattoos. They are super addictive.

@JSG-YT Ай бұрын

That's a 38m33s solve for me, beautiful puzzle!

@Vic-hy2ml Ай бұрын

I DID IT BY MYSELF!!!!!!! btw, Simon, it'd be nice if the difficulty of each puzzle was noted in the catalogue, sometimes I just want to do an easy and fun puzzle like this one, but i never know how difficult a puzzle is gonna be before trying to solve it... even a notation like easy/ intermediary/hard would be awesome! cheers!

@oak3001 Ай бұрын

I use the length of the video as a hint of the difficulty. For me, anything under 60 minutes for Simon is probably doable, but I know to not even try when it's 2 hours or more!

@Vic-hy2ml Ай бұрын

@@oak3001 same but sometimes it's long but doable, and sometimes it seems long but Simon or Mark talk for 30min abt something else at the puzzle. and sometimes it's short but awfully difficult

@VacantPsalm Ай бұрын

This is one of those puzzles I decide to watch because I can't do all this "know all the ways to add x numbers to get y" stuff in my head. The problem is when I'm watching it, it doesn't look too hard, so I'm mad I didn't try. But I know if I tried it, I would stubbornly bash my head against one idea and end up making it harder than it needs to be. I'll figure this goofy problem out eventually.

@Timlagor Ай бұрын

Woot! Managed to solve this one all by myself ..don't need to watch the video now ;)

@Anne_Mahoney Ай бұрын

But you will, of course -- it's always fun to see how Simon or Mark approaches a puzzle one has already worked through. 😺

@OverkillSD Ай бұрын

Solved in 27:54 (while using a suboptimal setup that adds a few minutes to my solve; I'm currently resting in bed with a broken foot, working on a K400+ keyboard). Lovely logic and some brilliant tricks. An absolute gem of a puzzle! I think my favorite chain of logic was the one focused on the doubler in box 8.

@thesatty Ай бұрын

46:44 for me. That was a great puzzle!

@krtwood Ай бұрын

Take a look at the game Filament as a possible next game to stream. It's top down so Simon friendly and I find it quite challenging.

@srwapo Ай бұрын

34:49, the fog helped me because it didn't clear when I got to Box 9, making me rework the 15 cage in Box 7 (I incorrectly ruled out the 6).

@whelmking6497 Ай бұрын

Way harder than I expected. Such a mind tweak to go 0-8 rather than 1-9. 56:20.

@ericpraline1302 Ай бұрын

Fun, and much less taxing than Mark's, thanks!

@rtheben Ай бұрын

Fogs are my favourites

@hubertnnn Ай бұрын

You made a mistake at the very beginning. The cells that you put 234 between X and V (R1C1 and R3C2) could be a doubled 1 and doubled 2.

@geoff544 Ай бұрын

You cant have 2 doublers in the same box. If you put a double 1 on a V it has to go with a 3 - then what do you do with the other V.

@jurgenbaumann67 Ай бұрын

I had finally a draw between 0-5 r1, 8-5-0 r7 and 5-8 r8 and was looking 2 minutes before I saw 0 had to be the only doubler stood in riddle.

@samgillmusic Ай бұрын

Another enjoyable fog puzzle, I got it out in 37:00

@ouUnIXM1ASRQvM8u Ай бұрын

01:19:51 for me. First time solved a puzzle with dobbles!

@jonathanzissu3827 Ай бұрын

31:57 You mentioned that the 11 cage had to be 3 and double 4 (3+4+4=11), but it COULD have also been 5 and double 3 (5+3+3=11). The assumption was wrong, but if you had made the correct analysis you could at least have seen that the top middle square in the top center section was not a 3 (and therefore must have been an 8). I didn't solve from there, but I'm guessing that was enough information to figure it out.

@matthewbirk6575 Ай бұрын

What’s going on with the nines in the middle of the puzzle on the quilt?

@bobblebardsley Ай бұрын

One of them is a 3, it just looks like it joins at the top.

@57thorns Ай бұрын

One of them is a 3 if you look closely.

@st0rmforce Ай бұрын

Lovely fog of war flow

@mats1365 Ай бұрын

At 15:30, did Simon miss the possibility of the rest of the cage being 0123 with a doubled 1? It’s easy to disprove, as the 13 pair means the cage can’t contain both 1 and 3 anymore, but he never acknowledged that

@GregDorn Ай бұрын

I thought the same thing. double-1 and 8 is ten so those two cells could also be 1s and doublers. Lots of logic flowed from that assumption which didn't seem to be proven at that point.

@fejpjones Ай бұрын

There can't be another doubler in box 2, so the doubled 1 is ruled out even so. And re the box 1 double1+8 logic, that would break the V clues, which require the V cells to be exactly 012345 with no doublers *except* for possibly the 0 (as it doesn't change the sum total from 15).