Investigating Sudoku's Primal Roots
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- čas přidán 15. 05. 2024
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Normal sudoku rules apply. Digits separated by a white dot are consecutive. Digits separated by a black dot are in a 1:2 ratio. Prime digits (2,3,5,7) must NOT be orthogonally adjacent to each other. Square roots with single digit perfect squares MUST be orthogonally adjacent to their square. (all 2’s must be adjacent to a 4, and all 3’s must be adjacent to a 9).
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▶ Contents ◀
0:00 Theme Music & News around the channel
1:12 Rules of today’s puzzle
3:00 Start Of Solve - Let's Get Cracking! - Zábava
If anyone is thrown by all the mathematical stuff, don't worry. You don't have to be a number theorist to solve this -- just pay attention to which digits can or must be next to each other.
I almost threw in the towel when I found a 9 that didn't have an adjacent 3.
I finished in 97 minutes. I should really pay attention to the wording of rules as I wrongly assumed that 4s and 9s also had to be buddies with 2s and 3s everywhere in the grid. Re-reading the rules clearly shows this only applies to 2s and 3s. I would have done this an hour faster if not for my silly mistakes. Otherwise, Great Puzzle!
I made the same mistake and couldn't figure out why it didn't work
Same thing, re started 3 times because i get a lonely 9 on box 7, took me 2 hours, mostly because of that ):
Not only is there a 3 in the corner in the final solution, but there's also a 2, a 5, and a 7 - a complete set of prime digits!
By the way, the almost chessboard colouring could have been done from the moment you placed your first prime. It is absolutely forced by the rules. Then there are only the few boxes with 5 possible prime locations that needed to be deduced, but it simplified the solve A LOT!
Yes, it's easy to see that the 3 in box seven must go on the diagonal. After that your observation leads to a speedy and elegant solve.
My start was so slow that I decided to watch you instead. But your explanation about column 8 make me realize what I missed in this puzzle. I tried again and did it! Yey! Happy happy! Thank you! 🎉
Hey Mark, thanks so much for doing the live solve of my first puzzle! To be honest, the 2-4 and 3-9 pairings were maybe more of a construction constraint than a helpful/required component of the solve, considering that one can get all the 2-4s without using the rule. I left the rule as maybe more of a helpful tip even though other sudoku logic seems to be able to be used to bypass it. The final disambiguation required it as well so something needed to be there. Anyway, it was great watching the solve! Thanks again.
Great puzzle Matt!
53:26 for me, once I sat down, focused, and finally made sure to remember how the last rule works. As the gorilla from my childhood would say, "Well that's just prime!"
I will always find it interesting that the kropki dot rule typically has "not all possible dots are given" included. You could say that for any rule. "Not all possible arrows are given" in an arrow puzzle where somewhere there is a string of 257 with no arrow. Not all possible renbans are given in probably 90% of puzzles. I don't know why, but this always interests me. I think I've even heard Mark and/or Simon think aloud during a rule-reading that they've discussed whether it was really necessary. I do seem to remember a recent puzzle where it was given as more of a negative (positive?) constraint, which I thought was a great application. Anyway, just musing.
Probably because there are many puzzles where all dots are given, so it works as a negative constraint. I don’t know of any puzzles where ‘all arrows/renbans/etc are given’.
@@stangerrits6712I hope some setters will take a note of what you just wrote. That could make an intresting negative constraint puzzle. Propably needs to be limited to orthogonal arrows or renbans to make it comprehensible (or maybe just straight ones).
I think I read in the comments once that purists would consider kropki puzzles to require the negative constraint. So if there was such a thing as "standard kropki rules apply", then this would include the negative constraint. However, in >95% of puzzles involving kropki I've seen on CtC, the negative constraint hasn't applied, and I agree it's strange that the absence of a rule often gets stated.
afaik the reason for "not all dots are given" being so common is that originally the kropki constraint was always (or almost always) all dots are given, and it was only later that the partial rule was introduced, and it then became the more popular of the two
Pure Kropki has the negative constraint, so it gets called out whenever it's not present.
Mark seems to keep forgetting that 2 and 3 can't be orthogonally adjacent, so 3 can never be placed in r7c8
Yes, and another interesting thing is that his argument for the presence of 6 with the dots in the eighth column would work equally well for the dots at the bottom and then quickly give him a sequence of four digits there towards the beginning of the video.
Still, I wasn't able to think of that fact about the 6 at all, and it took me four times as long as him to finish the puzzle 😆
and completely forgot that 3s must be adjacent to a 9 and 2s to a 4, but he still breezed through it far faster than I did.
Finished in 43:43. Didn't even think to use coloring. A fine puzzle.
Same here
21:28
Very nice use of unusual exclusions and compulsions here. Took a moment to assimilate everything but once clear in my head this flowed smoothly.
A very nice puzzle, solved in just under an hour. I got the 6 in box 8 first, by working through the possibilities of the dots in box 9. It all flowed nicely from there on.
It took me about 10 minutes to figure out that I really ought to be coloring the cells prime vs not prime to solve this one, and once I did, everything slid nicely into place.
that was fun and fairly quick once I had the combinations in my head
Wonderful and relaxing puzzle.
Finished in 30:48. Fun ruleset with a nice break-in.
Fun puzzle!
I entirely forgot about that last rule. I guessed on the deadly pattern. One guess failed, the other worked.
Pedant checking in
14:00 for me. Very nice puzzle!
A restart due to a mistaken assumption that proved false, then a few bifurcation rabbit trails that ran cold before I backed it all out and appreciated the logical path for solving. The bifurcation around boxes 1 and 7 and how it affected box 2 sometimes as well helped me see the intended logic with the 2357 rule being most critical and the 24 / 39 rule stepping in to help in a few places as well. Fun solve. Thanks!
Absolutely love your solve. Especially the flower at 20:00!
13:25 for me. this took me as long as the previous one.
The adjacent square rule could be used earlier and cuts out a bunch of work you did, but watching your solve I did find myself wondering if it was going to be needed at all :D
I felt a bit sorry for the square rule not being used for most of the puzzle.
38:36 - That was very interesting
46:45 for me today. This was very unique and interesting.
Did it in 39:42. I did it without coloring, but I wonder if I would have found it easier if I colored the primes.
44:36 for me. Nice puzzle!
5:39 Mark didn't catch it (yet?), and neither did I during my own solve, but the exact same logic of "three white dots => must contain a 6" applies to box 9, leading to a nice "6 in one of two cells" conclusion.
...one of which can immediately be ruled out, by the way.
Interesting how the non-straightness of the white dots seem to make them more difficult to think about. M visits them several times without realizing that 3 in r7c8 is out.
3:45 All primes are odd. 2, being the only even prime, is the odd prime out.
Commenting early in the video/my solve (around 7:00). r8c8 cannot be a 4, because the "bent" series of kropki dots would descend 4->3->2->1 and force 2 and 3 to be adjacent. Likewise, it can't be a 5 (would would descend to 2 again), nor start with 7 and ascend to an impossible 10. The options for that cell are much more limited than shown at this part of the video, which - if you follow the logic - almost immediately leads to placing a digit in r7c6.
I'm wondering... is it such that the moment you identify any prime cell in the grid, can you checkerboard the grid in such a way that you know all the possible prime cells (of course they won't all be prime as there would be 4 or 5 too many, depending on which color of the board you put them in)
As far as I can tell from playing around with a 4-set non-orthogonal-adjacent rule, there are 6 total ways to checker a board with that constraint. 4 are rotationally symetrical, and the other 2 are based on swapping a corner where the centre cell is filled in (and then forces all other corners of similar cells)
Great drsign just strange to think a square doesnt need to be afjacent to its root ...made an early blunder that didnt affect the solve as it was fixable at the end...rately the case as i thiught 9 needed to be adj to 3
I solved it! In 104:21.
Is it just me, or do others wind up with broken solves, and no idea where or when it went wrong, and need to start over? I think this puzzle had 3 broken attempts for me before a smooth completion on try #4. That's okay though, just makes it all that more rewarding when I do get it.
This was an interesting puzzle - I will definitely try it myself soon. I agree with a comment left a bit ago that it is not hard to get your head around the math part because the rules spell out which digits are in which categories without the solver needing to know very much about the specific terms. And it was, I think, a very smooth and good solve - thank you for demonstrating how coloring the primes vs non-primes is so helpful, and pointing out the diamond pattern that a prime in the center of a box edge must give rise to. And finally, thank you very much for admonishing us to not be too pedantic. So many times the rules or the puzzle is clear enough, definitely able to be solved, and there is no need to nit-pick a technical term or small difference between what the professional mathematician (or professional anything) would mean versus what the normal solver would interpret a rule to mean. It is tiresome to read that kind of thing in comments, and it does not enhance anyone's experience of solving, and may serve to either discourage a setter or confuse someone less experienced in whichever variant is employed. And, frankly, it might discourage or irritate you, yourself, which I hope none of us would ever have as an aim. Thank you for this video and everything you bring to us here at Cracking the Cryptic. My life, for one, would be much more boring without this great channel.
Wonderful comment, Emily!! 🙂
it's funny, but as Mark didn't consider the sqrt rule and ended uo in a deadly pattern, which was diamiguated by this rule. For me it was the opposite: I forgot about the prime rule and ended up in a deadly pattern, which I had to diambihuate by the prime rule.
Fun! 35:35
The 3 in the corner song always makes me smile!!😃
Took me a good while to get going, but then it falls apart pretty quickly. 43:55 for me
18:57 for me
12:08 for me
Anyone find the phrasing of the square-root rule confusing? Maybe -"all digits that are perfect squares must be orthogonally adjacent to their square root"- (oops, backwards) or "all digits with single-digit perfect squares must be adjacent to their square".
That would not work as not all 9’s are next to a 3 and not all 4’s are next to a 2.
It's inherently self-contradictory without further clarification anyway, as either way it implies 1s have to go next to other 1s.
36:41 for me and solver #1166.
He just completely forgot about that 2-4 and 3-9 rule.
I'm not sure he forgot about it, or just found he could keep making progress without it.
I don't even think the rule was necessary. I completed the puzzle without ever considering it.
@@marpocky I don't see anyway for Mark to disambiguate his sudoku deadly pattern at 28:45 without the 3-9 rule. (It seems the 2-4 rule wasn't needed.)
I feel called out lol My pedantry is justified though. Intentionally misinterpreting statements by being pedantic brings me great joy :)
As for this rule set, I think those are only there for people who don't know or don't remember what square roots are. It stops people from needing google to solve the puzzle.
26 minutes
Rules: 01:14
Let's Get Cracking: 03:04
Mark's time: 26m17s
Puzzle Solved: 29:21
What about this video's Top Tier Simarkisms?!
Three In the Corner: 2x (28:06)
And how about this video's Simarkisms?!
By Sudoku: 4x (22:51, 24:31, 24:49, 28:24)
In Fact: 4x (02:09, 15:48, 19:42, 23:31)
Ah: 4x (06:32, 10:22, 21:49, 26:17)
Weird: 4x (06:13, 12:17, 19:16, 21:38)
Sorry: 3x (18:18, 25:24, 27:18)
Goodness: 2x (12:39, 29:28)
Intriguing: 2x (29:14, 29:49)
Progress: 2x (14:06, 23:12)
Symmetry: 2x (29:37, 29:46)
Bother: 1x (06:27)
Clever: 1x (29:23)
Lovely: 1x (10:35)
Brilliant: 1x (29:20)
First Digit: 1x (18:55)
Obviously: 1x (02:01)
Wow: 1x (21:38)
Most popular number(>9), digit and colour this video:
Forty Eight (7 mentions)
Two (69 mentions)
Black (18 mentions)
Antithesis Battles:
Even (3) - Odd (2)
Black (18) - White (8)
Column (9) - Row (7)
FAQ:
Q1: You missed something!
A1: That could very well be the case! Human speech can be hard to understand for computers like me! Point out the ones that I missed and maybe I'll learn!
Q2: Can you do this for another channel?
A2: I've been thinking about that and wrote some code to make that possible. Let me know which channel you think would be a good fit!
2:30 context matters. but pedantery matters too.
"I think you will find it's spelled pedantry, actually."
(Or did I just get woooshed? 😂)
@@RichSmith77 waited for this. It is an example for when pedantry does not matter. but its also an opportunity to tolerate pedantry.
Well, if words inherently carry no positive meaning, and must be defined by their difference from other words, then perhaps, for those confused people, they should try interpreting puzzle rules in negation as well, i.e., what they don't mean. I'm just trolling all the absolutists here.
I solved that without even using the square number constraint…….
I don't think that's possible. Mark almost achieved this, but he had to use the square number constraint to resolve the final pattern at 28:41. Otherwise, he has two possible solutions.
@@RichSmith77 I definately didn’t use the square constraint toward the end of the solve, I don’t recall using it earlier either….. perhaps I had a logic error and got lucky
24:14 for me. very slow solve. 2 am is not a good time to solve sudoku.
Few minutes in and Mark already is confused by the primes' rule, considering sequences that require a 2 next to a 3......
Not a very fun ruleset, in my opinion. The general constraints about primes and roots act weirdly at a basic level and do not seem to generate elegant interactions. Luckily, they do not require computations, so they are not difficult to apply, but this in not enough to make them interesting to me.
First comment 😊😊😊
If you teach me how, I volunteer to edit your videos