ZegreS here! Very rewarding to see this featured since this puzzle took me VERY long to set. Also this is 4/5 difficulty - just so people set their expectations right. Thanks so much for solving and for the Ren shout out! I did come up with Marble Run (just got my book delivered and may hang that page on the wall) The sharp eyed will notice that this is just marble run in disguise ... in space. The success message (which had it's line breaks erased somehow) is a reference to the Beastie Boys song Intergalactic. I was originally going to only count cells on the galaxy towards cage sums, but this worked better. I would be VERY HONORED if Simon did a bit of Bestie Boys on his guitar some time in the future... (Sabotage?) Although I am honored already by this great feature!
Skipped due to unclear rules. The interpretations "In cages, digits not part of the galaxy sum to the given total." and "In cages not part of the galaxy, digits sum to the given total." both seem reasonable from the wording given. I didn't really want to guess which interpretation is correct, or to try one until it proves to be unsolvable, and then use the other.
@ckdo1974 Thanks for letting us all know you skipped it. I know I was wondering. Pretty sure either interpretation of the rules that you stated would both lead to the same, unique, solution.
Regarding sleeping to your videos, it's more that you are often genuinely engaged in and excited about whatever you're solving. It's calming but also interesting. Don't sell your ability to interest someone in an unfamiliar topic short! I've learned a lot from you guys and really improved my own solves. Thank you for doing what you do
I recognized the melody from Tom Odell right away I absolutely love the musical introduction, it kind of sets a calm and warm mood, perfect for the videos we watch to chill after a work day and get rid of stress. Bring them on!
Does anyone know which puzzle this was? I was wondering while watching if there was any potential in having a puzzle where the uniqueness assumption is required. Edit: I found the 'What Is Uniqueness?' video (Kill Them With Uniqueness by AFrayedKnot), which is what I was looking for!
At about 30:00, considering the total sum of column 5 reveals that the 7 and 17 cage must contain a galaxy cell, otherwise the central cell would have to be at least 10.
51:10 The more elegant way is to do math on column 5. If the 17 and 7 cages are both fully green then the 8 green cells in that column add up to 5+6+7+17=35 and that would require the singular cell in the middle to be a 10 which is impossible.
That logic is available as soon as you get the center box done (Simon gets it at about 26:00), and tells you you need a galaxy cell in both cages. I think its this episodes case of _Simon does it the hard way_
My way into it (admittedly only as a spectator to this video) was to note that if either 16 cage contained a red cell then the two green cells would need to be 7+9. Then using the rotational symmetry the other 16 cage would need to be 7+9 plus a red cell. And then there's no room for both the 7 and the 9 in box 5, using our old friend Sudoku!
I absolutely love galaxy puzzles when they appear on the channel and I can think of no better setter to bring us one that is out of this world! (P.S. whoever wrote the pun in the video description, please know that your hardwork is both noticed and appreciated) (P.P.S. Those are modified lyrics from Intergalactic Planetary, for which I sincerely hope Simon will feature the Beastie Boys on his guitar for the next puzzle)
@@zegres I had the Beastie Boys running through my head from the moment I opened this video. The earworm was so strong it competed with Simon at points.
Simon's joy over the 3 in the corner always makes me smile. It hasn't faded in years, in fact, it might have grown, and it's grown on me too; when I did sudokus on my own, I find myself looking for and singing about 3's in corners. :D
I finished in 110 minutes. I kept confusing myself by placing the digits I knew I had to count, inside the galaxy. It messed up three different times. I really enjoyed the break-in of utilizing the 7 and 17 clues in column 5. Very cool ruleset. Great Puzzle!
I laughed at 34:15 when Simon gave up with the literally one option left to sum up in the eighth box! Just like the other day when Mark noticed the missing skyscraper box and then ignored it for half of an hour :3
It was hysterical when he immediately gave up on box 8 after pencil marking 4 outside the 17 n 16 total which proves a counting 3 n 6 needed in there which would help him for 6 cages😆🤣
i absolutely LOVE all the collaboration recently, jane street, everyone involved in the fog novella, numberphile... keep it going! i've loved numberphile for ages and ages so it's a delight to see you doing things with the crew over there.
Loved the puzzle, and a great solve by Simon as always! Nearly got tricked at one point and had to go back a few steps. Remember that a 7 CAN go in a 3 or 4 cell 7 cage, even though you've already concluded that the sum is made up of 2 digits!
I tried this one and was convinced it wasn't possible. took a nap and came back to it and had a moment of inspiration and managed to get it. This was crazy hard for me to wrap my brain around though!
Wonderful puzzle and video! Unless I'm missing something, I believe as early as 30:00, once Simon deduced the central columns needs a galactic cell, knowing the 17/16 cells in box 8 need 5 non-galactic cells tells you the 16 cage has to be all non-galactic (which opens up a lot more logic)
There were a few areas where Simon was not perfectly efficient - there did seem to be a lot of distractions, but I am happy since I made it over an hour for the first time! The intended path was to do boxes 2 and 8 after the middle box, but the way Simon did it is completely legit and just a parallel solve path that is a bit harder. It would have helped him a lot more to think of the 16, 17 and 16, 7 cages separately and not as a block, but he got that idea into his head and it seemed hard to detach from it. There is a lesson there.
Around 33:00 all you have to do is consider the six white cells in column 5. Because 5 and 6 are not available, their minimum total is 25 (1+2+3+4+7+8) which exceeds the cage totals. Thus there must be red cells in these places, and so you can conclude that column 4 in box 2 and column 6 in box 8 are all green (since you only have one red cell to allocate to each of the two 2x3 rectangles). Simon went through the board looking at boxes that contained cages with impossible combined totals but did not really look for the same effect in rows and columns. In this particular case, there is no conclusion to be reached until the 5 and 6 have been placed in box 5.
Finished in 65:13. Some lovely logic trying to figure out what can and cannot be part of the galaxy. Interesting enough I chose the exact opposite colors of what Simon had for what was part of the galaxy (I had green, because it's a GO) and what wasn't part of the galaxy (I had red, because it's a NO). Fun puzzle!
56m57s. I love the logic of this! I had to use assumption for the sake of contradiction in a few spots, which makes me miss the "trial mode" of PUZ-PRE: the ability to say "let me mark this spot in my logic and then proceed along an assumption that I believe to be false; then, when I run into a contradiction, I can revert back to that spot and deduce that the assumption is false". It let me conclude, for instance, that only one cell among the eight used in cages in box 8 was part of the galaxy. Currently, I simulate this by shading the cell with my assumption gray just before proceeding along the logic, then using the back button liberally to just before I placed the gray shading to revert
The two 16 cell cages in box 2 and box 8 couldn't be 2 cell sum. Via rotational symmetry it would have made the centre digit a Schrödinger cell😁 beautiful
It feels like there is a potential short circuit in this puzzle: one can infer that any blank cells bordering a galaxy cell must be part of the galaxy because if they weren't they'd be ambiguous and the puzzle would be unsolvable. If we assume that solvability is not meant as a direct clue then this implies the shape of the blank areas is necessitated by the location of in-cage galaxy cells, from which we can infer many of their locations, particularly in boxes 1, 3, 7, and 9.
29:45 if the 7 and 17 cages in column 4 were all green, then you can use the secret. 7 + 17 + 5 + 6 in box 5 leaves the centre cell being a 10. That means the red cell must be in the 7 and 17 cages, so the 7 cage is a 3/4, the 17 is 8/9, and the 16 cages are both green
I don't know if it's been pointed out already as I haven't taken the time to real all the comments, but you mentioned that there must be a more elegant way to prove where the galaxy goes in boxes 2 and 8. If you look at the sum of column 5 it's easy to see it needs more galaxy squares than just the central digit. Great job I needed your help 3 times to solve this puzzle which hasn't happened on a three star puzzle in a while. (I think it deserves an extra difficulty star.)
I don't know if it's more elegant. But the way I solved that the 17-cage in box 8 wasn't three digits (51:08) was imagining the 7-cage in box 2 was three digita. That would be 1-2-4 leaving a minimum och 3+7+8 for the 17-cage given the 5-6 in the middle.
At 23'55" I was kinda hoping for the chair to have a series of speech balloons along the lines of "Hi! I'm Simon's chair. Nice to meet you." "How are you doing?" "Oh wait, he's coming back, catch you later."...
30:30 the 5th column, 7+17+5+6=35 but center cannot be 10; therefore red in column 5. 40:30 therefore according to him, the 16 cages in boxes 2 and 8 are completely green, and we can in order to connect these red cells he just found mark the R5C3 R5C7 cells as red too. I wonder if he'll ever count the secret 45 of column 5. 51:30 He doesn't find that out it looks like, but I think he would have liked it because it uses the secret. (every row, column, and box of sudoku adds up to 45).
@1.03.54 a simple way to say R9C1 is green is to say, since only one of the 14 cage cells is red, you can't reach the corner cell unless it is not orthogonally connected to the rest of the galaxy.
At 51:08 I think the secret would be useful. But it is all about what you happen to see. Down column five we have 7+17+5+6+r5c5 = 45 is there is not galaxy in the column. But that would make r5c5 10 so there is a galaxy in the cages in column 5. Meaning we can greanify all of the 16 cages.-
1:00:00 finish. I started off by considering if the galaxy could travel vertically from the center cell. If it did, it would place a 5 in r4c6 and a 6 in r6c4. This would break the puzzle, because the 6 cage in box 2 could not be two cells (sees both 4 and 5 in the column), and the 6 cage in box 8 could not be one cell (sees a 6 in the column). This places the 5 and 6 in column 5 of the center box, and the galaxy extends horizontally from the center. I then added the totals in column 5, and if nothing was galaxy, then the center cell would have to be a 10. Therefore, the 7 and 17 cages need to be two cells each. I flew through things from there, until I got to boxes 3 & 7, getting stalled for quite a while about the 7-8 pair in box 4. When I was down to just the corner cages, I was able to establish that the 3 cage in box 1 couldn't be a 1-2 pair. It would place an 8 as the only counting cell in the 8 cage, and an 8 in r6c1. It places the 2 in column 3 of box 4, and then a 2 in the 14 cage of box 7. If the 14 cage used the 2, it would be three cells, and the 8 would be a single cell cage (from the mirror restrictions) and broken (sees 8 in the column). If the 14 cage didn't use the 2, it would be two cells, a 5-9 pair. This would mean that the 8 cage couldn't be a single cell (sees 8 in the column), or two cells (sees 1-2 in the column and 5 in the box). Therefore, the 3 cage is a single cell 3. (This was the point at which I stalled out as I previously stated, with this being the last piece of logic until I broke through my block).
With uniqueness, I always assume that only applies to the numbers in the grid itself and not the colouring. So in this puzzle, I made all the uncaged digits in the corner boxes red as I knew they either were definitely were red to connect the galaxy or they could be either as they don't affect cage totals and there's no requirement for green to orthogonally connect.
Surely it's been noted by now but you can sort out boxes 2 and 8 easier (and earlier). Just ask what if the 7-cage in c5 was all non-galaxy. Then (assuming 5 and 6 are placed in box5) there is no way to also have a non-galaxy 17 cage, with 12456 used up. So those cages have 1 galaxy cell each. Which was forcing a lot of non-galacticity and that pretty much resolves those boxes. Alternately but similarly just use the secret and ask what the central digit must be if the 17- and 7-cages were galaxy-free.
Still watching the video, so dont know if he finds it later, but what i found beautiful is in column 5, if the 7 and 17 cage would both be green, that wouldnt work, as the 7 cage would be 124 and the lowest the 17 cage could contain is 378, which sums to 18
Even tho 9x9 is small, someones gonna devise an extension of this galaxy variant by having A "star"/center galaxy to which other galaxies rotate around/within
great entertainment from simon, as always, but when you put the 4s in box 2 you cant put 5&4 in box 8 so you need 6&3 to make up your 5 non galaxy so cages in box 2&8 are 1-5
The easiest way to see that there has to be another red cell in column 5 at around 30:00 is to just count the values. 7+17+5+6=35, even if you put a 9 in the middle cell, it does not add up to 45.
Another way to get to the same end which occurred to me while watching, if column 5 in box 2 is all green, it’s 124, and with 56 placed, you can’t make 17 in the cage in box 8. 3+7+8 is the lowest possible, which is 18.
i saw a beautiful deduction at around 28:00. can the 16 contain any galaxy? if it does, it can only have one cell of it, since you cant make 16 with less than 2 cells. with 1 galaxy cell, it has to contain a 7 and 9. it's counterpart would also be a 16 with a galaxy and so also contain 7 and 9. but then where do you put the 7 and 9 in col 5? both in the same cell. *checks the rules for Schrödinger cells* and so this is broken and so the 16 has to have no galaxy cells.
85:44 with a lot of help. I had to look at how to use the 6 cages in Boxes 2 and 8 to start the puzzle, then kept hitting walls and seeing it was because of dumb mistakes. NUMEROUS times it was because I typed in a digit for the cage total in the galaxy (instead of the vacuum of space between galaxies in this analogy...).
The rules as written (and described in the video) allow for any number of degenerate solutions, taking the entire grid as a single square galaxy and breaking each cage. What in the rules is supposed to prevent this? EDIT: I think I have it. Digits in cages (excluding digits in the galaxy) add up to the totals in the cage. I read it as "ignore cages that are part of the galaxy".
I'm a bit confused about the rules, what is constraining this to a single solution? Why can't I mark the whole grid as being in the galaxy? At that point there are no cage restrictions and I can fill in the board with any valid sudoku digits.
I think I get it, "digits in cages that are not part of the galaxy sum to the ..." implies that there must be one or more digits in each cage summing to the cage total.
The rules are a bit unclear, but the zero cage in the center should clear things up. (As in, the non galaxy cells add up to zero in the cage with no non galaxy cells)
Is it just me or is there a "rule" missing? I was initially confused by the mention of a galaxy and talk of "cancelling" cells! Shouldn't the ruleset start "Normal Sudoku rules apply. Build a galaxy of orthogonally connected cells." ??
Is it still possible to get the 1st book "Cracking The Cryptic's Greatest Hits - Volume 1"? I didn't know of the link, but is it too late to get it now?
On a similar note could skip all the maths at 1:03:36, r1c9 can never be red because it has to connect with the rest of the galaxy which would require a 1-cell 14 sum...
The uniqueness argument brings up a question I've had for a long time. If a puzzle's assignment is to find the correct digits, and the pattern (yin/yang, galaxy, pentominos, whatever) is considered not as the goal, but just as a way to accomplish that, would a puzzle be considered valid if it had ambiguous colouring, but a unique way of placing the digits?? (It would not feel as satisfying, I agree at least on that)
I think the common understanding of uniqueness requires both to be unique. If I was to make a puzzle with a unique grid but ambiguous coloring, I would explicitly state that in the rules.
The title of this puzzle makes me wonder if anyone has created a galaxy puzzle where the 'edge' constraint (i.e. galaxies cannot extend beyond the edge of the puzzle) does not apply.
The instructions are confusing. I read "That are not part of the galaxy" as modifying "cages", not "digits", so I was doing the puzzle wrong for several minutes.
Almost forgot to say, since this is a Beastie Boys themed puzzle and Simon mentioned Ren, I recommend everybody check out “What You Want” by Ren that is his Beastie Boys tribute.
I think the phrasing of the rules could be a bit clearer on this one - I read it to mean that if a CAGE is not part of the galaxy, then the digits inside can sum to anything but that number. Rather than that digits in cages sum to the total in the corner, but cells that are part of the galaxy do not contribute to the cage total
@@Ardalambdion I believe the 0-cage at the center is meant to clarify that--the non-galaxy digits sum to the total, even if the total is 0, so if the total's not 0 then there must be non-galaxy digits.
Early in the puzzle, the secret tells us that R7C4 cannot be 6 because then the whole box aside from R7C4 is non-galaxy. And that doesn't work in box 2 where only R3C6 would be galaxy. Was this not obvious? And then you know the two 6 cages contain a 6 and non-galaxy digit. In box 8, the only non-galaxy digits are 15, 24, or 123.
ZegreS here!
Very rewarding to see this featured since this puzzle took me VERY long to set.
Also this is 4/5 difficulty - just so people set their expectations right.
Thanks so much for solving and for the Ren shout out!
I did come up with Marble Run (just got my book delivered and may hang that page on the wall)
The sharp eyed will notice that this is just marble run in disguise ... in space.
The success message (which had it's line breaks erased somehow) is a reference to the Beastie Boys song Intergalactic.
I was originally going to only count cells on the galaxy towards cage sums, but this worked better.
I would be VERY HONORED if Simon did a bit of Bestie Boys on his guitar some time in the future... (Sabotage?)
Although I am honored already by this great feature!
based
Another beauty from you!! Loved everything about it!!
Skipped due to unclear rules.
The interpretations "In cages, digits not part of the galaxy sum to the given total." and "In cages not part of the galaxy, digits sum to the given total." both seem reasonable from the wording given.
I didn't really want to guess which interpretation is correct, or to try one until it proves to be unsolvable, and then use the other.
@ckdo1974 Thanks for letting us all know you skipped it. I know I was wondering. Pretty sure either interpretation of the rules that you stated would both lead to the same, unique, solution.
@@chris5619 Since the latter interpretation requires cages to be either completely inside or completely outside the galaxy, it will certainly not.
The "another dimension" text you get from finishing the puzzle is lyrics from the song Intergalactic by Beastie Boys!
It's the incorrect lyrics too. I'm not sure how they messed it up because the part that's wrong is the title of the song!
I notice it too! It was truly a musical ending.
@@agitatorjrit's the title of the puzzle though 🙂
@@andrewdipplecomedy so why when conflate them?
Regarding sleeping to your videos, it's more that you are often genuinely engaged in and excited about whatever you're solving. It's calming but also interesting. Don't sell your ability to interest someone in an unfamiliar topic short! I've learned a lot from you guys and really improved my own solves. Thank you for doing what you do
I recognized the melody from Tom Odell right away
I absolutely love the musical introduction, it kind of sets a calm and warm mood, perfect for the videos we watch to chill after a work day and get rid of stress.
Bring them on!
I'll take your word for it but it definitely sounded like Radio/Video by System of a Down: th-cam.com/video/DmmYAX8Phig/w-d-xo.html
At first I thought it was King Crimson's Book of Saturday... Then I realised the video was released on Tuesday...
Simon muttering “must not use uniqueness” reminds me of a puzzle he did a couple years back where using uniqueness was part of the solve path. 🤣
Does anyone know which puzzle this was? I was wondering while watching if there was any potential in having a puzzle where the uniqueness assumption is required.
Edit: I found the 'What Is Uniqueness?' video (Kill Them With Uniqueness by AFrayedKnot), which is what I was looking for!
th-cam.com/video/qJliK881Leo/w-d-xo.htmlsi=zlM6ON1n5i5rhuVs
At about 30:00, considering the total sum of column 5 reveals that the 7 and 17 cage must contain a galaxy cell, otherwise the central cell would have to be at least 10.
Rules: 07:11
Let's Get Cracking: 09:28
What about this video's Top Tier Simarkisms?!
The Secret: 5x (11:12, 11:17, 11:23, 11:26, 11:46)
Three In the Corner: 2x (1:10:06, 1:16:43)
Bobbins: 1x (37:31)
Knowledge Bomb: 1x (29:55)
Maverick: 1x (1:10:11)
Phistomefel: 1x (02:00)
And how about this video's Simarkisms?!
Symmetry: 16x (07:25, 07:42, 07:56, 10:34, 10:40, 13:57, 13:57, 17:29, 23:25, 25:51, 26:44, 29:34, 37:49, 39:56, 43:45, 1:08:33)
Sorry: 13x (10:07, 15:08, 22:29, 23:56, 24:02, 31:32, 36:02, 47:15, 48:41, 51:57, 54:37, 56:57, 1:02:06)
Ah: 13x (24:02, 24:15, 37:01, 37:31, 41:30, 42:22, 50:47, 52:31, 53:32, 54:48, 1:06:58, 1:08:33, 1:14:50)
Beautiful: 10x (37:22, 38:49, 38:49, 42:25, 42:47, 1:02:19, 1:02:20, 1:02:23, 1:03:31, 1:18:02)
By Sudoku: 9x (41:29, 54:58, 1:06:25, 1:06:29, 1:07:40, 1:08:11, 1:09:22, 1:15:05, 1:16:40)
Uniqueness: 9x (1:00:13, 1:00:59, 1:01:27, 1:04:21, 1:07:33, 1:08:59, 1:12:02, 1:15:19, 1:15:36)
Naughty: 6x (21:37, 21:41, 22:00, 59:18, 1:09:03, 1:12:27)
Obviously: 6x (11:08, 12:37, 17:27, 17:46, 36:13, 38:27)
Pencil Mark/mark: 6x (24:40, 27:37, 33:08, 35:54, 1:13:54, 1:13:59)
Hang On: 5x (24:56, 24:58, 27:12, 27:12, 50:17)
In Fact: 5x (00:40, 29:55, 30:01, 45:27, 52:23)
Clever: 4x (42:28, 1:07:18, 1:07:18, 1:17:45)
Fascinating: 4x (00:21, 01:43, 01:43, 02:48)
Nature: 4x (26:39, 27:02, 28:25, 29:34)
Cake!: 4x (04:03, 04:09, 04:38, 06:07)
Triangular Number: 4x (08:34, 10:15, 11:58, 17:52)
Weird: 4x (03:23, 18:17, 53:49, 58:22)
Wow: 3x (28:37, 33:23, 1:16:49)
Nonsense: 2x (31:53, 31:56)
Incredible: 2x (01:05, 02:09)
Shouting: 2x (00:39, 01:47)
What Does This Mean?: 2x (28:07, 41:22)
Have a Think: 2x (12:31, 54:05)
Unique: 2x (1:01:08, 1:01:15)
What on Earth: 1x (1:17:00)
Goodness: 1x (03:57)
Naked Single: 1x (1:11:01)
In the Spotlight: 1x (1:16:46)
Elegant: 1x (51:09)
Going Mad: 1x (1:17:19)
Gorgeous: 1x (1:09:22)
Discombobulating: 1x (54:40)
Come on Simon: 1x (57:20)
Surely: 1x (1:14:35)
Whoopsie: 1x (1:04:41)
Internal Logic: 1x (1:00:33)
Phone is Buzzing: 1x (29:03)
Almost Interesting: 1x (33:44)
Baffling: 1x (44:26)
Most popular number(>9), digit and colour this video:
Fifteen (14 mentions)
One (92 mentions)
Green (86 mentions)
Antithesis Battles:
Even (9) - Odd (0)
Outside (2) - Inside (0)
Row (15) - Column (15)
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!
this is amazing
A great puzzle and a Beastie Boys reference!! Today is a good day!!
27:50 I simply HAD to pause the video and shout "A ZED PENTOMINO OF GALACTIC PROPORTIONS EMANATING FROM THE PUZZLE." That sentence made me so happy.
as soon as i heard you play another love i liked the video. You really help me through tough times, thank you
@50:21 If column 5 is all green (except middle), it adds to 35. Middle digit would be a 10.
51:10 The more elegant way is to do math on column 5. If the 17 and 7 cages are both fully green then the 8 green cells in that column add up to 5+6+7+17=35 and that would require the singular cell in the middle to be a 10 which is impossible.
That logic is available as soon as you get the center box done (Simon gets it at about 26:00), and tells you you need a galaxy cell in both cages. I think its this episodes case of _Simon does it the hard way_
@@elLooto More aggravating, this is an episode of Simon not thinking about the secret!
My way into it (admittedly only as a spectator to this video) was to note that if either 16 cage contained a red cell then the two green cells would need to be 7+9. Then using the rotational symmetry the other 16 cage would need to be 7+9 plus a red cell. And then there's no room for both the 7 and the 9 in box 5, using our old friend Sudoku!
Well that was a whole lot of fun.
I did enjoy my time a ton.
Through the galaxy sped
'Mid the stars green and red
But I sadly got little work done.
Got my delivery !! Books, postcards, extra puzzles and bobbins cushions are everything i thought it would be!!
When I first saw this I didn't have a clue where to start. But once you understand it it flows so nicely
I absolutely love galaxy puzzles when they appear on the channel and I can think of no better setter to bring us one that is out of this world!
(P.S. whoever wrote the pun in the video description, please know that your hardwork is both noticed and appreciated)
(P.P.S. Those are modified lyrics from Intergalactic Planetary, for which I sincerely hope Simon will feature the Beastie Boys on his guitar for the next puzzle)
Thanks!! Very nice compliment!
I may do a sequel called Intergalactic some day where only galaxy cells contribute to cage totals...
@@zegres I had the Beastie Boys running through my head from the moment I opened this video. The earworm was so strong it competed with Simon at points.
I recognized the song from Weird Al's cover of it in his Polka Power!
Simon's joy over the 3 in the corner always makes me smile. It hasn't faded in years, in fact, it might have grown, and it's grown on me too; when I did sudokus on my own, I find myself looking for and singing about 3's in corners. :D
I love these videos so much!! Your content is always so lovely and interesting
I didn't really have a good day today. So hearing Simon's guitar intro today was really great. Thanks
35:50 ... Don't you tell me to stop!
Nice puzzle (and nice BB reference)!
32:37 for me. What a fantastic puzzle, loved it!!
I finished in 110 minutes. I kept confusing myself by placing the digits I knew I had to count, inside the galaxy. It messed up three different times. I really enjoyed the break-in of utilizing the 7 and 17 clues in column 5. Very cool ruleset. Great Puzzle!
I laughed at 34:15 when Simon gave up with the literally one option left to sum up in the eighth box! Just like the other day when Mark noticed the missing skyscraper box and then ignored it for half of an hour :3
It was hysterical when he immediately gave up on box 8 after pencil marking 4 outside the 17 n 16 total which proves a counting 3 n 6 needed in there which would help him for 6 cages😆🤣
At 1:03:34 we can see Simon's galaxy and at 1:17:21 we saying "exterminate" in a very cute way 😆
Very good Galaxy puzzle, with a lot of thinking! 😊
Beastie Boys - Intergalactic
🤘
i absolutely LOVE all the collaboration recently, jane street, everyone involved in the fog novella, numberphile... keep it going! i've loved numberphile for ages and ages so it's a delight to see you doing things with the crew over there.
Loved the puzzle, and a great solve by Simon as always!
Nearly got tricked at one point and had to go back a few steps. Remember that a 7 CAN go in a 3 or 4 cell 7 cage, even though you've already concluded that the sum is made up of 2 digits!
Took me 2 hours, but I'm glad I solved it! Nice puzzle
I tried this one and was convinced it wasn't possible. took a nap and came back to it and had a moment of inspiration and managed to get it. This was crazy hard for me to wrap my brain around though!
Wonderful puzzle and video! Unless I'm missing something, I believe as early as 30:00, once Simon deduced the central columns needs a galactic cell, knowing the 17/16 cells in box 8 need 5 non-galactic cells tells you the 16 cage has to be all non-galactic (which opens up a lot more logic)
There were a few areas where Simon was not perfectly efficient - there did seem to be a lot of distractions,
but I am happy since I made it over an hour for the first time!
The intended path was to do boxes 2 and 8 after the middle box,
but the way Simon did it is completely legit and just a parallel solve path that is a bit harder.
It would have helped him a lot more to think of the 16, 17 and 16, 7 cages separately and not as a block,
but he got that idea into his head and it seemed hard to detach from it. There is a lesson there.
My day is made ,❤❤Thanks for wishing my boss on behalf of me,Lots of love from India
Around 33:00 all you have to do is consider the six white cells in column 5. Because 5 and 6 are not available, their minimum total is 25 (1+2+3+4+7+8) which exceeds the cage totals. Thus there must be red cells in these places, and so you can conclude that column 4 in box 2 and column 6 in box 8 are all green (since you only have one red cell to allocate to each of the two 2x3 rectangles). Simon went through the board looking at boxes that contained cages with impossible combined totals but did not really look for the same effect in rows and columns. In this particular case, there is no conclusion to be reached until the 5 and 6 have been placed in box 5.
Finished in 65:13. Some lovely logic trying to figure out what can and cannot be part of the galaxy. Interesting enough I chose the exact opposite colors of what Simon had for what was part of the galaxy (I had green, because it's a GO) and what wasn't part of the galaxy (I had red, because it's a NO).
Fun puzzle!
After a rocky few days with CTC puzzles, it was good to get back on track with this voyage into the unknown, thanks.
27:57 “A Z pentomino of galactic proportions”. What a quote.
56m57s. I love the logic of this! I had to use assumption for the sake of contradiction in a few spots, which makes me miss the "trial mode" of PUZ-PRE: the ability to say "let me mark this spot in my logic and then proceed along an assumption that I believe to be false; then, when I run into a contradiction, I can revert back to that spot and deduce that the assumption is false". It let me conclude, for instance, that only one cell among the eight used in cages in box 8 was part of the galaxy. Currently, I simulate this by shading the cell with my assumption gray just before proceeding along the logic, then using the back button liberally to just before I placed the gray shading to revert
The two 16 cell cages in box 2 and box 8 couldn't be 2 cell sum. Via rotational symmetry it would have made the centre digit a Schrödinger cell😁 beautiful
It feels like there is a potential short circuit in this puzzle: one can infer that any blank cells bordering a galaxy cell must be part of the galaxy because if they weren't they'd be ambiguous and the puzzle would be unsolvable. If we assume that solvability is not meant as a direct clue then this implies the shape of the blank areas is necessitated by the location of in-cage galaxy cells, from which we can infer many of their locations, particularly in boxes 1, 3, 7, and 9.
This would count as uniqueness, which Simon and Mark avoid
29:45 if the 7 and 17 cages in column 4 were all green, then you can use the secret. 7 + 17 + 5 + 6 in box 5 leaves the centre cell being a 10.
That means the red cell must be in the 7 and 17 cages, so the 7 cage is a 3/4, the 17 is 8/9, and the 16 cages are both green
I don't know if it's been pointed out already as I haven't taken the time to real all the comments, but you mentioned that there must be a more elegant way to prove where the galaxy goes in boxes 2 and 8. If you look at the sum of column 5 it's easy to see it needs more galaxy squares than just the central digit. Great job I needed your help 3 times to solve this puzzle which hasn't happened on a three star puzzle in a while. (I think it deserves an extra difficulty star.)
This was a fantastic puzzle. 31:09 for me today.
Love the guitar playing 😊
What a beautiful break in!!
Please I’d love to see simon solve Broken Secrets, it is such an interesting puzzle!!
The message at the end is a reference to the Beastie Boys song Intergalactic.
I don't know if it's more elegant. But the way I solved that the 17-cage in box 8 wasn't three digits (51:08) was imagining the 7-cage in box 2 was three digita. That would be 1-2-4 leaving a minimum och 3+7+8 for the 17-cage given the 5-6 in the middle.
At 23'55" I was kinda hoping for the chair to have a series of speech balloons along the lines of "Hi! I'm Simon's chair. Nice to meet you." "How are you doing?" "Oh wait, he's coming back, catch you later."...
30:30 the 5th column, 7+17+5+6=35 but center cannot be 10; therefore red in column 5.
40:30 therefore according to him, the 16 cages in boxes 2 and 8 are completely green, and we can in order to connect these red cells he just found mark the R5C3 R5C7 cells as red too. I wonder if he'll ever count the secret 45 of column 5.
51:30 He doesn't find that out it looks like, but I think he would have liked it because it uses the secret. (every row, column, and box of sudoku adds up to 45).
@1.03.54 a simple way to say R9C1 is green is to say, since only one of the 14 cage cells is red, you can't reach the corner cell unless it is not orthogonally connected to the rest of the galaxy.
At 51:08 I think the secret would be useful. But it is all about what you happen to see.
Down column five we have 7+17+5+6+r5c5 = 45 is there is not galaxy in the column. But that would make r5c5 10 so there is a galaxy in the cages in column 5. Meaning we can greanify all of the 16 cages.-
" why do I start there rather than starting with something simple?" Simon finally heard me shouting. 1:02:10 lol
1:00:00 finish. I started off by considering if the galaxy could travel vertically from the center cell. If it did, it would place a 5 in r4c6 and a 6 in r6c4. This would break the puzzle, because the 6 cage in box 2 could not be two cells (sees both 4 and 5 in the column), and the 6 cage in box 8 could not be one cell (sees a 6 in the column). This places the 5 and 6 in column 5 of the center box, and the galaxy extends horizontally from the center. I then added the totals in column 5, and if nothing was galaxy, then the center cell would have to be a 10. Therefore, the 7 and 17 cages need to be two cells each. I flew through things from there, until I got to boxes 3 & 7, getting stalled for quite a while about the 7-8 pair in box 4.
When I was down to just the corner cages, I was able to establish that the 3 cage in box 1 couldn't be a 1-2 pair. It would place an 8 as the only counting cell in the 8 cage, and an 8 in r6c1. It places the 2 in column 3 of box 4, and then a 2 in the 14 cage of box 7. If the 14 cage used the 2, it would be three cells, and the 8 would be a single cell cage (from the mirror restrictions) and broken (sees 8 in the column). If the 14 cage didn't use the 2, it would be two cells, a 5-9 pair. This would mean that the 8 cage couldn't be a single cell (sees 8 in the column), or two cells (sees 1-2 in the column and 5 in the box). Therefore, the 3 cage is a single cell 3. (This was the point at which I stalled out as I previously stated, with this being the last piece of logic until I broke through my block).
With uniqueness, I always assume that only applies to the numbers in the grid itself and not the colouring. So in this puzzle, I made all the uncaged digits in the corner boxes red as I knew they either were definitely were red to connect the galaxy or they could be either as they don't affect cage totals and there's no requirement for green to orthogonally connect.
Oh the way Simon's eye light up at 3 in the corner potential
1:12:08 row 3 column 8 is a naked single
It can't be 1235 by the column, 46 because the 7 cages need those, and 79 by the row
I don't live in Cork anymore but I'd definitely get the bus down for the chance to get a photo with Simon lol
Lol, he can crack insane Sudoku puzzles. Beasty Boys' lyrics stump him though. haha
Surely it's been noted by now but you can sort out boxes 2 and 8 easier (and earlier). Just ask what if the 7-cage in c5 was all non-galaxy. Then (assuming 5 and 6 are placed in box5) there is no way to also have a non-galaxy 17 cage, with 12456 used up. So those cages have 1 galaxy cell each. Which was forcing a lot of non-galacticity and that pretty much resolves those boxes.
Alternately but similarly just use the secret and ask what the central digit must be if the 17- and 7-cages were galaxy-free.
Still watching the video, so dont know if he finds it later, but what i found beautiful is in column 5, if the 7 and 17 cage would both be green, that wouldnt work, as the 7 cage would be 124 and the lowest the 17 cage could contain is 378, which sums to 18
At 40:00, why couldn't the 8 cage in Box 4 have a 134 within it that was green? I don't think Simon ruled that out.
Even tho 9x9 is small, someones gonna devise an extension of this galaxy variant by having
A "star"/center galaxy to which other galaxies rotate around/within
Very exciting puzzle.
Ah the Beastie Boys. Haven't thought about them in ages.
Your welcome! Now go and listen to What You Want by Ren.
21:56 for me. the break in was a mental bifurcation, but the rest was easier and using metalogic helped.
great entertainment from simon, as always, but when you put the 4s in box 2 you cant put 5&4 in box 8 so you need 6&3 to make up your 5 non galaxy so cages in box 2&8 are 1-5
The easiest way to see that there has to be another red cell in column 5 at around 30:00 is to just count the values. 7+17+5+6=35, even if you put a 9 in the middle cell, it does not add up to 45.
Another way to get to the same end which occurred to me while watching, if column 5 in box 2 is all green, it’s 124, and with 56 placed, you can’t make 17 in the cage in box 8. 3+7+8 is the lowest possible, which is 18.
i saw a beautiful deduction at around 28:00. can the 16 contain any galaxy? if it does, it can only have one cell of it, since you cant make 16 with less than 2 cells. with 1 galaxy cell, it has to contain a 7 and 9. it's counterpart would also be a 16 with a galaxy and so also contain 7 and 9. but then where do you put the 7 and 9 in col 5? both in the same cell. *checks the rules for Schrödinger cells* and so this is broken and so the 16 has to have no galaxy cells.
I think Simon ought to have a House in 2 Corner catchphrase.
85:44 with a lot of help. I had to look at how to use the 6 cages in Boxes 2 and 8 to start the puzzle, then kept hitting walls and seeing it was because of dumb mistakes. NUMEROUS times it was because I typed in a digit for the cage total in the galaxy (instead of the vacuum of space between galaxies in this analogy...).
"Save the world."
"LANTERNPANTHER"
Not very often you see a cage summing to zero, this should be something special!
The rules as written (and described in the video) allow for any number of degenerate solutions, taking the entire grid as a single square galaxy and breaking each cage. What in the rules is supposed to prevent this?
EDIT: I think I have it. Digits in cages (excluding digits in the galaxy) add up to the totals in the cage. I read it as "ignore cages that are part of the galaxy".
i understood it like you, its poorly worded for sure^^
At first I thought the same, yr edit made me understand the rules
I couldn't figure this out either. There needs to be a rule about not breaking cages to make it solvable.
The cage in the middle sums to zero, so this should clear any confusion.
Thank you! This made me insane. Now I can try to solve it.
I'm a bit confused about the rules, what is constraining this to a single solution? Why can't I mark the whole grid as being in the galaxy? At that point there are no cage restrictions and I can fill in the board with any valid sudoku digits.
I think I get it, "digits in cages that are not part of the galaxy sum to the ..." implies that there must be one or more digits in each cage summing to the cage total.
The rules are a bit unclear, but the zero cage in the center should clear things up. (As in, the non galaxy cells add up to zero in the cage with no non galaxy cells)
121:37, very rewarding puzzle! I loved figuring out how the galaxy had to grow throughout the solve.
Is it just me or is there a "rule" missing? I was initially confused by the mention of a galaxy and talk of "cancelling" cells! Shouldn't the ruleset start "Normal Sudoku rules apply. Build a galaxy of orthogonally connected cells." ??
Is it still possible to get the 1st book "Cracking The Cryptic's Greatest Hits - Volume 1"? I didn't know of the link, but is it too late to get it now?
53:38 "We don't know _where_ the domino is" don't we?
On a similar note could skip all the maths at 1:03:36, r1c9 can never be red because it has to connect with the rest of the galaxy which would require a 1-cell 14 sum...
Boxes 4, 5, & 6 combined remind me of the Ant Nebula. Box 8 reminds me of the Eagle Nebula mirrored (with box 2 being an upside down version).
That intro really reminded me of the song Sight of Spira
Very nice guitar intro
The uniqueness argument brings up a question I've had for a long time. If a puzzle's assignment is to find the correct digits, and the pattern (yin/yang, galaxy, pentominos, whatever) is considered not as the goal, but just as a way to accomplish that, would a puzzle be considered valid if it had ambiguous colouring, but a unique way of placing the digits??
(It would not feel as satisfying, I agree at least on that)
I think the common understanding of uniqueness requires both to be unique. If I was to make a puzzle with a unique grid but ambiguous coloring, I would explicitly state that in the rules.
the column4 cages cant be full 3cell cages because they add up to 24 and with the 11 in box5, the middle r5c5 square would have to be 10.
54:35 for me. Beautiful puzzle!
The title of this puzzle makes me wonder if anyone has created a galaxy puzzle where the 'edge' constraint (i.e. galaxies cannot extend beyond the edge of the puzzle) does not apply.
I believe that is the Beastie Boys, intergalactic.
Now I'd like to have the Vegan chocolate cake recipe !
Please show the Broken Secrets solve!
The Zed-Pentomino of Galactic Proportions!
The instructions are confusing. I read "That are not part of the galaxy" as modifying "cages", not "digits", so I was doing the puzzle wrong for several minutes.
I like my sugar with coffee and cream!
At first I thought the music was King Crimson's Book of Saturday... Then I realised the video was released on Tuesday...
Almost forgot to say, since this is a Beastie Boys themed puzzle and Simon mentioned Ren, I recommend everybody check out “What You Want” by Ren that is his Beastie Boys tribute.
I think the phrasing of the rules could be a bit clearer on this one - I read it to mean that if a CAGE is not part of the galaxy, then the digits inside can sum to anything but that number. Rather than that digits in cages sum to the total in the corner, but cells that are part of the galaxy do not contribute to the cage total
That confused me as well.
Solved in 56:40. Not bad from me.
Those are lyrics to Intergalactic by the Beastie Boys, late 90's rap from NYC.
End message is Beastie Boys' Intergalactic.
With that title, you should wear a Jedi robe.
It was in the wash :)
I assume that the galaxy isn't allowed to swallow entire cages?
@@Ardalambdion I believe the 0-cage at the center is meant to clarify that--the non-galaxy digits sum to the total, even if the total is 0, so if the total's not 0 then there must be non-galaxy digits.
So Simon knows R.E.M. but not the Beastie Boys. Hmmm…
i misunderstood the rules. there is nothing written about the squares outside of cages. i thought they were apart of the galaxy too.
Early in the puzzle, the secret tells us that R7C4 cannot be 6 because then the whole box aside from R7C4 is non-galaxy. And that doesn't work in box 2 where only R3C6 would be galaxy. Was this not obvious? And then you know the two 6 cages contain a 6 and non-galaxy digit. In box 8, the only non-galaxy digits are 15, 24, or 123.
Just opened the video as my two ctc greatest hits books arrived. I may not attempt the video puzzle tonight!