apetersen here. The intent of the grey line in box one was to drive home the point that renban + region sum lines could still meet the requirement without leaving a box. Nestling it by the opening digit guaranteed that it would be completely visible, so there would be no doubt that it was complete. Apologies to any other solvers who were distracted by its existence. It was meant to clarify, not confound.
That's what I thought! I appreciate the Mario school of explaining by showing. Simon doesn't notice it but it makes it clear to him that the black line dropping shouldn't be taken for granted. 10/10 puzzle.
for instance when he uses the most convoluted way to prove that very first 9. Instead of just noting that it has to be a 9 because somewhere on that line there's an 8 so the single digit must be able to be higher than 8.
Just to point out but that is why i don't get bent when he misses things. His work on the puzzle when he leaves a number somewhere always teaches me a new logic and that is why i watch. Hell i can easy. It's hard and new ways of looking at hard that i need instruction on.
At the start of 99% of all these puzzles are the words "normal sudoku rules apply", a phrase Simon would do well to remember. A decent 35 minute video compressed into 57 minutes.
@@SleepyHarryZzz Huh. I haven't run through and checked by measuring the sound manually, but I understood that TH-cam's speed-up process doesn't alter the pitch. It certainly doesn't appear to me that people are speaking an octave higher at 2 times the speed (which is what happens when you double the frequency of a note, it's the same note, but one octave higher). I can imagine that there would be some difference, depending on how the process is done, but it seems pretty much negligible to my (albeit far from perfect) ear.
Pfft, what do you mean, accent? Simon has no accent. I'm kidding, of course. Even though his accent is very much like my own, everyone has an accent, even if you don't "hear" it.
I really like these fog puzzles. As a relatively new solver of these challenging puzzles, not only is it nice to have immediate feedback when you get something right, but you also don't have to stare at 81 blank cells and wonder where to start! It is a wonderful feeling to have the setter guide me, while still forcing me to find the logic involved. Spectacular!
Me: the first digit is 9 because you have region sum line with all digits 1-9 so the 1 cell in the region must be 9 Simon: *drops the secret just because he can* (and finds a somewhat complicated way to prove the 9 with the secret 🤣)
'Complicated' is in the eye of the beholder. Have to say Simon's way was the first 'obvious' intuitive thing I saw, and it was your method that I had to think about for a minute before 'realising'
They’re (edit: complementary) logic but in the opposite way have how Simon did it. It’s a 9 by the simple fact it’s a sole cell in a region on a region sum line that has all the digits 1-9 (by the renban rule), so it has to be the biggest number, like you said. Then you can think about what it means for the region sum and realize a 9-cell region sum lines in this puzzle must go through 5 boxes because of “the secret”, and that’s what tells you how the line moves. It’s really silly to try and do it the other way around and actually requires a lot more investigation than needed.
Just finished the puzzle. Haven't watched the video yet, but I read this comment and was like "...Oh. Why did I use the secret?" It's true what they say. If all you have is a hammer, every problem looks like a nail.
@@mattinm - no, a 9-cell line doesn't have to go through five boxes - just an odd number of boxes. in fact three out of the four 9-cell lines go through three boxes!
My guess would be the 3-cell line in Box 1 is there to teach the solver that lines can exist within a single box, which helps clarify the grey line in Box 7 and force you to consider more-heavily the possibilities of the black line. If that initial line wasn't there, you might be left confused about the interpretation of the rules by the time you got to the black line, whereas this just clarifies it immediately upon the first digit.
This is a puzzle that purely shows why I love this channel because that logic to obtain the black line was so hard for me and so having Simon work it out helps so immensely.
re: duplicate line color That was a mistake on my part. Originally, I had a different rainbow of colors on the lines, but found it bothersome that the lines I could draw with the pen tool as a solver didn't match the given lines, so I edited them. You can see that the thermo bulb actually did get updated to the lighter grey, but I managed to miss recoloring that line itself. (Edit: I just went back and looked. my saved f-puzzles link has the corrected coloring, so I must have generated my SudokuPad link before fixing the line. #facepalm) Fortunately, both lines are quite quickly contained and couldn't possibly reach each other. Unfortunately, it makes the statement in the rules about distinct colors confusing at best.
I think the lines being grey works well to lessen the issue, I had no issue understanding that they were different lines, especially since you see the top line in its complexity right from the start.
I thought them being the same shade of grey meant they had the same numbers on them, so I used that as a clue. it turned out they did, so no harm done, just a funny coincidence, lol
38:09 This felt very approachable up until the blue and black lines which left me pondering two possibilities that took me an age to clarify. A really fun setting though.
Simon, I greatly appreciate your kind words in regards to my email the other day. I thankfully have return home to my family after the long 6 months. And just in time for an amazing fog puzzle!
I always love these fog of war puzzles and just had an idea for an extension to them: thick fog. in this, some cells have thicker fog and need 2+ adjacent digits to clear the fog instead of the usual 1. im not good at designing puzzles nor implementing the software for playing it, but if there's a genius constructor out there that needs an idea for a new puzzle type, you're welcome to it
I've been watching these two, Mark and Simon, do puzzles since they started their 2 puzzles a day series during COVID. I get so much pleasure in both of them and their different styles and positive energy. Thank you both for being a very weirdly important part of my day. Weird? it's sudoku. I find pleasure in watching sudoku? Yes, weird. And thank you again.
When describing "orthogonally connected"" your explanation is very clear, but you one time used what I believe was the best illustration by using colors. You colored two boxes on a diagonal and said, "These cells are not orthogonally connected, because they do not share an edge. I can make them orthogonally connected if I color this (one of the other two in the 2x2 square) cell." Thank you so much for these videos, you are saving the sanity of the world!
I love when I open a sudoku and just sit for a minute wondering how I could possibly break into the puzzle. And then 30 minutes later be sitting with it all solved, having only the slightest notion of time having passed.
I really enjoyed that one. Simon's deduction about the black line is the sort of thing I watch and think: I'd never get that. But I do think it was more complicated than necessary. The blue line had to have either a 1 or 8 on it (but not both), and that 1 or 8 had to be in box 6. It took me a while to realise, but the region sum (N=14 or 21) then means that the other two digits on the blue line in box 6 have to be 6 and 7. That gets you further without having to make such in-depth (and very impressive) deductions about the black line.
I love when explaining the yellow line, Simon talks about dividing by 5 and the secret and addition etc, when all you need to know is that there's only one cell that is populated by the yellow line in box 1. Meaning that it has to be 9, as the largest digit cannot be on a domino in the rest of the line because it will break both the region sum and renban rules. XD Great solve Simon. Other than that oversight, you again have solved a puzzle I would never have even thought about attempting. Love your work!
42:14 here and quite happy with it. Beautiful puzzle! Interestingly I started with the purple and green lines at the bottom left before moving to the yellow and orange lines so you can start in many ways.
I watched the first few minutes of this solve, decided to try it, got several hours in, doing fantastically, getting a digit along the black line in box 3 correct and revealing more fog, allowing me to fill in a different digit, BUT THEN THAT DIGIT DIDN'T REVEAL FOG! Which means I messed up somewhere, but I'm not good enough to go back and figure out where, so I had to start all over. Final result was a total of 6 hours on this puzzle. That was so grueling, but this was the first puzzle I've decided to solve before watching. Feeling accomplished, but that accomplishment feels somewhat diminished because the fog told me I was wrong; but even ignoring all the fog meta rules, I would have eventually seen that the puzzle was broken in a different way and the end result would be the same--restart the puzzle and re-prove the logic. So yes, ACCOMPLISHMENT!
This is the first one of these puzzles I've completely solved by myself and it only took 194 minutes :D It's an amazing feeling, I highly recommend actually trying these yourself!
Its so interesting. You solve some puzzles in 50 min that I have no chance on ever solving and then there is this thing that I can absolutely do, altough a bit slower.
Simon, you asked about the grey line in box 1. I think from the rules "Each line has a distinct color." So I think that the grey lines I box 1 and box 7 are intended to be region sum lines together both equaling 21 (6,7,8). Otherwise I imagine they would have had different colors.
It also forces the path of the orange line. I don't know if there was another way to arrive at that path of the orange line and that it must take 5 cells in box 1 and could not take 4 cells in box 1 and 3 in box 2.
@@khurramali907Because the only way you’d logically see the gray line is placing the 9. Whether the gray line is there or not you know that the orange line doesn’t go in those cells, because the orange line wouldn’t be in those cells. So it forces the line either way.
My thought too. I've seen a few build-your-own-region-sum-lines puzzles where an important part of the rules is that any region sum line must cross a boundary. Obviously that's not the case here (or it would've said so in the rules), but I still found it helpful to see confirmation of it so early on.
The 9 method of solving the blue and black on the right was interesting and probably simpler than my approach. From the position you have at 37:00 in the video, I tackled it a different way by asking whether 1 could be on the blue line. If it were, the blue line would sum to 28 total and 14 in each box. But then in box 3, that meant the cells not on the black line sum to 1 + 8 + 14 = 23, leaving a sum of 22 on the black line in box 3. Since the black line contains 9 but not 8 in box 1, the black line must pass into another box, and sums to 22 in each box it passes through. So the only option is an 8 cell line (2-9, summing to 44) across two boxes, but this doesn't fit the remaining foggy region, which only had space for 7 cells without entering a third box. Ergo, 1 was not on the blue line.
For the column 9 line, I worked it out in a slightly different way, although I'm not sure if it was more or less complicated. My thought process was around where does 9 go in box 3. If the line was only 3 cells long it obviously couldn't contain a 9 since it would have to be 789 and the 8 is already used in the box. If it extended into box 6 then it had to be at least 5 cells long if it contained a 9 since 4 cells would leave a single cell in box 6 which can't work due to region sums clashing with renban. If it is at least 5 cells long then it must be at least 7 cells long to get back to even (3-9) which pushes it into box 9 due to how much fog is revealed. That would mean each box would sum to 15. The options to get to 15 with a 9 would be 1+5 which couldn't work due to the 1 in the box or 2+4 which can't work because the 4 is on the blue line in box 3. Therefore in box 3 the 9 must exist on the black line which means it cannot contain a 1, placing the 1 in box 6. Placing the 1 in box 6 (and then 9) revealed the black line entirely and from there the logic was effectively the same.
85:33, thank you for pointing out the fact that a box adds up to 45 at around 41:10. i had already discovered the whole black line and that one fact gave me all i needed to finish. very fun challenge.
"Let's not do things in such a straight forward manner when complexity is available to us." This should be engraved on my tomb stone - never has one sentence summed up my entire existence so accurately.
I handled blue and black completely different. Thing to note is that blue is divisible by two, meaning it is either a run from 1-7 or 3-9. Assuming the first, the 1 can only go in one position and blue requires a 6,7 pair in box six to get to the correct sum. The consequence is that this same pair goes on the black line in box three together with 9 which is not on the blue line to create a sum of 22. Since black is now not a valid renban that sum must be matched in box six but this box does not contain enough cells that could be part of the black line to make that work. Thus the blue line digits are now known to be from 3-9, with a 6,7,8 triple in box six and the black line segment in box three is 2,6,7 where 2 can be placed.
That was a brilliant concept. I managed it slowly then came to a complete halt once the final blue and black lines were revealed. I chuckled at the black line telling me nothing and spent a very long time seeing no way of disambiguating, so finally I decided to go to a random late moment in Simon's solve all of which seemed to match mine but not as advanced, and in his first sentence he mentioned region sum line, and instantly |I| realised that I had totally forgotten that part of the rules despite their importance earlier!!!!. Then it was a simple finish. Overall I took 136 minutes, probably more than half forgetting that rule.
I took a different approach to the black line in Box 3. We know the blue line is 7 digits long so that gives the possible values of 1-7, 2-8, and 3-9. We can eliminate 2-8 because that sums to an odd number and not divisible by 2. That leaves 1-7 which sums to 28 and 3-9 which sums to 42. This results in region sums of 14 and 21 respectively. Along with the 1 and 8 in Box 3, that leaves a remaining sum of 22 and 15 respectively for the black line in Box 3. If 1-7 on the blue line, that forces a 9 onto the black line whose sum would be 22. The only possible combinations sans an 8 are 679 whose order we know, 697. If 3-9 on the blue line, that forces a 2 onto the black line whose sum would be 15. The two remaining cells must sum to 13; 49, 58, and 67. We can eliminate 49 because 4 must be on the blue line in Box 3. We can eliminate 58 because of the 8 in Box 3. That leaves 267 whose order we know, 627. That means the Black line in Box 3 must be 6[29]7. The 7 in R3C9 shows us that the Black line extends into Box 6. We can eliminate 697 as a possibility because the region sums of the blue line, 21, and the black line, 22, sum to 43 which would force a 2 into R4C7 which breaks with the 2 in R4C5. This gives us a 627 on the black line in Box 3.
Great puzzle. I was flying until I hit the blue line. Really appreciated the insights about the black line. Thanks for the videos. I actually started with the 5 on the purple line, but it sounded like the creator did intend us to start with the 9 on the yellow.
Yay. First time i catch Simon making a mistake in real time and not after he himself discovers his own blunder. And I don't care if it was silly, easy to spot, and to correct. I caught it when it was made and i am proud of myself for doing so.
I finished in 55:34 minutes. I never thought that region sums could be used separately like that, as shown with the grey lines. It's kind of an interesting twist on it. Great Puzzle!
That took me 51:36. I found it quite difficult! A couple of bits of the instructions did puzzle me, but I was able to work it out (without watching the video) and got there in the end.
I think the rules would allow lines to re-enter boxes. But they would be different line sections, so each section in the box would have the same total. This prevents a line only taking one cell with each of the two sections in one box, as they would necessarily repeat a digit. That's why Simon ruled out a line returning to a box a few times.
I got the blue and black lines a bit differently. If the sum for the blue line was 14, the sum for the black line would have to be 22. If the black line were only in box 3, it would have to be 679 or 589, neither of which are consecutive. If the black line went into box 6, it would have to have a total of 44 and be 8 cells, but we can see that it can't fit 5 cells in box 6. Therefore the sum for the blue line is 21, and it must have a 9 on it and not have a 1, placing a 1 in r4c9, which reveals that the black line does continue into box 6.
I disagree. The black line can have 5 cells in box 6, forming an inverted L with the digits 23458 in some order. The 9 would then go top left in box 6. Where is my logic wrong?
@@michaelabrahamson6512 I only started looking at these lines after getting R7C6, so I could see that R6C7 was empty and therefore couldn't contain a fifth cell of the black line. I guess you could look at them earlier and have your option available at that point?
I can't believe it! I made a mistake and had to unwind -- and it was almost exactly the same mistake as Simon, entering the wrong number in r3c1! I actually made mine much earlier, simply mistyping when I was eliminating a possibility there, removing the digit that actually was the correct one rather than the one next to it on the keypad. So later on, I also ended up with the wrong digit there, and I think it was the one Simon put there. Beautiful puzzle, by the way.
I think the 678 line was in box 1 to help the solver rule 7 out as the middle digit (since another line already was a thermo). Your reasoning showed this hint was not necessary to solve the puzzle.
It took me an hour, and my tea got cold, but it was well worth it. Or maybe not: maybe I could sue this channel for so many cups of tea and coffee getting cold while I focus on the solve. That's one to consider.
Simon in box 3 instead of your convoluted method of working out , if you just noticed that 8 was already in the box. That meant that as the box was completely full of renban lines and you had to place 9 on one of them, then the blue line was 3,4,5,6,7,8,9. The fire placing 1 in box 6 and the puzzle was cracked.
I think the gray line in box 1 is meant primarily to emphasize the non-consecutive constraint of the line. Without the line it does appear that you could place the numbers in those cells "in order" and then be able rearrange the 7s and 8s in boxes 4 and 7 and still arrive at a valid solution
@@jamisonlovely No, according to the puzzle setter, it was to demonstrate that you could have a line within a single box, and was placed there to show that near the intended start of the solution. The orange line was forced the moment that you figured out the 9 had to be where it was on the yellow line, regardless of the grey one.
How frustrating. I got to the last major deduction - I realized the black line had to grow out of box 3 (in the most obtuse way possible), but I flubbed it, plonked the 1 in the wrong spot, and just called it a puzzle. It was really fun though, that was a neat puzzle and I'm honestly pretty pleased with myself to have gotten as far as I did.
22:37 for my time (conflict checker off), I was a bit unsure on some of my logic but did make it through without blindly guessing, so there's that. 😅 Very cool puzzle, props to apetersen!
14:46 Another way to do this would be to realize that a nine-cell renban line must have a 9 on it and that 9s are very easy to place on region sum lines that only take up one cell of a box.
Regarding the blue and black lines, since we know the blue line is either 1-7 (for 28) or 3-9 (for 42), the total of the 3 black cells in box 3 is either 15 or 22 (just by using the secret and subtracting). 22 is just not going to work; it's only (remote) possibility is if it was an 8-cell line in two boxes (2-9; 44), but that would require 5 black line cells in box 6, which can't work with only 4 foggy cells available. So, the blue line is 3-9, and the black cells in box 3 total 15.
This was a fun and very approachable puzzle, it took me 52:32 to solve. Though I did make one mistake on the blue line in box 6, but after looking at it again, I was wrong about which extreme it could go, but I got a free digit from the mistake. Though figuring out why I was wrong proved it so the digit didn't help in the end. Welp time to watch Simon solve it.
At 13:15, you can deduce that starting 9 with either reading of the rules. Simon disproved it if you are going to treat each new entry into the box as a new N. But if you read the rules to mean you should add up all yellow line cells in the box, itt would require you to evenly divide the 45 sum into just 4 boxes, which is impossible.
33:11 - not too overly complicated, a lot of the lines were very intuitive to figure out. Eventually got bogged down for a bit until was able to suss out numbers on the black line everything through some logic with box 6's blue section and then everything started falling into place!
With the grey line, knowing the shape of the pink line you know that it must sum to 5. Because the top and the bottom grey line have the same digits as they are the same colour, you also can conclude that the yellow line segment in box 4 must be 5 and 4, and from that you can also get the order of the digits too. This then clears the fog for the green line shape also, without you having to figure out its shape yourself.
28:53 for me. Got the pink 5 first, then the yellow 9 (by realising it had to be a 9-cell line). Not forgetting that all lines had to be both equal sum and renban helped a lot, I think.
I am paused at 24:03 and had a thought that may come up by Simon later in the video, but if it does not I am quite proud of this revelation after the pink line and "5" discussion (although I may be a bit slow on the uptake) and I wonder if the creators of the puzzle saw this and made the puzzle around this revelation. Any region-sum renban line N long that when passing through a region with any segment having a length of 1 must be the value of N and be ODD. All other regions to follow the renban rule do allow this rule to exist. ie: if a line is 3 long, 1 segment must be 1 length and be the value 3 the other segment is 2 length and domino 2,1. 7 long, it passes through no less or more than 4 regions with one region being length 1, the length 1 cell is a 7, the remainder are the dominos 1,6 2,5, 3,4. 5 and 9 length are explained in the video. It doesn't work with even digits for a number of reasons, but for example a line of length 8 cannot have a 1 segment length must pass through 4 regions with 1 segment being length of 1 and will become the value 8, the remainder lines then become dominos 7,1 6,2 5,3 as it cannot use 4,4 due to the orthogonal rule, so it is only 7 long and breaks the renban rule.
Again I'm confounded by the length of this video... You can literally place a nine into the grid from the start... and that creates a seamless path to complete the puzzle. Finished in 16m03s.
There are definitely some deductions that can be made about the blue and black lines in Box 3 near the end. We already know the 7-length blue line sums to either 28 or 42, meaning the sum on the blue line within each box is either 14 or 21. But if it's 14 in box 1, the value of the black line is 22. At that point, it's impossible, because if the black line lives within the box, it's a 3-length renban, and 8 is already used up in the box. If the black line extends down, 22 in a box is too much, being nearly half of 45. You'd need the other five digits that weren't 1 to be on the line in the next box, and based off the geometery we can see, that can't happen. Having the blue line be 21 in each box sets the black line to a much more reasonable sum of 15 in Box 3.
I was able to complete this, but it took me over 2 hours as I'm not used to a lot of the elements. I will say that I tried to do a lot of subtraction math. I just watched Simon figure out box 7 through simple renban and sudoku, but I actually took the box's sum of 45 and subtracted out the 15 worth of green line and the 5 from purple. That meant I needed a sum of 20 amongst the remaining four digits, three of them being consecutive. I came up with either 6,7,8 and 4, or 7,8,9 and 1. But the non-lined square already saw a 1 in column 2.
13:20 9 cell renban with non-repeating digits; so either way, regardless of how the line segments are counted - you can't have two different line segments of 1 cell in size in the same box, and you can't have a 9-cell renban in only 4 boxes
I'm pretty sure the medium grey line is there because the setter didn't know about the secret (or didn't want to have the solvers to need to know it), because it is another way to deduce where the high and low digits on the orange line are.
@@hhjk4 Except you only expose the grey line at the same time as you expose the orange line - when you place the single 9. There are plenty of other lines that don't have disambiguation. Plus, the puzzle setter confirmed that it was simply to demonstrate that a line could be within a single box, without crossing into another, with a single sum region.
"They haven't really done scratch cards yet." That's a really good idea, Simon. (I won't be able to "un-scratch" because I'll forget in an instant on my phone on the software -- but I can ignore it or cover it up), but that's a really good idea. Fantastic, in fact. Good idea (@1:07, btw) Excellent idea. 😂☕️☕️☕️☕️☕️(
Actually, (@2:23) that's an idea for the next book of yours (a "scratch/fog" on one side, an empty grid on the other (ya/a person can fill in the lines, in this case, and whatever digit on the empty one) and scratch on the other. There's an idea, Simon. (Two pages for one sudoku though, so I don't know) That's an ideal though. Kudos still to and for you. ;)😄
43:21 Simon figured out a different way than I finished the puzzle. If the blue line in box 6 has a 1 on it, the blue line in box 6 must be a 1-6-7, and the blue line in box 3 must be 2-3-4-5. This means the black line in box 3 is 6-7-9 (no 8 and sums to 22). The only way this could work (and cannot) is if it went into box 6 and took 8-5-4-3-2. There is not enough fog room in box 6 to do so.
At 46:20 Simon says "That cell's clearly not blue or black" and until I saw your comment I failed to see that the fog had been uncovered and there's clearly no line there. Thank you!
I went a slightly different path with blue and black lines. After proving that black line must leave box 3 (in slightly different way, here I applaud the easy and elegant Simon's logic), I concluded that sum of blue cells is same in both boxes, sum of black cells is same in both boxes, thus the sum of cells without lines in them must also be equal in boxes 3 and 6, i.e. sum of all cells without lines in box6 must be 8+1 = 9. And that puts huge pressure on R4C7, with all the other constraints (fixed 1 in R4C8-9), the only viable option is 3, and since R6C7 can't be 6 (leaves no space for 6 on blue line), cells R6C7 and R6C8 must be 2-4 pair. The next conclusion is that R9C9 is the only option for the 4 in box9 and... ... can you imagine my surprise when the 4 in bottom right corner revealed itself being ON THE BLACK LINE !!!
That's a rather beautiful way of solving it, going after outsiders rather than digits on the lines. Then boom! that 4 in the corner revealing all you need to know from then on. Nice!
Not sure if I was right, but I took the thermo rule as a negative constraint which meant the red line could be solved much earlier as the 6 in r7c7 would have meant there were 2 correct thermos.
I know the 78's do not do much to progress the solve, but resolving them sooner, like when you got the eight, would have helped me not be in a panicked state for so long seeing things you can get done.
I think this puzzle is solvable without the thermo rule, is it? I might have made a mistake, but I figured out that R9C2 had to be 6 before clearing the fog and seeing the thermo bulb, by coloring the 69/78s. I thought that was quite interesting and was really proud of myself, but was confused about the thermo rule :D
I struggled with the blue line quite badly. Ran into a wall at that point. I understood how the length and parity and region sum leads to the 21 or 14 logic, but ended up solving it very slowly by laboriously proving the position of the 7 was the same on the black line no matter which of the two possibilities the blue line took, which then gave a 7 in the box below. It was not a smooth solve for me.
I got into this place where I knew that the black line had to be either 6 long or 9 long straight down column nine. But then there was no place for a 3 if it were 6 long, which would force c9r7-9 to be 1, 2, and 3, totaling 6, which would make c9r1-6 total 39 when it when they would have to total 2*N and therefore be even
apetersen here. The intent of the grey line in box one was to drive home the point that renban + region sum lines could still meet the requirement without leaving a box. Nestling it by the opening digit guaranteed that it would be completely visible, so there would be no doubt that it was complete. Apologies to any other solvers who were distracted by its existence. It was meant to clarify, not confound.
Very nice puzzle! Thanks for explaining your thought process about the line
Thanks for explaining! Very much enjoyed watching Simon solve your puzzle!
Thanks for explaining.. This was a fun one to solve!
I definitely appreciated the rules disambiguation; I wish more setters were as attentive to making the rules clear. Thanks lots for a fun puzzle!
That's what I thought! I appreciate the Mario school of explaining by showing. Simon doesn't notice it but it makes it clear to him that the black line dropping shouldn't be taken for granted.
10/10 puzzle.
"Let's not do things in a straightforward manner when complexity is available to us." Words to live by from Simon.
How is it Simon managed to say what we've all been thinking for years?
for instance when he uses the most convoluted way to prove that very first 9. Instead of just noting that it has to be a 9 because somewhere on that line there's an 8 so the single digit must be able to be higher than 8.
Just to point out but that is why i don't get bent when he misses things. His work on the puzzle when he leaves a number somewhere always teaches me a new logic and that is why i watch. Hell i can easy. It's hard and new ways of looking at hard that i need instruction on.
That’s our Simon! 😄
At the start of 99% of all these puzzles are the words "normal sudoku rules apply", a phrase Simon would do well to remember. A decent 35 minute video compressed into 57 minutes.
Simon is the sole reason my thinking process has an accent when doing Sudoku
I watch all CtC vids as 2x speed so the solving voice in my head when doing my own speaks quickly and relatively high-pitched 😂
@@SleepyHarryZzz 😄
Simon is the reason I think about Scooby Doo!
@@SleepyHarryZzz Huh. I haven't run through and checked by measuring the sound manually, but I understood that TH-cam's speed-up process doesn't alter the pitch. It certainly doesn't appear to me that people are speaking an octave higher at 2 times the speed (which is what happens when you double the frequency of a note, it's the same note, but one octave higher). I can imagine that there would be some difference, depending on how the process is done, but it seems pretty much negligible to my (albeit far from perfect) ear.
Pfft, what do you mean, accent? Simon has no accent.
I'm kidding, of course. Even though his accent is very much like my own, everyone has an accent, even if you don't "hear" it.
I really like these fog puzzles. As a relatively new solver of these challenging puzzles, not only is it nice to have immediate feedback when you get something right, but you also don't have to stare at 81 blank cells and wonder where to start! It is a wonderful feeling to have the setter guide me, while still forcing me to find the logic involved. Spectacular!
Watching Simons videos makes me realise I don’t over think as much as I think I do
Haha so truueee
Same! 😂
😄
Or at least you didn’t until now 😆
Me: the first digit is 9 because you have region sum line with all digits 1-9 so the 1 cell in the region must be 9
Simon: *drops the secret just because he can* (and finds a somewhat complicated way to prove the 9 with the secret 🤣)
'Complicated' is in the eye of the beholder. Have to say Simon's way was the first 'obvious' intuitive thing I saw, and it was your method that I had to think about for a minute before 'realising'
They’re (edit: complementary) logic but in the opposite way have how Simon did it. It’s a 9 by the simple fact it’s a sole cell in a region on a region sum line that has all the digits 1-9 (by the renban rule), so it has to be the biggest number, like you said.
Then you can think about what it means for the region sum and realize a 9-cell region sum lines in this puzzle must go through 5 boxes because of “the secret”, and that’s what tells you how the line moves.
It’s really silly to try and do it the other way around and actually requires a lot more investigation than needed.
yeah his way is beyond convoluted
Just finished the puzzle. Haven't watched the video yet, but I read this comment and was like "...Oh. Why did I use the secret?"
It's true what they say. If all you have is a hammer, every problem looks like a nail.
@@mattinm - no, a 9-cell line doesn't have to go through five boxes - just an odd number of boxes. in fact three out of the four 9-cell lines go through three boxes!
My guess would be the 3-cell line in Box 1 is there to teach the solver that lines can exist within a single box, which helps clarify the grey line in Box 7 and force you to consider more-heavily the possibilities of the black line. If that initial line wasn't there, you might be left confused about the interpretation of the rules by the time you got to the black line, whereas this just clarifies it immediately upon the first digit.
I think that that first little line in box 1 was primarily to force the orange line.
I did the black line wrong and inadvertently "cheated" myself to a solution.
@@MattYDdraig The orange line is forced either way once the 9 is placed.
You're right. My apologies.
This is a puzzle that purely shows why I love this channel because that logic to obtain the black line was so hard for me and so having Simon work it out helps so immensely.
When working on comics at night
And I sleep I must valiantly fight
Each puzzle you solve
Helps to boost my resolve.
Your voice is an utter delight.
re: duplicate line color
That was a mistake on my part. Originally, I had a different rainbow of colors on the lines, but found it bothersome that the lines I could draw with the pen tool as a solver didn't match the given lines, so I edited them. You can see that the thermo bulb actually did get updated to the lighter grey, but I managed to miss recoloring that line itself. (Edit: I just went back and looked. my saved f-puzzles link has the corrected coloring, so I must have generated my SudokuPad link before fixing the line. #facepalm)
Fortunately, both lines are quite quickly contained and couldn't possibly reach each other. Unfortunately, it makes the statement in the rules about distinct colors confusing at best.
I think the lines being grey works well to lessen the issue, I had no issue understanding that they were different lines, especially since you see the top line in its complexity right from the start.
I thought them being the same shade of grey meant they had the same numbers on them, so I used that as a clue. it turned out they did, so no harm done, just a funny coincidence, lol
38:09
This felt very approachable up until the blue and black lines which left me pondering two possibilities that took me an age to clarify.
A really fun setting though.
Simon, I greatly appreciate your kind words in regards to my email the other day. I thankfully have return home to my family after the long 6 months. And just in time for an amazing fog puzzle!
I always love these fog of war puzzles and just had an idea for an extension to them: thick fog. in this, some cells have thicker fog and need 2+ adjacent digits to clear the fog instead of the usual 1. im not good at designing puzzles nor implementing the software for playing it, but if there's a genius constructor out there that needs an idea for a new puzzle type, you're welcome to it
Smog Of War 😄👍
I've been watching these two, Mark and Simon, do puzzles since they started their 2 puzzles a day series during COVID. I get so much pleasure in both of them and their different styles and positive energy. Thank you both for being a very weirdly important part of my day. Weird? it's sudoku. I find pleasure in watching sudoku? Yes, weird. And thank you again.
When describing "orthogonally connected"" your explanation is very clear, but you one time used what I believe was the best illustration by using colors. You colored two boxes on a diagonal and said, "These cells are not orthogonally connected, because they do not share an edge. I can make them orthogonally connected if I color this (one of the other two in the 2x2 square) cell."
Thank you so much for these videos, you are saving the sanity of the world!
I love when I open a sudoku and just sit for a minute wondering how I could possibly break into the puzzle. And then 30 minutes later be sitting with it all solved, having only the slightest notion of time having passed.
This
Half the puzzles on this channel, I'd spend the whole 30 minutes just trying to break in.
I really enjoyed that one. Simon's deduction about the black line is the sort of thing I watch and think: I'd never get that. But I do think it was more complicated than necessary. The blue line had to have either a 1 or 8 on it (but not both), and that 1 or 8 had to be in box 6. It took me a while to realise, but the region sum (N=14 or 21) then means that the other two digits on the blue line in box 6 have to be 6 and 7. That gets you further without having to make such in-depth (and very impressive) deductions about the black line.
Well described! That's how I did it too. It had to be less complicated or I wouldn't have thought of it!
I love how caring you are for new people, always explaining and teaching. Thank you!
I love when explaining the yellow line, Simon talks about dividing by 5 and the secret and addition etc, when all you need to know is that there's only one cell that is populated by the yellow line in box 1. Meaning that it has to be 9, as the largest digit cannot be on a domino in the rest of the line because it will break both the region sum and renban rules. XD
Great solve Simon. Other than that oversight, you again have solved a puzzle I would never have even thought about attempting. Love your work!
This was very fun, especially the way it totally falls apart in the end, without being a coloring puzzle
I agree with Simon, the spirit of a 'Region Sum' line is that it goes to another box.
42:14 here and quite happy with it. Beautiful puzzle! Interestingly I started with the purple and green lines at the bottom left before moving to the yellow and orange lines so you can start in many ways.
This puzzle was a lot of fun. Not to hard not to easy. Beautifully leading through the fog.
This puzzle is something special. Delightful logic.
I watched the first few minutes of this solve, decided to try it, got several hours in, doing fantastically, getting a digit along the black line in box 3 correct and revealing more fog, allowing me to fill in a different digit, BUT THEN THAT DIGIT DIDN'T REVEAL FOG! Which means I messed up somewhere, but I'm not good enough to go back and figure out where, so I had to start all over. Final result was a total of 6 hours on this puzzle. That was so grueling, but this was the first puzzle I've decided to solve before watching. Feeling accomplished, but that accomplishment feels somewhat diminished because the fog told me I was wrong; but even ignoring all the fog meta rules, I would have eventually seen that the puzzle was broken in a different way and the end result would be the same--restart the puzzle and re-prove the logic. So yes, ACCOMPLISHMENT!
This is the first one of these puzzles I've completely solved by myself and it only took 194 minutes :D
It's an amazing feeling, I highly recommend actually trying these yourself!
Solved it in 39:31
One of the puzzles I enjoyed the most. Many thanks to apetersen for giving us this puzzle
What an amazing puzzle! It was so much fun to solve.
Thanks. apetersen!
MY FIRST SOLVE !! Thank you for this amazing puzzle !
Woohoo! I got this one! 119 minutes, but this was my first successful line puzzle with a reasonably difficult break-in!
Its so interesting. You solve some puzzles in 50 min that I have no chance on ever solving and then there is this thing that I can absolutely do, altough a bit slower.
Simon, you asked about the grey line in box 1. I think from the rules "Each line has a distinct color." So I think that the grey lines I box 1 and box 7 are intended to be region sum lines together both equaling 21 (6,7,8). Otherwise I imagine they would have had different colors.
I think the gray line is just there to demonstrate the lines can be contained within a single 3x3 box,
That is correct. Sorry for any confusion or concern.
It also forces the path of the orange line. I don't know if there was another way to arrive at that path of the orange line and that it must take 5 cells in box 1 and could not take 4 cells in box 1 and 3 in box 2.
@@khurramali907Because the only way you’d logically see the gray line is placing the 9. Whether the gray line is there or not you know that the orange line doesn’t go in those cells, because the orange line wouldn’t be in those cells. So it forces the line either way.
Exactly my thought.
My thought too. I've seen a few build-your-own-region-sum-lines puzzles where an important part of the rules is that any region sum line must cross a boundary. Obviously that's not the case here (or it would've said so in the rules), but I still found it helpful to see confirmation of it so early on.
The 9 method of solving the blue and black on the right was interesting and probably simpler than my approach. From the position you have at 37:00 in the video, I tackled it a different way by asking whether 1 could be on the blue line. If it were, the blue line would sum to 28 total and 14 in each box. But then in box 3, that meant the cells not on the black line sum to 1 + 8 + 14 = 23, leaving a sum of 22 on the black line in box 3. Since the black line contains 9 but not 8 in box 1, the black line must pass into another box, and sums to 22 in each box it passes through. So the only option is an 8 cell line (2-9, summing to 44) across two boxes, but this doesn't fit the remaining foggy region, which only had space for 7 cells without entering a third box. Ergo, 1 was not on the blue line.
That's exactly how I did it, too!
For the column 9 line, I worked it out in a slightly different way, although I'm not sure if it was more or less complicated. My thought process was around where does 9 go in box 3.
If the line was only 3 cells long it obviously couldn't contain a 9 since it would have to be 789 and the 8 is already used in the box. If it extended into box 6 then it had to be at least 5 cells long if it contained a 9 since 4 cells would leave a single cell in box 6 which can't work due to region sums clashing with renban. If it is at least 5 cells long then it must be at least 7 cells long to get back to even (3-9) which pushes it into box 9 due to how much fog is revealed. That would mean each box would sum to 15. The options to get to 15 with a 9 would be 1+5 which couldn't work due to the 1 in the box or 2+4 which can't work because the 4 is on the blue line in box 3.
Therefore in box 3 the 9 must exist on the black line which means it cannot contain a 1, placing the 1 in box 6. Placing the 1 in box 6 (and then 9) revealed the black line entirely and from there the logic was effectively the same.
85:33, thank you for pointing out the fact that a box adds up to 45 at around 41:10. i had already discovered the whole black line and that one fact gave me all i needed to finish. very fun challenge.
"Let's not do things in such a straight forward manner when complexity is available to us." This should be engraved on my tomb stone - never has one sentence summed up my entire existence so accurately.
If it is, make sure to get it engraved spiralling around the front, back and sides of your tombstone so nobody can read it from a stationary position.
That was fun to solve and great to watch Simon solve it. Thank you for an amazing puzzle and an entertaining video
I handled blue and black completely different. Thing to note is that blue is divisible by two, meaning it is either a run from 1-7 or 3-9. Assuming the first, the 1 can only go in one position and blue requires a 6,7 pair in box six to get to the correct sum. The consequence is that this same pair goes on the black line in box three together with 9 which is not on the blue line to create a sum of 22. Since black is now not a valid renban that sum must be matched in box six but this box does not contain enough cells that could be part of the black line to make that work. Thus the blue line digits are now known to be from 3-9, with a 6,7,8 triple in box six and the black line segment in box three is 2,6,7 where 2 can be placed.
This puzzle was quite easy for me, took me 25 minutes to solve.
Loved it.
The Blue/Black lines had me stumped for far too long. I worked it out by realising the blue line had to be high. Loved it.
Rules: 05:02
Let's Get Cracking: 09:25
Simon's time: 44m50s
Puzzle Solved: 54:15
What about this video's Top Tier Simarkisms?!
The Secret: 6x (12:13, 13:59, 13:59, 14:06, 17:19, 54:35)
Maverick: 2x (04:00, 36:26)
Three In the Corner: 1x (52:15)
Nori Nori: 1x (14:15)
And how about this video's Simarkisms?!
Hang On: 16x (12:40, 16:17, 19:36, 22:26, 22:27, 22:27, 22:32, 22:32, 25:23, 28:24, 30:10, 35:22, 44:51, 45:32, 45:32, 45:42)
Ah: 10x (15:21, 15:21, 17:44, 22:20, 22:27, 26:49, 29:38, 34:44, 35:22, 36:48)
In Fact: 8x (01:04, 09:00, 09:46, 18:03, 39:57, 47:03, 52:08, 56:24)
Lovely: 6x (11:56, 24:14, 24:17, 24:19, 33:03, 56:38)
Brilliant: 6x (01:34, 49:13, 49:16, 52:58, 53:00, 57:15)
Sorry: 4x (08:05, 28:02, 35:33, 53:38)
Clever: 4x (32:13, 32:16, 47:28, 53:15)
Beautiful: 4x (33:01, 47:16, 47:23, 56:56)
By Sudoku: 4x (33:55, 36:19, 49:11, 50:19)
What on Earth: 3x (10:16, 44:02, 53:29)
Naked Single: 3x (24:47, 50:28, 52:21)
That's Huge: 3x (32:46, 32:46, 52:11)
Shouting: 2x (03:00, 04:05)
What Does This Mean?: 2x (05:26, 06:51)
Have a Think: 2x (11:52, 15:13)
Useless: 1x (51:04)
The Answer is: 1x (44:06)
Break the Puzzle: 1x (45:56)
Extraordinary: 1x (01:38)
Disconcerting: 1x (35:19)
Surely: 1x (53:29)
Proof: 1x (03:05)
Unbelievable: 1x (03:05)
Obviously: 1x (53:09)
Whoopsie: 1x (47:43)
Box Thingy: 1x (36:33)
Wow: 1x (43:16)
Thingy Thing: 1x (41:30)
Most popular number(>9), digit and colour this video:
Fifteen (14 mentions)
One (100 mentions)
Blue (16 mentions)
Antithesis Battles:
Highest (2) - Lowest (0)
Black (14) - White (0)
Column (16) - Row (4)
FAQ:
Q1: You missed something!
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That was a brilliant concept. I managed it slowly then came to a complete halt once the final blue and black lines were revealed. I chuckled at the black line telling me nothing and spent a very long time seeing no way of disambiguating, so finally I decided to go to a random late moment in Simon's solve all of which seemed to match mine but not as advanced, and in his first sentence he mentioned region sum line, and instantly |I| realised that I had totally forgotten that part of the rules despite their importance earlier!!!!. Then it was a simple finish. Overall I took 136 minutes, probably more than half forgetting that rule.
The only thing echoing back through time is applause 👏
I took a different approach to the black line in Box 3.
We know the blue line is 7 digits long so that gives the possible values of 1-7, 2-8, and 3-9. We can eliminate 2-8 because that sums to an odd number and not divisible by 2. That leaves 1-7 which sums to 28 and 3-9 which sums to 42. This results in region sums of 14 and 21 respectively. Along with the 1 and 8 in Box 3, that leaves a remaining sum of 22 and 15 respectively for the black line in Box 3.
If 1-7 on the blue line, that forces a 9 onto the black line whose sum would be 22. The only possible combinations sans an 8 are 679 whose order we know, 697.
If 3-9 on the blue line, that forces a 2 onto the black line whose sum would be 15. The two remaining cells must sum to 13; 49, 58, and 67. We can eliminate 49 because 4 must be on the blue line in Box 3. We can eliminate 58 because of the 8 in Box 3. That leaves 267 whose order we know, 627.
That means the Black line in Box 3 must be 6[29]7. The 7 in R3C9 shows us that the Black line extends into Box 6.
We can eliminate 697 as a possibility because the region sums of the blue line, 21, and the black line, 22, sum to 43 which would force a 2 into R4C7 which breaks with the 2 in R4C5. This gives us a 627 on the black line in Box 3.
Great puzzle. I was flying until I hit the blue line. Really appreciated the insights about the black line. Thanks for the videos. I actually started with the 5 on the purple line, but it sounded like the creator did intend us to start with the 9 on the yellow.
Yay. First time i catch Simon making a mistake in real time and not after he himself discovers his own blunder. And I don't care if it was silly, easy to spot, and to correct. I caught it when it was made and i am proud of myself for doing so.
I finished in 55:34 minutes. I never thought that region sums could be used separately like that, as shown with the grey lines. It's kind of an interesting twist on it. Great Puzzle!
Brilliant puzzle. I was pretty quick for my standards today and did it in 48 minutes.
That took me 51:36. I found it quite difficult! A couple of bits of the instructions did puzzle me, but I was able to work it out (without watching the video) and got there in the end.
IMO, the rules as written are ambiguous as to whether region sum lines are allowed to reenter a box. Really enjoyed the solve, thanks Simon ❤
I think the rules would allow lines to re-enter boxes. But they would be different line sections, so each section in the box would have the same total. This prevents a line only taking one cell with each of the two sections in one box, as they would necessarily repeat a digit. That's why Simon ruled out a line returning to a box a few times.
I just ordered my copies of volumes 1 and 2. Can’t wait!
I just started the video and I already like it, because I love fog puzzles
Fantastic setting!!!!
Really enjoyed the puzzle! Excited to hear we’ll get to hear Simon read poetry!!
We have been chomping at the bit for that reward when it was first announced. 😁
@@davidrattner9 yes! And more lengthy guitar numbers!! 😃
31:32 for me. Very chill puzzle after several days of incredibly hard ones.
I got the blue and black lines a bit differently. If the sum for the blue line was 14, the sum for the black line would have to be 22. If the black line were only in box 3, it would have to be 679 or 589, neither of which are consecutive. If the black line went into box 6, it would have to have a total of 44 and be 8 cells, but we can see that it can't fit 5 cells in box 6. Therefore the sum for the blue line is 21, and it must have a 9 on it and not have a 1, placing a 1 in r4c9, which reveals that the black line does continue into box 6.
I disagree. The black line can have 5 cells in box 6, forming an inverted L with the digits 23458 in some order. The 9 would then go top left in box 6. Where is my logic wrong?
@@michaelabrahamson6512 I only started looking at these lines after getting R7C6, so I could see that R6C7 was empty and therefore couldn't contain a fifth cell of the black line. I guess you could look at them earlier and have your option available at that point?
@@iabervon OK, that makes sense. At my point in the puzzle, that square wasn't cleared of fog yet. Thanks a mill.
I can't believe it! I made a mistake and had to unwind -- and it was almost exactly the same mistake as Simon, entering the wrong number in r3c1! I actually made mine much earlier, simply mistyping when I was eliminating a possibility there, removing the digit that actually was the correct one rather than the one next to it on the keypad. So later on, I also ended up with the wrong digit there, and I think it was the one Simon put there.
Beautiful puzzle, by the way.
I think the 678 line was in box 1 to help the solver rule 7 out as the middle digit (since another line already was a thermo). Your reasoning showed this hint was not necessary to solve the puzzle.
This puzzle is fun and not very difficult. Just great !!!
It took me an hour, and my tea got cold, but it was well worth it. Or maybe not: maybe I could sue this channel for so many cups of tea and coffee getting cold while I focus on the solve. That's one to consider.
Only have 3 line sudoku left to solve on the app. Great job once again!
Simon in box 3 instead of your convoluted method of working out , if you just noticed that 8 was already in the box. That meant that as the box was completely full of renban lines and you had to place 9 on one of them, then the blue line was 3,4,5,6,7,8,9. The fire placing 1 in box 6 and the puzzle was cracked.
I think the gray line in box 1 is meant primarily to emphasize the non-consecutive constraint of the line. Without the line it does appear that you could place the numbers in those cells "in order" and then be able rearrange the 7s and 8s in boxes 4 and 7 and still arrive at a valid solution
No, it's there to force the orange line to follow it's path.
@@jamisonlovely No, according to the puzzle setter, it was to demonstrate that you could have a line within a single box, and was placed there to show that near the intended start of the solution. The orange line was forced the moment that you figured out the 9 had to be where it was on the yellow line, regardless of the grey one.
How frustrating. I got to the last major deduction - I realized the black line had to grow out of box 3 (in the most obtuse way possible), but I flubbed it, plonked the 1 in the wrong spot, and just called it a puzzle. It was really fun though, that was a neat puzzle and I'm honestly pretty pleased with myself to have gotten as far as I did.
22:37 for my time (conflict checker off), I was a bit unsure on some of my logic but did make it through without blindly guessing, so there's that. 😅 Very cool puzzle, props to apetersen!
14:46 Another way to do this would be to realize that a nine-cell renban line must have a 9 on it and that 9s are very easy to place on region sum lines that only take up one cell of a box.
A clean 37:35 for me! Wow, that had some fascinating logic.
Regarding the blue and black lines, since we know the blue line is either 1-7 (for 28) or 3-9 (for 42), the total of the 3 black cells in box 3 is either 15 or 22 (just by using the secret and subtracting). 22 is just not going to work; it's only (remote) possibility is if it was an 8-cell line in two boxes (2-9; 44), but that would require 5 black line cells in box 6, which can't work with only 4 foggy cells available. So, the blue line is 3-9, and the black cells in box 3 total 15.
13:56 for me. Great puzzle!!
That's 3 in the spotlight is a puzzle you must do!
Loved this puzzle, and the first one I managed to solve completely on my own - even if my logic wasn't nearly as smooth as Simon's.
First time i have ever talked to a TH-cam video. Simon missing sudoku on cells he has just pencil marked was the reason.
This was a fun and very approachable puzzle, it took me 52:32 to solve. Though I did make one mistake on the blue line in box 6, but after looking at it again, I was wrong about which extreme it could go, but I got a free digit from the mistake. Though figuring out why I was wrong proved it so the digit didn't help in the end. Welp time to watch Simon solve it.
At 13:15, you can deduce that starting 9 with either reading of the rules.
Simon disproved it if you are going to treat each new entry into the box as a new N. But if you read the rules to mean you should add up all yellow line cells in the box, itt would require you to evenly divide the 45 sum into just 4 boxes, which is impossible.
Great idea and execution, well done!
34:18 ... as I continue to catch up on the foggies
Nice puzzle!
33:11 - not too overly complicated, a lot of the lines were very intuitive to figure out. Eventually got bogged down for a bit until was able to suss out numbers on the black line everything through some logic with box 6's blue section and then everything started falling into place!
With the grey line, knowing the shape of the pink line you know that it must sum to 5. Because the top and the bottom grey line have the same digits as they are the same colour, you also can conclude that the yellow line segment in box 4 must be 5 and 4, and from that you can also get the order of the digits too. This then clears the fog for the green line shape also, without you having to figure out its shape yourself.
28:53 for me. Got the pink 5 first, then the yellow 9 (by realising it had to be a 9-cell line). Not forgetting that all lines had to be both equal sum and renban helped a lot, I think.
I am paused at 24:03 and had a thought that may come up by Simon later in the video, but if it does not I am quite proud of this revelation after the pink line and "5" discussion (although I may be a bit slow on the uptake) and I wonder if the creators of the puzzle saw this and made the puzzle around this revelation. Any region-sum renban line N long that when passing through a region with any segment having a length of 1 must be the value of N and be ODD. All other regions to follow the renban rule do allow this rule to exist. ie: if a line is 3 long, 1 segment must be 1 length and be the value 3 the other segment is 2 length and domino 2,1. 7 long, it passes through no less or more than 4 regions with one region being length 1, the length 1 cell is a 7, the remainder are the dominos 1,6 2,5, 3,4. 5 and 9 length are explained in the video. It doesn't work with even digits for a number of reasons, but for example a line of length 8 cannot have a 1 segment length must pass through 4 regions with 1 segment being length of 1 and will become the value 8, the remainder lines then become dominos 7,1 6,2 5,3 as it cannot use 4,4 due to the orthogonal rule, so it is only 7 long and breaks the renban rule.
81:00 for me. Took me ages to solve the path of the black line, but I eventually made it. Great puzzle!
89:43. This was tough but satisfying!
Again I'm confounded by the length of this video... You can literally place a nine into the grid from the start... and that creates a seamless path to complete the puzzle. Finished in 16m03s.
A really excellent puzzle ❤
There are definitely some deductions that can be made about the blue and black lines in Box 3 near the end. We already know the 7-length blue line sums to either 28 or 42, meaning the sum on the blue line within each box is either 14 or 21. But if it's 14 in box 1, the value of the black line is 22. At that point, it's impossible, because if the black line lives within the box, it's a 3-length renban, and 8 is already used up in the box. If the black line extends down, 22 in a box is too much, being nearly half of 45. You'd need the other five digits that weren't 1 to be on the line in the next box, and based off the geometery we can see, that can't happen.
Having the blue line be 21 in each box sets the black line to a much more reasonable sum of 15 in Box 3.
I was able to complete this, but it took me over 2 hours as I'm not used to a lot of the elements.
I will say that I tried to do a lot of subtraction math. I just watched Simon figure out box 7 through simple renban and sudoku, but I actually took the box's sum of 45 and subtracted out the 15 worth of green line and the 5 from purple. That meant I needed a sum of 20 amongst the remaining four digits, three of them being consecutive. I came up with either 6,7,8 and 4, or 7,8,9 and 1. But the non-lined square already saw a 1 in column 2.
"Chorus of disapproval" made my day. :-).
13:20
9 cell renban with non-repeating digits; so either way, regardless of how the line segments are counted - you can't have two different line segments of 1 cell in size in the same box, and you can't have a 9-cell renban in only 4 boxes
Interesting, thanks. I kept forgetting they were renbans as well as equal sums.
I'm pretty sure the medium grey line is there because the setter didn't know about the secret (or didn't want to have the solvers to need to know it), because it is another way to deduce where the high and low digits on the orange line are.
I'd say there's a more important pupose: without it, the orange line wouldn't have a forced path
Duh, obviously. Otherwise only Marcs favourite people could've done the puzzle. 💁♂️
@@hhjk4 Except you only expose the grey line at the same time as you expose the orange line - when you place the single 9. There are plenty of other lines that don't have disambiguation. Plus, the puzzle setter confirmed that it was simply to demonstrate that a line could be within a single box, without crossing into another, with a single sum region.
@@JustAnotherBuckyLover oh, you're right. Sorry!
"They haven't really done scratch cards yet."
That's a really good idea, Simon.
(I won't be able to "un-scratch" because I'll forget in an instant on my phone on the software -- but I can ignore it or cover it up), but that's a really good idea.
Fantastic, in fact.
Good idea
(@1:07, btw)
Excellent idea.
😂☕️☕️☕️☕️☕️(
Actually, (@2:23) that's an idea for the next book of yours (a "scratch/fog" on one side, an empty grid on the other (ya/a person can fill in the lines, in this case, and whatever digit on the empty one) and scratch on the other.
There's an idea, Simon.
(Two pages for one sudoku though, so I don't know)
That's an ideal though.
Kudos still to and for you. ;)😄
43:21 Simon figured out a different way than I finished the puzzle.
If the blue line in box 6 has a 1 on it, the blue line in box 6 must be a 1-6-7, and the blue line in box 3 must be 2-3-4-5.
This means the black line in box 3 is 6-7-9 (no 8 and sums to 22). The only way this could work (and cannot) is if it went into box 6 and took 8-5-4-3-2. There is not enough fog room in box 6 to do so.
At 46:20 Simon says "That cell's clearly not blue or black" and until I saw your comment I failed to see that the fog had been uncovered and there's clearly no line there. Thank you!
I went a slightly different path with blue and black lines. After proving that black line must leave box 3 (in slightly different way, here I applaud the easy and elegant Simon's logic), I concluded that sum of blue cells is same in both boxes, sum of black cells is same in both boxes, thus the sum of cells without lines in them must also be equal in boxes 3 and 6, i.e. sum of all cells without lines in box6 must be 8+1 = 9. And that puts huge pressure on R4C7, with all the other constraints (fixed 1 in R4C8-9), the only viable option is 3, and since R6C7 can't be 6 (leaves no space for 6 on blue line), cells R6C7 and R6C8 must be 2-4 pair.
The next conclusion is that R9C9 is the only option for the 4 in box9 and...
... can you imagine my surprise when the 4 in bottom right corner revealed itself being ON THE BLACK LINE !!!
That's a rather beautiful way of solving it, going after outsiders rather than digits on the lines. Then boom! that 4 in the corner revealing all you need to know from then on. Nice!
Not sure if I was right, but I took the thermo rule as a negative constraint which meant the red line could be solved much earlier as the 6 in r7c7 would have meant there were 2 correct thermos.
Aren't the two 3-length lines both valid thermos with the bulb in the middle?
Whoops. You’re absolutely right. I cheated my way to victory. Shame, I felt quite clever for a couple of days, not often I try these puzzles.
This was a fun one.
I know the 78's do not do much to progress the solve, but resolving them sooner, like when you got the eight, would have helped me not be in a panicked state for so long seeing things you can get done.
I think this puzzle is solvable without the thermo rule, is it? I might have made a mistake, but I figured out that R9C2 had to be 6 before clearing the fog and seeing the thermo bulb, by coloring the 69/78s. I thought that was quite interesting and was really proud of myself, but was confused about the thermo rule :D
I struggled with the blue line quite badly. Ran into a wall at that point. I understood how the length and parity and region sum leads to the 21 or 14 logic, but ended up solving it very slowly by laboriously proving the position of the 7 was the same on the black line no matter which of the two possibilities the blue line took, which then gave a 7 in the box below. It was not a smooth solve for me.
I got into this place where I knew that the black line had to be either 6 long or 9 long straight down column nine. But then there was no place for a 3 if it were 6 long, which would force c9r7-9 to be 1, 2, and 3, totaling 6, which would make c9r1-6 total 39 when it when they would have to total 2*N and therefore be even