As regards to not being used to SET working 2 ways, I ended up finding a far more complicated SET by taking the top 2, middle, and bottom 2 rows to cancel out 4 horizontal rows. All 4 horizontal rows ended up getting cancelled after arrow work, and left me with 17 cells adding up to 45, giving me the exact same digits in the exact same spaces, but only after much more work! SET is weird.
Aad has ever been my favorite constructor. This puzzle is beautiful and elegant as always. Especially the x-wing logic on 3s is top notch construction.
SUCH a nice puzzle. Got a bit stuck on the X wing in the mid-solve, but found the set right away (though was at 90 degrees to yours, Simon) and was really tickled by the symmetry. Not at all a fiendish puzzle, and a good one for anybody who is beginning to get acclimatised to SET.
Anyone else find this break-in? I highlighted C3,C4,C6,C7 and R3,R4,R6,R7 which included the arrows twice each, so highlighting the circles as well gives 8 sets of 45, leaving the 17 remaining cells adding to 45. I feel like this might be the intended route?
Simon’s absolute refusal to pencil mark any of the arrows was definitely on brand. 😂 Also, did Aad specifically design this puzzle to create the fastest elimination of a 3 in a corner?
It is such an impossible looking sudoku. It's amazing how you find the logic to crack such puzzles. This is probably the best arrow sudoku I have ever seen.
It's good because it's cool while approachable, and theefor perfect for the channel. We all need a phistomefel some of the time, but most of us needs these brilliant yet doable puzzles most of the time (and sometimes something in the middle :P Top Work Aad, as always ❤❤❤❤
I had a simpler breakin. Highlight the cells in r3,4,6,7 and c3,4,6,7 - you're double counting all the arrow cells, but not the arrow heads, so cancel out the double counting by also excluding the arrow heads. The remaining cells must sum to 45. Once you work out you can't put a 2 in the remaining cells r2, or a 1 in r8, you have no degrees of freedom. Very good puzzle.
I love Aad's puzzles, but as many commented, it's the first one involving (new) sets that I completed by myself. And what puzzles me more is that my solution seems a lot more simple than Simon's and others I've read here. Surely I missed something. I just took the set of columns 3,4,6,7 and rows 3,4,6,7, and noticed that the "arrows numbers" zones were duplicated, so if I add the "arrows total" cells, that would mean the total would be 8 * 45, and that the remaining cells total would equal 45. It's pretty low for 17 cells and there's only one way to fill it right. It seems there are a lot of ways to solve this one with sets. I like that.
There’s a second Scrabblegrams puzzle within the article. Here are the clues if anyone wants to attempt it: Baker dozen (8) Monopoly square (4, 7) Cajun stew (9) Religious (6) I’ve fed a fox (9) Egg with bacon (6, 8) Li’l deer (4) Apart (7) Vitamin studier (12) Thinly (7) A CEO (13) For me, the first 2 and the deer clue were quite easy, I should’ve guessed the third more quickly, I was _wayyyyy_ too confused by the fox clue, I was proud of getting the egg one (my mom used to eat these at our favorite restaurant when I was a kid), I got the wrong word at first for someone who studies vitamins (I just knew it’d end in “-ist”), and I had the right word for the last one but then second guessed myself when I shouldn’t have. 😅
I was wondering whether that was a coincidence (I doubt it), an inherent property of the SET shenanigans or (my best bet) Aad having a bit of a flourish just because he can. And why not!
I did the set a bit differently. I highlighted the green that you did, then the circles in orange and then I added the top row to create an equivalence. When you do that you end up with a bunch of orange digits that must add up to 30 or less and it turns out that it forced one of the cells to be a 1, and the rest of them to be the minimum they can be giving you a ton of information in the puzzle.
I had a different approach to the break-in: take the set 1 as C1, C3, C4, C6, C7, and set 2 as R1, R2, R5, R8, R9. Subtract the common cells, subtract the arrows and circles. The remainder in set 1 has a minimum sum of 30, and the remainder in set 2 has a maximum sum of 30 (and is a 6789 quad). Observe that to make the minimum sum of set 1 work, R1C1 and R9C1 must be a 45 pair, which is resolved by the given 5 in box 7. The remaining cells in set 1 are 1's, 2's, and 3's. Repeat the exercise, except use C9 instead of C1 in set 1, and you have a mirror result: R1C9 and R9C9 must be a 45 pair, and all cells in set 1 solve by sudoku. (You can swap rows and columns, and do the exercise again to get the 123 triples and 6789 quads in R1 and R9, which I did not think to do, and it not strictly neccessary, but it saves a little bit of time.) The puzzle solves easily from there.
I started with different set. I used {r1,r2,r5,r7,r9} and {c3,c4,c6,c7}, after removing digits that are in both sets and then removing all arrows I was left with {r1c1,r1c2,r1c5,r1c8,r1c9, r2c1,r2c9, r5c1,r5c5,r5c9, r8c1,r8c9, r9c1,r9c2,r9c5,r9c8,r9c9} which must sum to 45 and the only way to achieve this is to have 45 in corners and 123 everywhere else (minimizing top&bottom row or left&right column get sum of 30 - 12345 x2, so remaining 7 cells sum to 15, minimum middle cell can be is 3 and minimum sum of remaining cells is 12 - 123 x2, making all cells 5 or less with 45 in corners and 3 in the middle).
As still a novice with SET, I wanted two sets of the same number of digits from 1 to 9. Therefore, I used the same horizontal rows as Simon's second version, but instead, I used columns 1, 2, 8, and 9 as the vertical version. I removed the common digits, and then arrows reflecting the common sums. I was left with five cells in columns 1 and 9 and the extreme cells of columns 2 and 8 in one set, and a smattering of digits in the other set -- specifically, a couple arrows and digits in column 5. A nice thing happened: I could replace the arrows with the circles in column 5, leaving me with six digits in column 5. Comparing the minimum and maximum, required the remaining three digits in column 5 to sum to 6, 7, or 8. Given digits forced the minimum digits in columns 2 and 8 upward a couple times (and the maximum of the three column-5 digits downward) until the three digits in column 5 could only sum to 6. Those three cells were R1C5, R5C5, and R9C5 that had to be 1, 2, and 3. I reached the same position as Simon after his SET analysis. I followed up quite slowly, applying the arrows, and removing possible digits. 26:00 Simon considered one pair of the cornermarked 3s, but didn't consider the other pair and how they break the puzzle. 28:50 He's doing it now.
Random observation, mulling a bit about the break-in (which I found, but then got stuck at the X-wing of 3s). This scissors arrangement of arrows limits the central cell to be 3 at most, right? So ruling out 1 and 2 from the central cell in any way (like it is done with givens in this puzzle)- the high-low distribution (1-5 vs 6-9) in the perimeter is forced. Nice!
I got stuck for so long that I had to pause and watch the video until Simon got to his X-wing resolution of the threes along the arrows. That was the piece I was missing, so I paused the video, unpaused my game, and continued onward to the end. My time today was 44:16, solver number 1276, but this one needs an asterisk of getting a hint. (I did unpause the video and watch to the end after solving my grid.)
Well, it doesn't really matter what "rotation" we start with. The seven(!) orange digits must sum to 45 *less* than the eight(!) green digits. And since four of the green digits always see each other, the *absolute maximum* we can get out of the green digits is 60 (2×(6+7+8+9)). So the absolute maximum that all of the orange digits can sum to is 60-45=15. That is *not much* when you need to fill seven cells. What's more is we can rule out that the orange digit in box 5 is a 1, since there is already a 1 in that box. Since of the remaining six orange digits again always three see each other in a row, we can place a maximum of two 1s in orange cells. We can also never place three 2s in the orange cells, since the given 2 in row 2 sees sees both orange cells in row two and of the other orange cells, again, there is an absolute maximum of two that don't see each other. So even absolutely minimising the orange cells still means we need to place two 1s, two 2s and three 3s, which - wouldn't you know it - sums to exactly 15. Which was also our maximum, so that is, in fact, what needs to go in the orange cells. We also know pretty exactly where they need to go. There must be a 3 in the orange cell in box 5, because that is the only way you can ever place three of any digit in the orange cells. The other two, of course, then can't be in boxes 4 or 6, since they see the orange digit in box 5. And there also can't be a 3 in box 3, since there already is a given one. That forces us to put another 3 in the orange cell in box 1, which then also sees the one in box 7, placing the last orange 3 in box 9. Next, we know that we need to place two 2s, but there can't be one in the orange cell in box 3, since that sees a given 2. There also can't be one in the orange in box 4, since that would see both other possible spots for 2s, meaning we couldnt place another one, forcing us to place at least one 4, which would break the puzzle. So the two orange 2s go in boxes 6 and 7. Which leaves two 1s to place in the orange cells in boxes 3 and 4 and, just like that, we have more than doubled our number of digits in the grid. And then of course if we *do* consider the rotation, that's *another* six digits we can immediately place by much the same method, tripling our original digits
Simon, I don't know why you so often over-look the "simple" way to solve a cell, but it is so amusing at times watching you over-look something, work out a series of logic, and then complete the cell you had an easier way of resolving before hand. And frankly I don't care why, you are entertaining to watch as you solve, and see things I'd spend ages looking for. I did manage to get the initial break in after looking at it and not seeing a "simple set theory" grouping, but only after watching you mull over it for a bit.
I did it via a completely different set theory cancellation but ended up in the same place as Simon did with 1,2,3,4,5 restrictions in the corners and the remaining 6789 pattern. Weird, not sure which way Aad was expecting the solve to go.
I have tried playing the puzzle on the link provided, however I cannot open it. The same goes for all the other puzzles. Can somebody please tell me why I cannot access the puzzle? Thank you.
Wow! I noticed the Phistomophelian nature of the puzzle right away. Unfortunately it didn't help me solve the puzzle. Still a little bit proud of myself.
As 'set theory' goes, the angle of entry wasn't difficult. However, if you've never gotten acquainted with 'set theory', this would be right next to impossible.
My limericks are always the cleanest To keep the good feelings between us But when I heard trapeze Rhymed with wallet and keys My best see.ed like Lady From Venus.
Sometimes different sets break in the puzzle. (Mine, for example, were different from both versions of Simon's. I wanted the same number of cells in both sets.) Who knows which set Aad had in mind?
I love this so much. The puzzle itself is nice, but SImon solving 1+(7 or 8) = (7 or 9) by noting the requirement for an even number, and not seeing that 1+7 does not equal 7 or 9, and THEN no doing the 1+8=9 calculation at all. It's so classic Simon, and I'm here for it.
Been watching you on and off for a couple years, I don't watch every puzzle and im not good at sudoku myself, but I always seem to come back to these after a while. Glad you're still making these
I'm usually very bad at set and this was the first time (apart from some phistomefel ring puzzles) that I figured out which sets to use completely on my own
In April 2020 I discovered CTC and Aad van de Watering for the first time. I'll always have a soft spot for Aad's puzzles, as his was the first one I solved here, and I don't think I've missed one since. This one was lovely -- as always.
OMG WOW I GOT A SET THEORY BREAK IN ALL ON MY OWN THIS IS LIKE THE FIRST TIME EVER AND I'M SO EXCITED 🤣🤣 I used rows 1,2,5,8 and columns 3,4,6,7, which gave me a set of 12 digits that had a minimum of 30, and a set of 4 digits that had a maximum of 30, and from there it was fairly straightforward for an 18 minute solve.
@@Mephistahpheles That's where I've been for the last couple of years - I could follow the explanation no problem, but could never make the leap of intuiting to use SET and which sets to use.
I am kind of amazed that I was able to solve this one and this a great example of how my skills are shaped by CTC videos. I started the puzzle thinking that it shouldn't be too difficult to find restrictions in the circles since there are so many arrows. Then I quickly realized that it wasn't a trivial solve. So then I remembered what Simon always says that if nothing is obvious then the answer is usually set. But here is where I usually struggle, finding a good set that yields the type of relationship from where deductions can be made. But I got it right this time and was able to solve the puzzle. CTC brings joy to your day!
I just want to say I really enjoy your videos, I'm going through a rough patch but seeing a new upload from you really cheers me up. Your simple joy when solving puzzles is infectious. Mark too!
@@lukebpowell keep finding activities/people/entertainment that “lift” you up every day. This channel helps me a lot! It’s like my friends, Simon and Mark (and the kind people in comments) come by every day to cheer me. I like to watch humorous RU-vids, lots of cute funny animals and hobbies that take my mind off the rough stuff.
Just over an hour for me. I got a bit stuck in the middle not noticing the simple fact that certain digits had to always be different and forcing a lot of other digits. Once I stopped being blind it was smooth sailing.
So sorry about your fallen trees! The scrabble grams are amazing!!! So scrabble grams guy and one of the birthday people are from Georgia! Yay Georgians!! I think I would definitely like (and probably already have had) wine with chocolate cake. I think it would go well with a red wine 🍷- maybe old vine Zinfandel? I like the coinage “Phistomefelian!” Always ❤set theory resolvable puzzles! And the pure joy Simon expresses when solving them!!!
I'm usually one to despise puzzles that require finding min-max relationships with well-chosen sets of digits, but surprisingly, I luckily stumbled on the solution and found this one fairly enjoyable. Or was it because I'm getting used to this style? Either way, I can imagine the frustration of running in circles looking for something interesting around these scissors while not having this very useful set theory tool in hand.
I finished in 99 minutes. I knew that SET must have been involved and I was so close to coming to the answer. I had everything set up and I just didn't think about that green was 45 more than orange. I had to watch the video and it sucks that I couldn't find it. The rest of the puzzle was not easy, even after doing on SET. Great Puzzle!
It took me a bit longer to commit to the SET path, but I found a slightly different variation where you start with rows 3467 and columns 3467 in the same set, and compare them to all the boxes except for the middle one. It's a bit messier to balance the colors but you get to the same position in the end without having to add 45 on one side of the equation or duplicate the logic with symmetry.
That is what I did too! I was trying to spot what to do and decided to embrace madness comparing 8 sets of digits. Had a little gasp when I got the 3 in the middle of the puzzle.
Loved this puzzle and this video. It’s great having both, I always try myself as much as possible then come to the video when I goet stuck. This was the first time I’ve broken into a puzzle using sets on my own which I was really happy with but still needed simon to spot what the 3 Xiang meant. :) Thanks for a great solve and I’m so impressed at how quickly you do all the sodoku at the end. 🎉
I am so proud of myself for this puzzle: I stumbled for several minutes and then I though "I don't get it, let me see Simon's solve"... and then, before I finished that thought "Wait, every time I cannot make a start, it's because it's set... let me see"... and it's the first time I solve a set-based puzzle without help! Now on to watching your solution, and see if you did something completely different...
