“Every time you do a Phistomefel puzzle, you’re in the presence of genius...”. True! The genius is called Simon... One of the joys of this channel is the real and heartfelt respect you show for these amazing puzzle setters, but the other joy is seeing your genius solving these sudoku puzzles. Deep, deep, deep respect for you, You solve these extremely difficult puzzles with relative ease and a smile on your face and even find time to explain the logic behind the madness to us normal simpletons.
We definitely need a "How I set a puzzle"-video from Phistomefel eventually. Possibly as a grand Finale. Or a guest spot in your new podcast. His puzzles definitely have a special place in this channel.
@@andykey78 Don't know. I think Phistomefel was referred to as a he when simon talked about their contribution to the latest app, but I could be wrong. Not important anyway.
Slightly easier break-in: Highlight columns 1, 4, 6 and 9. While preserving the sum, try to turn that area into horizontal rows. You can do it except for exactly 2 problem cells. And you can already guess which cells those end up being.
That is beautiful. I bet you the devil himself did not realise this alternative break-in. The 9x9 grid has so many isomorphisms of sets of digits flowing from Phistomefel Set Theory that adding well placed arrows turn isomorphisms of those sets into equalities of sums. Idea for setters: use this idea to construct *inequalities* with kropki, thermos or other devious means.
@@longwaytotipperary I have a special talent to sound profound but what I say could be said much simpler by someone with more talent. I am also a mathematician and try to be pedantically precise. I am also incredibly vain 😎
I have to wonder if Simon would have found this break-in nearly as quickly had he not known who set the puzzle. The approach definitely seemed to include an early element of "well this is Phistomofel so let's try set theory". Entirely reasonably of course!
When I started binging this channel I was like "these guys are genius, so many techniques, so good at spotting the right numbers..." Now I'm more like "hey! You missed the 6 over there! Look at that x wing, what are you doing? Still haven't looked at the 6! Oh god, why?" 😂
We are the beneficiaries of a free graduate school level education in logical reasoning combined with unfailing humanity. And we make friends, read each other's comments and recognise so much in each other: OMG, that is *me* what s/he just said!
I always find it amusing when I see a move that you can make by sudoku but when Simon finds it he uses some dizzying logic. I think the reason is that he has to gear his brain for the deep stuff so much that there isn't bandwidth for the easy stuff.
“Where’s the 6 gonna go in row 3? Box 2 is full on row 3, there’s a 6 on the arrow in box 1, you have to have the 6 in row 3 in box 3! Simon look at row 3! Look, that forces a 1 onto the arrow and...”
I always enjoy watching Simon solve a puzzle that I can stare at for hours with no luck. Even if he doesn't feel like he's solving quickly sometimes, he's still finding the logic and solving them faster than most!
Now I'm thinking about Jovi_al's setting video, where he said that difficulty isn't a synonym of beautiful. I usualy love Phistomefel puzzles (or should I say watching Simon do it) but this time, I thought that it was just to complicated. As Jovi_al said, the solver be rewarded after figuring out some great logic
Another glorious episode of Simon battling his foe Dr Moriarty. Simon, a good Christian, loves his enemy, so much is clear. I am proud to report from the home front that I did find the break in, also with set => sum logic. Simon was so right to spot the arrows pointing along the perimeter; that *must* have been Phistomefel's intended telegraph. Today the universe was not so much singing as featuring some tortured music, like the first movement of Mahler's Sixth. Beauty is sometimes not easily seen as beautiful but emerges from paying the price of a long and sometimes desperate battle. The battles most worth fighting turn out to be not with the enemy but with one's own self. I am learning ethics, morality and spirituality from watching a guy solving puzzles. How weird is that? Simon, have I told you that I love you?
The Phistomefel puzzle,which Simon recalls in the 13th minute of this video, and which leads him to consider using set theory for the breakin, is the puzzle ‘Little Killer Arrows’. which was featured in the ‘The most beautiful question ever asked’ ctc episode in March this year. In both of these puzzles the breakin process can be described as follows. 1. Start with an uncoloured grid and bi-colour an equal number, n, of rows (red) and columns (cyan or blue) to cover as many circles and arrow lines as possible. This requires a bit of judgement or possibly trial and error. No intersection cell of the coloured lines should contain a circle. 2. Uncolour the n*n intersection cells. 3. For each coloured circle. Ignore if any part of its attached arrow line has the same colour as the circle. Otherwise, uncolour the circle, then colour any uncoloured attached arrow line cell, with the circle’s colour and uncolour any attached arrow line cells that were already coloured. At the end of this process, the sum of the remaining red cells must equal the sum of the remaining blue cells. In the March puzzle, it is found that, after colouring rows 1 and 9 and columns 1 and 9 and following the above process, 12 red cells, and 6 blue cells remain. The minimum sum (two times six factorial = 42) of the 12 red cells is then found to equal the maximum possible sum of the 6 blue cells and the breakin follows. In this puzzle, the above process, after colouring rows 1,4,6,9 and columns 1,4,6,9, ends with just one red cell and one blue cell which therefore must contain the same value. Both are great puzzles, but both take a while to solve!
My wife asked if I was coming upstairs after dinner. I tried to say something eloquent but the only word she heard was Phistomefel. It was enough, she understood it would not be a short video.
I'm at the point where I can follow non-Phistomefel Ring set theory well, which is an improvement. Still haven't been able to spot it in a puzzle myself yet.
Amazing that Phistomefel cam make puzzles with such ridiculous break-ins and then consistently keep the difficulty going through out the rest of the puzzle.
57:29 Fortunately I jumped straight to SET because it was Phistomefel! 😂 I added a couple of extra rows and columns compared to Simon's version which led to everything cancelling to the exact same point, but his logical twist was a beautiful variation. Sublime in how the two thermos then forced so much and opened the puzzle up.
I don't think I could find that break in in a million years. But after watching Simon explain how the thermos connected I tried to solve the puzzle after that and it didn't feel very difficult. Challenging for sure but nothing too exoteric is needed to get to a solution. The takeaway though is that I guess I need lots more practice to understand the geometry and relationships of the clues provided. How do you even begin down the journey of taking rows 1 and 9 and working around the grid until you find something useful? I was even more impressed because Simon started by looking for leftover/common digits with set theory and then switched to looking for equivalent sums! This was a brilliant solve!
Happy to report that I saw that break-in right away. Simon has done a similar break in before and the arrow circles around the perimeter of the grid were a dead give-away
'Now I'm going to show you something that's actually intelligent'....@53:40 of a Phistomefel puzzle...makes me pause my popcorn eating to wait in anticipation!
About 1:01:30. I think the easiest break-in is to note that there needs to be a 3 on the arrow on R6C2 or R6C3. Therefore R1C1 needs to be a 3, it's the last available slot on the first column. That resolves the 2, 3 and 4 on box 3. Finally, where do 1 and 2 go on column 9? Considering that 1 is already locked on R7C9-R8C9, the R9C9 can't be a 2 because of the thermo. Therefore R7C9-R8C9 is a 1-2 pair. I think the puzzle becomes easy then.
You can start a bit easier by taking sets: S1=r1+r4+r6+r9 and S2= c1+c4+c6+c9. After removing arrows you end up with 4 squares in box 5. It could also be solved easier if you remembered later that r4c5+r6c5=r5c4+r5c6.
27:41 is my time. You just had to watch for where 123 and sometimes 4 went on the arrow stems. This often combined with other cells that could only be 123 and the puzzle quickly broke open. Haven't watched the video yet, but break-in was basically given. Not sure what the title is about. Sure, it's kind of an interesting idea, but it's telegraphed really well. edit: Simon, you overcomplicated the break-in. It's actually quite simple. Just shade rows 1, 4, 6 and 9 in red for example. Then shade the columns 1, 4, 6 and 9 in green. These are where most of the arrows are located. Remove all cells that have both colours. Those cancel out. Then remove all the arrows where the circle is a different colour than the stem. You'll end up with 4 squares in the center box that you eventually found. By subtraction, the tips of those arrows must be equal. Done. Took me under 90s. Maybe I got lucky. But all those arrows on the same rows and columns were just screaming out at me.
Solved it in 34:23 with just some direction to confirm it was set theory to begin with. The break-in is bonkers. To have prepared and planned that in advance and have the puzzle unravel from that is absurd. Every time I do a Phistomefel puzzle, I am forever amazed that he keeps making puzzles that make me absurdly impressed (like Sisyphus) at the fine detail that goes into crafting the path of solution so that you're rewarded for the right path and can't just brute-force them at all. Kudos on the solve, and on yet another masterpiece in the channel
I think we need to start scoring the difficulty by the number of planes passing during the solve. Can you feel the temptation around 45 minutes towards bifurcation...
Very proud I got this one. Had the break in after almost half an hour (used some "Phistomefely" set theory with R1,4,6,9 and C1,4,6,9). Took me 84 minutes total, but what a genius puzzle, I loved it :)
@ 0:27:44 you remove 9 from box 5 cell 6. but you didn't continue to examine the cell. It also can not be 8 as 4 is already on the line. this would only leave 6/7 as options and give you 2/3 as options in box 5 cell 2. I would say that is your biggest weakness. once you get a single deduction on a cell you don't continue to look at it but move back to the general picture.
Same here - I was wondering how many other 4s he would put in column 9 and how long he would stare at them trying to work out what a 4 would do to the box/row. It's a new sport. Mind you I would never have got that far in the sudoku. That break-in was indeed crazy. Paraphrasing Darius Sawyer 'Phistomefel=Set theory' (probably).
I used a different solve path. Once you have drawn the X in two colors that you know are equal, I not only used that information to connect the two thermos, I also used it to find that the 5 box runs on opposite edges of the grid had to sum to 57 or 58, and was able to squeeze that knowledge into solving the whole puzzle.
Spoiler: The idea to have the geometry of the grid force the two ends of the thermos together is genius. It seems so elegant, but I never would have thought something like that was possible.
You can also get the break in by starting with columns 2, 3, 7 and 8 and subtracting rows 2, 3, 7 and 8. The rest follows similarly but you get straight to the row/column 5 pattern
This is how I did it; felt more natural. Well, rather than subtracting them I equated them, and eliminated commonalities like their intersections and shared arrows/bulbs.
It is the same break-in really, so you didn't miss anything major. But i found this way of doing it far clearer: Highlight rows 1 4 6 9 purple, and columns 1 4 6 9 green. Remove any overlap and arrows you can, that are outside box 5. You now have a little colourful box drawn in box 5. :) Remove the relevant colouring on the arrow that's fully in box 5, then remove remaining overlap. You now have a virtual arrow from the other "planet" in box 5, in R4C4-5. And then the thermo connection as you did. The virtual arrow isn't necessary, but i found it cute. :) Also, the kind of "bent" arrow this grid is filled with, absolutely screams SET to me. The above break-in was genuinely how i did it, and with little hesitation.
A bit late, but I had a much easier break-in for the first 27-and-a-half minutes of the video, taking only about 5 minutes to determine the connection between thermometers. I did this by selecting 2 more rows/columns than Simon to compare as equal sets. Selecting Rows and Columns 1/4/6/9 as two sets (rows vs columns): 1. After removing the overlaps, you are left with two sets of colored cells that all fall onto arrows. 2. (optional) For any arrow that the circle and length of arrow are opposite colors, cancel them out as well. 3. (optional) This leaves only 4 colored squares in the central box, 2 of each color. Their sums must be equal to each other. 4. The value in each circle is equal the the length of the arrow. Remove the color of each circle and fill it in across the length of their arrow, and remove any cell with both colors. 5. This leaves only r3c5 and r4c4, which must now be equal in value. You technically only need to follow Steps 1, 4 & 5 above. Steps 2 and 3 merely illustrate the solution method and simplify Step 4 slightly.
There is always that question: do I try this one or I just watch the video? Usually, like for a lot of us, the length of the video is the reference. But this time, I heard that it is from Phistomephel. Sorry I don’t have a full day unfortunately to try to solve it by myself. I will enjoy the video though. Thank you.
A full day?!? I wish I had that level of skill! Pretty sure I could lock myself away like some kind of sudoku monk and all anyone would find decades later would be my skeleton and an empty sudoku grid!
Ya' spent all that time establishing the key equalities in the center, and then left half of those cells unfinished for most of the solve. You're brilliant at finding subtle deductions, Simon, but you get so excited by the next gem that you move on before you milk the first one dry.
In mathematics there are the trailblazers who brim over with ideas (the Eulers, Galois, Riemanns etc) and the careful sweepers who tidy up results, bring rigour to bear (the Cauchys, Weierstrasses etc) and together hey enable us, consumers of other people's genius, to make progress on incredible but reliable foundations. In master class Sudoku like Simon and Mark give us, both forms of genius are required but if I have to choose, I'll opt for Euler. Scanning I can learn myself much earlier than understanding the problem of the puzzle itself.
I may be missing something (quite likely) but the equality he works out for the central box at the start is that r5c4 + r5c6 = r4c5 + r6c5 (grey = yellow). From 29:10 he has half those filled in (r5c4 = 5 and r6c5 = 9) and the other two reduced to two options (r5c7 = 6 or 7, r4c5 = 2 or 3). Of those options, either 2 and 6 or 3 and 7 would work for the equation. So I'm missing how the equation helps at this point?
Though the break-in I used ended up being the same overall as Simon's, I feel the way I arrived at it was a bit more natural. Consider Rows 2, 3, 7 and 8. Also consider Columns 2, 3, 7 and 8. Across all of these, you'll notice the same pattern of 3 arrows and 2 bulbs offset (i.e. rows 2 and 3 contain exactly 2 bulbs and 3 arrows). I used one color to highlight the rows, and another to highlight the columns. Now, we can immediately equate them as having the same sum because there are 4 rows and 4 columns. Let's call the rows Purple and the columns Green. We can first off remove the intersections safely, removing colors from them without affecting the overall equation. (Cells r2c2, r2c3, r3c2, r3c3 in Box 1; r2c7,r2c8, r3c7, r3c8 in Box 3; r7c2, r7c3, r8c2, r8c3 in Box 7; and r7c7, r7c8, r8c7, r8c8 in Box 9). Next we can remove each instance of a bulb of one color that relates to the arrow of another color, since a bulb and its arrow have the same total. This removes color from the bulbs in r1c2, r1c3, r2c9, r3c9, r7c1, r8c1, and r9c7, r9c8 along with their associated arrows. This leaves us with a total of 8 squares of green and 8 squares of purple in a kind of windmill pattern. We can consolidate the 'off center' green and purple squares that lie along an arrow, and replace the sum of those cells with their associated bulb (i.e. making r5c1, r5c9 green, and r1c5, r9c5 purple). This will end up having 6 purples and 6 greens, with all purples aligning in Column 5 and all greens aligning in Row 5. Now this leaves us at Simon's logic, wherein we can recognize that since green = purple, and r5c5 is common to both, the remainder of those rows must also be equal. Therefore r4c5+r6c5 = r5c4 + r5c6.
I'm very happy with myself in that once Simon had put the grey and yellow in cell 5 I was able to spot the thermos being tied together faster than him... However I would have had no chance whatsoever at getting to that point in the first place. Incredible puzzle!
Alternative solve at 52:40: In row 5, we know from the initial break-in that r5c1+r5c2+r5c3 = r5c7r5c8+r5c9... The only way to maintain that equation is if r5c3 = 6 (if we make it 7, then there's no way to reach at least 17 in r5c7+r5c8+r5c9).
It was only because of the title of this video that I resorted to set theory fairly early on, else I probably wouldn't even got the idea myself... So thanks for that! Now I can still be a little proud of myself
51:45 He always comes to conclusions by the most interesting route. It also can't be 4 as that sees the only two places for 4 in box 3, which I'd been looking at forever. Though the fact that removing 4 from the circle did nothing, kept me from going too crazy lol.
This is fascinating. I started doing Sudoku puzzles in the newspaper when I worked in a restaurant. I’ve never seen a puzzle like this and I feel rather dense but I subscribed anyway 😊
I also got in by the R3C5 = R4C4 but got there more directly. Take columns 1, 4, 6 and 9 then use the arrows to move the sums to rows 1, 4, 6 and 9; you will immediately see that R3C5 must equal R4C4.
Although I think I would not have been able to get the break-in, I'm proud of myself for immediately seeing the pattern of important cells around the perimeter and knowing there was some kind of SET going on...
@26:38 Very cool (now ya have an X-Wing on 9s in rows 1 & 9 in boxes 2 & 8), so ya take a nine out of that r1c3 circle cell. [Along with other things, I'm sure] Cool puzzle (and cool patterns) lol. 😁 Edit: No other 9s (other than those) in row 1 & 9 in other words, that's for sure. So, if ya look at the possible placements of 9 in box9, they're in row7 in two spots (the top) - which puts box7's 9s in row8 (the middle) [[becuse they're in row9 in box8 (the bottom)]]. Super cool.
58:14 Instead of the impossibility of two 9s in row 5, there is a much more pedestrian reason why the 2/3 in box 5 cannot be a 2: it would make purple and red equal. [edit] A little later: where does 2 go in row 9? It cannot be on the circle of the arrows or on the thermo, 'cos 1 cannot be in the bulb by sudoku. Ergo, 2 in row 9 is in box 7. At this stage any edible fruit is low hanging, I think.
33:31 The arrow in box 3 cannot add to 7 because only 3+4 is available which clashes with the 1/2 pair. I *am* getting better at spotting minor deductions that my hero Simon misses. Praise be!!!
Something was missed (I have no idea what) becuse that arrow in row9 of box7 was never used. (I purposely filled that "4" that ended up on there as the last digit in the grid (that 4 just happened to work with an entirely filled-in grid. In other words, box7 was filled in last (the two digits on that arrow). Great job, Simon. [Something was missed though, (maybe that "1" being placed on the two arrow cells in box9), I don't know. It sure worked out great, though, Lots a' pairs happenin' lol. 😆 Edit: well, maybe it *was* used (the circle part of it was used ).
@33:31 simon: "what am i missing here" me: "how the 'devil' should i know... you tell me... i couldn't see anything you already did... till you did it!" that is... situation normal... good.. everything is still right with the world
Really fun break-in on this one! Proud to have gotten it in just under 20 minutes. Unfortunately, the rest of the puzzle was quite a slog for me; ended up finishing in just under two hours.
Wow solving this by HILO parity was insane..doable but alot of branching/depthsearch even tho they were short....incredible... The HI LO play eas phenomenon esp in box5
I keep seeing this in the comments, and I don't understand how it helps? Greys and yellow sum to either 11 or 12, but that's just as apparent from the pencil-marks. What am I missing?
56:59 for my solve. I can't believe I've beaten Simon on this one. Actually, the break-in took me only three minutes to spot and is much easier than showed by Simon. I just added columns 1, 4, 6 and 9 and systematically replaced arrows cells by their counterpart and ended up with rows 1, 4, 6 and 9 with the sole exception of both thermo cells to be inverted, which implied they had same value. The offset arrows really yelled at me to do that, so I started with columns 1 and 9 and quickly realized I had to add columns 4 and 6. But gosh did I struggle with the rest of the puzzle!
You do remember that, if a box can only have a particular digit in a single row/column, that digit can't be in any other box in that row/column? You had a bunch of eliminations that you ignored for ages
I was wondering for a moment if the set theory was going to end up defining the middle box as a magic square. It didn't, but I'd like to see that accomplished.
@@jsharvey1961 Oh, absolutely! Don’t get me wrong, Simon is amazing - it’s because of his videos that I’ve mastered the skills to get through these puzzles on my own in the first place.
wow, I think I would have explored the set theory, but I am not sure in a million years I would have carried it that far. I would have thrown it out as a red herring.
“Every time you do a Phistomefel puzzle, you’re in the presence of genius...”. True! The genius is called Simon...
One of the joys of this channel is the real and heartfelt respect you show for these amazing puzzle setters, but the other joy is seeing your genius solving these sudoku puzzles. Deep, deep, deep respect for you, You solve these extremely difficult puzzles with relative ease and a smile on your face and even find time to explain the logic behind the madness to us normal simpletons.
Ditto what Theo Van der Steen said!!!
I do enjoy watching a great solver and explainer solve a puzzle by a great setter.
I spotted, before Simon, a really clever trick that would have broken the puzzle wide open. My trick was completely wrong, but that's not the point!
We definitely need a "How I set a puzzle"-video from Phistomefel eventually. Possibly as a grand Finale.
Or a guest spot in your new podcast.
His puzzles definitely have a special place in this channel.
Step 1: So you’re going to need to sacrifice a goat...
Are you sure Phistomefel is a man? 🤔
@@andykey78 Don't know. I think Phistomefel was referred to as a he when simon talked about their contribution to the latest app, but I could be wrong. Not important anyway.
@@andykey78 you're right, might be some kind of Sudoku deity, not bound to our conventional societal constructions
Narrated by Morgan Freeman bc Phistomefel doesn't want his voice heard by mere mortals 🤫🤗🤗
Phistomefel is easily my favorite constructor to watch Simon solve.
Saaaame
The Holmes and Moriaty of Sudoku.
They got chemistry...
Totally normal cat!
I have a hard time deciding if my fav is Phistomefel or if its watching him solve TotallyNormalCat.
It was an absolute joy to contribute to that puzzle pack and say something about a TH-cam channel that means a heck of a lot to me.
You know Simon's having a tough time when he starts Goodliffe-ing.
Slightly easier break-in:
Highlight columns 1, 4, 6 and 9. While preserving the sum, try to turn that area into horizontal rows. You can do it except for exactly 2 problem cells. And you can already guess which cells those end up being.
That is beautiful. I bet you the devil himself did not realise this alternative break-in.
The 9x9 grid has so many isomorphisms of sets of digits flowing from Phistomefel Set Theory that adding well placed arrows turn isomorphisms of those sets into equalities of sums. Idea for setters: use this idea to construct *inequalities* with kropki, thermos or other devious means.
Very clever and elegant.
@@amoswittenbergsmusings I have no idea what you're saying - but sounds brilliant!
@@longwaytotipperary I have a special talent to sound profound but what I say could be said much simpler by someone with more talent. I am also a mathematician and try to be pedantically precise. I am also incredibly vain 😎
@@amoswittenbergsmusings I'm impressed! :-)
I have to wonder if Simon would have found this break-in nearly as quickly had he not known who set the puzzle. The approach definitely seemed to include an early element of "well this is Phistomofel so let's try set theory". Entirely reasonably of course!
After 40 minutes of staring at the puzzle I managed to find that break-in.
I'm very proud of myself. 🤣
When I started binging this channel I was like "these guys are genius, so many techniques, so good at spotting the right numbers..."
Now I'm more like "hey! You missed the 6 over there! Look at that x wing, what are you doing? Still haven't looked at the 6! Oh god, why?" 😂
I have an ointment for that?
We are the beneficiaries of a free graduate school level education in logical reasoning combined with unfailing humanity. And we make friends, read each other's comments and recognise so much in each other: OMG, that is *me* what s/he just said!
I always find it amusing when I see a move that you can make by sudoku but when Simon finds it he uses some dizzying logic. I think the reason is that he has to gear his brain for the deep stuff so much that there isn't bandwidth for the easy stuff.
“Where’s the 6 gonna go in row 3? Box 2 is full on row 3, there’s a 6 on the arrow in box 1, you have to have the 6 in row 3 in box 3! Simon look at row 3! Look, that forces a 1 onto the arrow and...”
I always wondered how thermometers sound. 25:50
i laughed so much
I always enjoy watching Simon solve a puzzle that I can stare at for hours with no luck. Even if he doesn't feel like he's solving quickly sometimes, he's still finding the logic and solving them faster than most!
I love the smile when simon says do have a go knowing he is kidding..
no joke. i often try the puzzl b4 watchin
Phrase of the day (5:39):
"In clover" - in ease and luxury
Astonishing. It makes me wonder just how much more difficult these puzzles can get?!
Now I'm thinking about Jovi_al's setting video, where he said that difficulty isn't a synonym of beautiful. I usualy love Phistomefel puzzles (or should I say watching Simon do it) but this time, I thought that it was just to complicated. As Jovi_al said, the solver be rewarded after figuring out some great logic
he or she? I believe the discord anniversary puzzle pack says she
Another glorious episode of Simon battling his foe Dr Moriarty. Simon, a good Christian, loves his enemy, so much is clear.
I am proud to report from the home front that I did find the break in, also with set => sum logic. Simon was so right to spot the arrows pointing along the perimeter; that *must* have been Phistomefel's intended telegraph.
Today the universe was not so much singing as featuring some tortured music, like the first movement of Mahler's Sixth. Beauty is sometimes not easily seen as beautiful but emerges from paying the price of a long and sometimes desperate battle. The battles most worth fighting turn out to be not with the enemy but with one's own self.
I am learning ethics, morality and spirituality from watching a guy solving puzzles. How weird is that?
Simon, have I told you that I love you?
I am glad that when too tired to follow your logic i went to sleep.
Loved you crunching through this!!
Thanks Simon.
The Phistomefel puzzle,which Simon recalls in the 13th minute of this video, and which leads him to consider using set theory for the breakin, is the puzzle ‘Little Killer Arrows’. which was featured in the ‘The most beautiful question ever asked’ ctc episode in March this year.
In both of these puzzles the breakin process can be described as follows.
1. Start with an uncoloured grid and bi-colour an equal number, n, of rows (red) and columns (cyan or blue) to cover as many circles and arrow lines as possible. This requires a bit of judgement or possibly trial and error. No intersection cell of the coloured lines should contain a circle.
2. Uncolour the n*n intersection cells.
3. For each coloured circle. Ignore if any part of its attached arrow line has the same colour as the circle. Otherwise, uncolour the circle, then colour any uncoloured attached arrow line cell, with the circle’s colour and uncolour any attached arrow line cells that were already coloured.
At the end of this process, the sum of the remaining red cells must equal the sum of the remaining blue cells.
In the March puzzle, it is found that, after
colouring rows 1 and 9 and columns 1 and 9 and following the above process, 12 red cells, and 6 blue cells remain. The minimum sum (two times six factorial = 42) of the 12 red cells is then found to equal the maximum possible sum of the 6 blue cells and the breakin follows. In this puzzle, the above process, after colouring rows 1,4,6,9 and columns 1,4,6,9, ends with just one red cell and one blue cell which therefore must contain the same value.
Both are great puzzles, but both take a while to solve!
Yay! He called it "Chatting the Cryptic". I hope that catches on.
Simon is awesome.
So happy to have contributed to the puzzle pack!
My wife asked if I was coming upstairs after dinner. I tried to say something eloquent but the only word she heard was Phistomefel. It was enough, she understood it would not be a short video.
Thank you for finally including a button with the rules in the browser app!
I'm at the point where I can follow non-Phistomefel Ring set theory well, which is an improvement. Still haven't been able to spot it in a puzzle myself yet.
I've only been able to solve a handful of Phistomefel's puzzles as they are often beyond me, however the few I have solved have been an utter delight.
Amazing that Phistomefel cam make puzzles with such ridiculous break-ins and then consistently keep the difficulty going through out the rest of the puzzle.
39:34 "I hadn't spotted that". Literally went on about it for ages at about 12:00
I don't even need to go back to know exactly what youre talking about here lol
57:29
Fortunately I jumped straight to SET because it was Phistomefel! 😂
I added a couple of extra rows and columns compared to Simon's version which led to everything cancelling to the exact same point, but his logical twist was a beautiful variation.
Sublime in how the two thermos then forced so much and opened the puzzle up.
I don't think I could find that break in in a million years. But after watching Simon explain how the thermos connected I tried to solve the puzzle after that and it didn't feel very difficult. Challenging for sure but nothing too exoteric is needed to get to a solution.
The takeaway though is that I guess I need lots more practice to understand the geometry and relationships of the clues provided. How do you even begin down the journey of taking rows 1 and 9 and working around the grid until you find something useful? I was even more impressed because Simon started by looking for leftover/common digits with set theory and then switched to looking for equivalent sums! This was a brilliant solve!
Happy to report that I saw that break-in right away.
Simon has done a similar break in before and the arrow circles around the perimeter of the grid were a dead give-away
To make things easier for judging difficulty, they could just write phistomefel instead of 5 stars
'Now I'm going to show you something that's actually intelligent'....@53:40 of a Phistomefel puzzle...makes me pause my popcorn eating to wait in anticipation!
About 1:01:30. I think the easiest break-in is to note that there needs to be a 3 on the arrow on R6C2 or R6C3. Therefore R1C1 needs to be a 3, it's the last available slot on the first column. That resolves the 2, 3 and 4 on box 3. Finally, where do 1 and 2 go on column 9? Considering that 1 is already locked on R7C9-R8C9, the R9C9 can't be a 2 because of the thermo. Therefore R7C9-R8C9 is a 1-2 pair. I think the puzzle becomes easy then.
You can start a bit easier by taking sets: S1=r1+r4+r6+r9 and S2= c1+c4+c6+c9. After removing arrows you end up with 4 squares in box 5.
It could also be solved easier if you remembered later that r4c5+r6c5=r5c4+r5c6.
27:41 is my time. You just had to watch for where 123 and sometimes 4 went on the arrow stems. This often combined with other cells that could only be 123 and the puzzle quickly broke open. Haven't watched the video yet, but break-in was basically given. Not sure what the title is about. Sure, it's kind of an interesting idea, but it's telegraphed really well.
edit: Simon, you overcomplicated the break-in. It's actually quite simple. Just shade rows 1, 4, 6 and 9 in red for example. Then shade the columns 1, 4, 6 and 9 in green. These are where most of the arrows are located. Remove all cells that have both colours. Those cancel out. Then remove all the arrows where the circle is a different colour than the stem. You'll end up with 4 squares in the center box that you eventually found. By subtraction, the tips of those arrows must be equal. Done. Took me under 90s. Maybe I got lucky. But all those arrows on the same rows and columns were just screaming out at me.
Solved it in 34:23 with just some direction to confirm it was set theory to begin with. The break-in is bonkers. To have prepared and planned that in advance and have the puzzle unravel from that is absurd. Every time I do a Phistomefel puzzle, I am forever amazed that he keeps making puzzles that make me absurdly impressed (like Sisyphus) at the fine detail that goes into crafting the path of solution so that you're rewarded for the right path and can't just brute-force them at all. Kudos on the solve, and on yet another masterpiece in the channel
I think we need to start scoring the difficulty by the number of planes passing during the solve.
Can you feel the temptation around 45 minutes towards bifurcation...
Very proud I got this one. Had the break in after almost half an hour (used some "Phistomefely" set theory with R1,4,6,9 and C1,4,6,9). Took me 84 minutes total, but what a genius puzzle, I loved it :)
@ 0:27:44 you remove 9 from box 5 cell 6. but you didn't continue to examine the cell. It also can not be 8 as 4 is already on the line. this would only leave 6/7 as options and give you 2/3 as options in box 5 cell 2. I would say that is your biggest weakness. once you get a single deduction on a cell you don't continue to look at it but move back to the general picture.
The amount of time those two 4s in box 3 were eliminating 4s in the rest of column 9 almost drove me insane :p
Same here - I was wondering how many other 4s he would put in column 9 and how long he would stare at them trying to work out what a 4 would do to the box/row.
It's a new sport. Mind you I would never have got that far in the sudoku. That break-in was indeed crazy. Paraphrasing Darius Sawyer 'Phistomefel=Set theory' (probably).
I used a different solve path. Once you have drawn the X in two colors that you know are equal, I not only used that information to connect the two thermos, I also used it to find that the 5 box runs on opposite edges of the grid had to sum to 57 or 58, and was able to squeeze that knowledge into solving the whole puzzle.
Spoiler: The idea to have the geometry of the grid force the two ends of the thermos together is genius. It seems so elegant, but I never would have thought something like that was possible.
The puzzle called 'Moles!' has a much more straightforward version of this trick (also by Phistomefel)
It appeared on the channel very recently.
You can also get the break in by starting with columns 2, 3, 7 and 8 and subtracting rows 2, 3, 7 and 8. The rest follows similarly but you get straight to the row/column 5 pattern
This is how I did it; felt more natural. Well, rather than subtracting them I equated them, and eliminated commonalities like their intersections and shared arrows/bulbs.
It is the same break-in really, so you didn't miss anything major. But i found this way of doing it far clearer:
Highlight rows 1 4 6 9 purple, and columns 1 4 6 9 green.
Remove any overlap and arrows you can, that are outside box 5. You now have a little colourful box drawn in box 5. :)
Remove the relevant colouring on the arrow that's fully in box 5, then remove remaining overlap.
You now have a virtual arrow from the other "planet" in box 5, in R4C4-5.
And then the thermo connection as you did.
The virtual arrow isn't necessary, but i found it cute. :)
Also, the kind of "bent" arrow this grid is filled with, absolutely screams SET to me. The above break-in was genuinely how i did it, and with little hesitation.
A bit late, but I had a much easier break-in for the first 27-and-a-half minutes of the video, taking only about 5 minutes to determine the connection between thermometers.
I did this by selecting 2 more rows/columns than Simon to compare as equal sets.
Selecting Rows and Columns 1/4/6/9 as two sets (rows vs columns):
1. After removing the overlaps, you are left with two sets of colored cells that all fall onto arrows.
2. (optional) For any arrow that the circle and length of arrow are opposite colors, cancel them out as well.
3. (optional) This leaves only 4 colored squares in the central box, 2 of each color. Their sums must be equal to each other.
4. The value in each circle is equal the the length of the arrow. Remove the color of each circle and fill it in across the length of their arrow, and remove any cell with both colors.
5. This leaves only r3c5 and r4c4, which must now be equal in value.
You technically only need to follow Steps 1, 4 & 5 above. Steps 2 and 3 merely illustrate the solution method and simplify Step 4 slightly.
There is always that question: do I try this one or I just watch the video? Usually, like for a lot of us, the length of the video is the reference. But this time, I heard that it is from Phistomephel. Sorry I don’t have a full day unfortunately to try to solve it by myself. I will enjoy the video though. Thank you.
A full day?!? I wish I had that level of skill!
Pretty sure I could lock myself away like some kind of sudoku monk and all anyone would find decades later would be my skeleton and an empty sudoku grid!
@@JacobDGoldman same 😅
speechless.. I wasn't able to break into this puzzle.. and watching the break in.. how genius xD
52:08 and suddenly the 2 positions for 9 in row 4 I've been staring at forever become meaningful with an x-wing.
Ya' spent all that time establishing the key equalities in the center, and then left half of those cells unfinished for most of the solve. You're brilliant at finding subtle deductions, Simon, but you get so excited by the next gem that you move on before you milk the first one dry.
In mathematics there are the trailblazers who brim over with ideas (the Eulers, Galois, Riemanns etc) and the careful sweepers who tidy up results, bring rigour to bear (the Cauchys, Weierstrasses etc) and together hey enable us, consumers of other people's genius, to make progress on incredible but reliable foundations.
In master class Sudoku like Simon and Mark give us, both forms of genius are required but if I have to choose, I'll opt for Euler. Scanning I can learn myself much earlier than understanding the problem of the puzzle itself.
I may be missing something (quite likely) but the equality he works out for the central box at the start is that r5c4 + r5c6 = r4c5 + r6c5 (grey = yellow). From 29:10 he has half those filled in (r5c4 = 5 and r6c5 = 9) and the other two reduced to two options (r5c7 = 6 or 7, r4c5 = 2 or 3). Of those options, either 2 and 6 or 3 and 7 would work for the equation.
So I'm missing how the equation helps at this point?
Though the break-in I used ended up being the same overall as Simon's, I feel the way I arrived at it was a bit more natural. Consider Rows 2, 3, 7 and 8. Also consider Columns 2, 3, 7 and 8. Across all of these, you'll notice the same pattern of 3 arrows and 2 bulbs offset (i.e. rows 2 and 3 contain exactly 2 bulbs and 3 arrows).
I used one color to highlight the rows, and another to highlight the columns. Now, we can immediately equate them as having the same sum because there are 4 rows and 4 columns. Let's call the rows Purple and the columns Green.
We can first off remove the intersections safely, removing colors from them without affecting the overall equation. (Cells r2c2, r2c3, r3c2, r3c3 in Box 1; r2c7,r2c8, r3c7, r3c8 in Box 3; r7c2, r7c3, r8c2, r8c3 in Box 7; and r7c7, r7c8, r8c7, r8c8 in Box 9).
Next we can remove each instance of a bulb of one color that relates to the arrow of another color, since a bulb and its arrow have the same total. This removes color from the bulbs in r1c2, r1c3, r2c9, r3c9, r7c1, r8c1, and r9c7, r9c8 along with their associated arrows.
This leaves us with a total of 8 squares of green and 8 squares of purple in a kind of windmill pattern. We can consolidate the 'off center' green and purple squares that lie along an arrow, and replace the sum of those cells with their associated bulb (i.e. making r5c1, r5c9 green, and r1c5, r9c5 purple). This will end up having 6 purples and 6 greens, with all purples aligning in Column 5 and all greens aligning in Row 5.
Now this leaves us at Simon's logic, wherein we can recognize that since green = purple, and r5c5 is common to both, the remainder of those rows must also be equal. Therefore r4c5+r6c5 = r5c4 + r5c6.
Grab some popcorn and enjoy a phistomefel video
I looked up the word genius and it said "Phistomefel". Every puzzle is a wondrous work of art.
Next in recommendations for me: The Devil's hardest puzzle, 63 minutes. This one 68 minutes. So I guess we have a new hardest puzzle from the Devil.
I'm very happy with myself in that once Simon had put the grey and yellow in cell 5 I was able to spot the thermos being tied together faster than him... However I would have had no chance whatsoever at getting to that point in the first place. Incredible puzzle!
Hahahaha I thought the same thing, but I have no doubt Simon would have spotted it in an instant had he not been explaining everything
@@mohamadalsalman7094 So true.
Alternative solve at 52:40: In row 5, we know from the initial break-in that r5c1+r5c2+r5c3 = r5c7r5c8+r5c9... The only way to maintain that equation is if r5c3 = 6 (if we make it 7, then there's no way to reach at least 17 in r5c7+r5c8+r5c9).
From the initial break-in (at 21:15) we only know the reds sum to the same as the oranges. We don't know the two sides of the reds are the same.
Consider my mind blown. Most amazing break in ever
If Simon was bamboozled, what chance do us mere mortals have?
It was only because of the title of this video that I resorted to set theory fairly early on, else I probably wouldn't even got the idea myself... So thanks for that! Now I can still be a little proud of myself
51:45 He always comes to conclusions by the most interesting route.
It also can't be 4 as that sees the only two places for 4 in box 3, which I'd been looking at forever.
Though the fact that removing 4 from the circle did nothing, kept me from going too crazy lol.
This is fascinating. I started doing Sudoku puzzles in the newspaper when I worked in a restaurant. I’ve never seen a puzzle like this and I feel rather dense but I subscribed anyway 😊
You'll love the channel! :-)
very very few things bring me the truest purest most wonderful form of happiness like hearing simon say "i haven't got a scooby doo".
What a remarkable puzzle. Am not going to beat myself up too much about getting a nudge or two from Simon on this one.
I also got in by the R3C5 = R4C4 but got there more directly. Take columns 1, 4, 6 and 9 then use the arrows to move the sums to rows 1, 4, 6 and 9; you will immediately see that R3C5 must equal R4C4.
Amazing puzzle and a great solve. I was so happy when I realized that the thermos form voltron (join into one longer thermo)!
Although I think I would not have been able to get the break-in, I'm proud of myself for immediately seeing the pattern of important cells around the perimeter and knowing there was some kind of SET going on...
@26:38
Very cool (now ya have an X-Wing on 9s in rows 1 & 9 in boxes 2 & 8), so ya take a nine out of that r1c3 circle cell.
[Along with other things, I'm sure]
Cool puzzle (and cool patterns) lol. 😁
Edit:
No other 9s (other than those) in row 1 & 9 in other words, that's for sure.
So, if ya look at the possible placements of 9 in box9, they're in row7 in two spots (the top) - which puts box7's 9s in row8 (the middle) [[becuse they're in row9 in box8 (the bottom)]].
Super cool.
i cant get enough of you solving sudoku puzzels
"The thermometer now goes boop boop boop boop, boop boop boop boop boop!"
25:52
If i had 7 dogs i'd boop their snoots like this :D
simon: there is nothing at all in this puzzle to go on.
me: This is how I feel in the more advanced puzzles on the various apps. LMAO
58:14 Instead of the impossibility of two 9s in row 5, there is a much more pedestrian reason why the 2/3 in box 5 cannot be a 2: it would make purple and red equal.
[edit] A little later: where does 2 go in row 9? It cannot be on the circle of the arrows or on the thermo, 'cos 1 cannot be in the bulb by sudoku. Ergo, 2 in row 9 is in box 7. At this stage any edible fruit is low hanging, I think.
Beautiful join of two thermos.
Ah yes the Devil strikes again, can't wait for another epic battle from Sudokuman
another 1 hour+ video… awesome 😎
33:31 The arrow in box 3 cannot add to 7 because only 3+4 is available which clashes with the 1/2 pair. I *am* getting better at spotting minor deductions that my hero Simon misses. Praise be!!!
Something was missed (I have no idea what) becuse that arrow in row9 of box7 was never used.
(I purposely filled that "4" that ended up on there as the last digit in the grid (that 4 just happened to work with an entirely filled-in grid.
In other words, box7 was filled in last (the two digits on that arrow).
Great job, Simon.
[Something was missed though, (maybe that "1" being placed on the two arrow cells in box9), I don't know.
It sure worked out great, though,
Lots a' pairs happenin' lol. 😆
Edit: well, maybe it *was* used (the circle part of it was used ).
@33:31
simon: "what am i missing here"
me: "how the 'devil' should i know... you tell me... i couldn't see anything you already did... till you did it!"
that is... situation normal... good.. everything is still right with the world
Really fun break-in on this one! Proud to have gotten it in just under 20 minutes. Unfortunately, the rest of the puzzle was quite a slog for me; ended up finishing in just under two hours.
I see the devil, I click like! Not before the dislike bot unfortunately!
First time I tied with Simon! CtC does make you smarter.
Simon solves another Phistomefel puzzle. It is he that must be frustrated as he cannot stump Simon. Touche!!
Wow solving this by HILO parity was insane..doable but alot of branching/depthsearch even tho they were short....incredible...
The HI LO play eas phenomenon esp in box5
I don't understand why he didn't keep some of the colors. The grey and yellow squares would have helped a lot! Either way, great solve as usual!
I keep seeing this in the comments, and I don't understand how it helps?
Greys and yellow sum to either 11 or 12, but that's just as apparent from the pencil-marks. What am I missing?
I am so excited for this one. I can tell it is going to be good from the length of the video.
Four punctuation marks at the end of the title?!!?
Probably deserved for this puzzle...
Just started the video, but 1 hour for 5/5 Phistomefel seems like an achievement!
56:59 for my solve. I can't believe I've beaten Simon on this one. Actually, the break-in took me only three minutes to spot and is much easier than showed by Simon. I just added columns 1, 4, 6 and 9 and systematically replaced arrows cells by their counterpart and ended up with rows 1, 4, 6 and 9 with the sole exception of both thermo cells to be inverted, which implied they had same value.
The offset arrows really yelled at me to do that, so I started with columns 1 and 9 and quickly realized I had to add columns 4 and 6.
But gosh did I struggle with the rest of the puzzle!
That was something incredible. I could only get some triplets in the middle column.
Cantor would like to have a word with you lol.
The more correct statement would have been that Phistomefel pioneered (or helped to pioneer) the application of Set Theory to Sudoku
Ah Phistomefel... that means there's probably going to be a lot of set theory
What a run of amazing puzzles we've been having lately. Phistomefel does it again!
Another way to look at it is all the arrows cancel out by set theory except for the two arrows with bulbs in box 4
You do remember that, if a box can only have a particular digit in a single row/column, that digit can't be in any other box in that row/column? You had a bunch of eliminations that you ignored for ages
I was wondering for a moment if the set theory was going to end up defining the middle box as a magic square. It didn't, but I'd like to see that accomplished.
Woohoo, first time I’ve solved a Phistomophel puzzle faster than Simon :) Amazing puzzle, remarkable break-in!
Well yes, but you weren't explaining every move for the rest of us and doubling your time either.
@@jsharvey1961 Oh, absolutely! Don’t get me wrong, Simon is amazing - it’s because of his videos that I’ve mastered the skills to get through these puzzles on my own in the first place.
I think Phistomefel himself has used a similar trick before with R1 and 9, C1 and 9, but this takes it further.
20:35 the secret 🤫🤗🤗
53:50 NOW I'm going to show you something intelligent. After an hour! 😂
wow, I think I would have explored the set theory, but I am not sure in a million years I would have carried it that far. I would have thrown it out as a red herring.
Did anyone giggle like an evil Demon before the solve started?