An Incredible Sudoku Discovery

[Music] [Applause] [Music] hello and welcome to sunday's edition of cracking the cryptic and the most extraordinary sudoku discovery by philip newman now some of you may remember philip's name because we covered a puzzle of his a few months ago on the channel which was called tatooine sunset now that generated an awful lot of discussion in the community it was a brutally difficult classic sudoku and the puzzle on the screen is a classic sudoku now we don't do classic sudoku's very often but we are choosing this one with good reason today is of course pi day um it's the uh well it's the 14th of march obviously and if you write that in a certain way 3.14 it's redolent of course of the irrational number that we all know and love um but what on earth has philip done here well as i say this is a classic sudoku and it contains just 22 digits which is a relatively small number but not remarkable in and of itself there are sudoku's that have unique solutions with just 17 digits this one has 22. 22 would suggest it's probably quite a hard puzzle and indeed the testers say this is quite a hard puzzle but we'll get to that in a minute the 22 digits that in this puzzle are arranged rather beautifully symmetrically in the grid what do i mean by that well i mean if you were to rotate this square around the grid um 180 degrees you would find this square and you find there's a digit in both of these squares and that's true for any digit we pick in this grid if we pick this digit rotate it round it's the equivalent of this square if there is a digit in this square this square has a rotational counterpart here so it's a feature of very good sudoku puzzles is that they often have symmetrical patterns to them this one does it's it's nice but it's not that remarkable these 22 digits are arranged over exactly seven rows of the sudoku that's quite interesting but not remarkable except you may think well 22 digits arranged over seven rows 22 divided by seven is often used as an approximation for yup pi so there is a definite pie theme going on but here's the kicker the 22 digits that philip has put in this puzzle are the first 22 digits of pi and they're the first 22 digits of pi in order 3.14159265 etc now my knowledge runs out around here but if you go to the internet you'll find lots of sources this is what rather nice one i found um where you know the the the latter digits are there so two six five you can see three five eight nine seven nine three three five eight nine seven nine three etcetera these are the correct 22 digits first digits of pi in order and apparently this has made a solvable sudoku puzzle so i mean i use the word discovery at the start of this video because that this exists in nature is astounding to me that you can put the first 22 digits of pi symmetrically in the 9x9 grid and that will yield a uniquely solvable sudoku puzzle is it's it's incredibly weird it's incredibly weird it's like it's like a gift from the universe and you know philip has discovered it i've no idea how i suspect uh i think he's a brilliant mathematician and also something of a computer whiz so i mean it's just amazing and i happen to know that his wife's birthday is none other than pi day today so a very happy birthday to philip's wife and i hope that us solving this on the channel goes some way uh to making it a good day for the pair of you um now we'll get we'll get to the rules in a minute it won't take long to explain the rules of this puzzle it's a classic sudoku but a couple of things i wanted to mention before before we get started um over on patreon we have got stop scott strosal's solution video uh for his tracking the triptych sudoku sudoku challenge and that's definitely worth looking at that is that challenge was seriously hard i found it very difficult and scott goes through goes through his own puzzles there which is always quite an interesting thing to hear so that's we've released that this afternoon we've got the wonders of the world sudoku hunt that many of you are enjoying that's over there too and we probably won't release this today but we will in the coming days release a video marx made of him attempting to solve last week's six times crossword so monday through saturday in an average of six minutes per puzzle uh i won't tell you whether he achieved it or not but i will tell you it's worth watching especially if you have any interest in cryptic crossword solving um because it's pretty humbling and i say that as somebody who is you know who is okay at solving cryptic crosswords myself it's it's baffling how quick he is um so yeah do do have a look at that if that might float your boat now what are the rules of this puzzle they are normal sudoku rules apply i.e we've got to put the numbers one to nine once each in each box column and row and that's it so do have a go at this yourself if you're new to the channel you may not be aware but you can always play the puzzles yourself you just click the link under the video it will take you to a page that looks identical to this one whereupon i get to play let's get cracking and see how we can solve this puzzle i can put a 3 in the grid there straight away there we go we can solve it 9 in the grid straight away that's just these 9s interacting 3 up here straight away can't i'm not going to pencil mark where a one can only go in three positions in box three i don't like to do that in classic sudoku this seven is giving me a seven here so those squares now i've got to be one two and four in some order and in fact look we've got a two and a four in column seven already so that's a one and we can get rid of the one pencil marked from these squares um what else have we got here we've got two just use the pencil marks two and the two's there place the two in this square six now has become powerful look in row four because it can't go in these squares it's definitely not in those squares so it's got to go in here these squares are now one four and eight in some order can't put one here can't put four there this square must be a seven by sudoku just to complete the row these squares are one four and six in some order and we have a one and a six already in the column so this is four this is a one sixth pair this is a very unusual for me to have so much of the grid done uh this early on in the solve um but it's a pleasant change uh five and eight have to go into this row to complete it we've got a five here five and eight fives in one of those squares as is nine there's a nine in one of those squares too so let's shift the pencil marks around um five nine four has to be down here now ah this is nice so oh by the way if you're not used to my pencil marks fours in the corner of cells like this this is box logic so what i'm saying here is that in the box that the pencil marks appear in these corner pencil marks the four can only go in two places in that box here or here where i put digits in the center of a cell like this one that's cell logic not box logic what i'm saying about this particular cell is that it can only be five or nine and these this sort of combination of pencil marks is how i solve all puzzles basically um so four has to go here by sudoku that gives me the 4 and the 2. so again i can see that 2 is in one of three positions here so i could do that but i don't like to in classic sudoku in variant sudoku i will do that all the time but not in classic sudoku unless i get very badly stuck eight has to be in one of two places let's put it in like that one has to be in two places now in box three because of the one we've now got down here [Music] okay and we now we're now running into a bit of an impasse i suspect three has to be in one of those two cells two four four ah yeah look four in box two where does it go it's got to go here by sudoku which places four here which means this is a 4 and we get a 1 8 pair in box 4 2 and 6 have not been placed in box 1 yet where do they go they're gonna have to go into those two squares and in fact i'm now seeing i didn't see it before but twos the two has to go there so the six goes here that two will allow me now to pencil mark the twos into those two squares i'm happy to pencil mark into two squares in a box and these squares have got to be seven and eight to complete the column eights are an x swing now in these positions look what do i mean by an x-wing well if we if we look at the eight positions here in the finished solution we'll either see an eight in this square and if we do we'll see one in this quest we'll either see the both of these squares being an eight or we'll see both of those squares being an eight one of those things must be true now that means so this is where the x-wing gets its name because you can sort of do a slash of an x down here and a slash of an x down here but that means that there can't be any more eights in any of those squares because if we do try and put an eight here for example what will happen we'll have to put two eights into those squares and that will break the rules of sudoku so don't do that that's naughty so now we should ask where the eight goes in row two it's not here so there's definitely an eight in one of these two cells over on the left hand side [Music] okay so what do we do now is this where we're going to grind to a complete standstill it might be um this column maybe we've now got six digits in this column oh no i haven't look i've got six here but i can do better than that six and one so this this has got to be four and seven and the four can't go here so the four and the seven go in this isn't a four these squares are one and eight to complete the column so we've actually done really well here um there's a small piece of logic we can do with one so if we look at one one is locked into one of four places in box nine now i could pencil mark that but it's overkill but what i do notice is that the ones therefore are locked into row eight and row nine in both box eight and box nine so that allows me to ask where does one go in row seven well like it can't go here it can't go here so it's got to be in one of these three and it's therefore got to be in one of those two so it looks like i'm grinding to a halt now six oh no no i looked at ones let's look at six and seven six and seven have to not be there six and seven have to not be there there's a six seven pair in the corner i can see that's going to do something for the ones but let's just check what the sixes and sevens do over here now so si ah yeah hang on six now has to be in one of those two squares where it joins its friend the one so we now know that these two squares have to be a one and a six therefore they cannot be anything else so we can put one and six into here and now we get a seven into this square which means we get we get an x-wing on sevens in the top this puzzle how can this puzzle exist it's not just extraordinary that it you know you can make a classic sudoku out of a perfect arrangement of pi in order in seven rows of the sudoku but it's actually a really good sudoku it's quite incredible and look sevens i've got an x swing on sevens same logic as with these eights over here so now we know the sevens are either in these two squares or they're in these two squares which means that there's no seven here there's no seven in any of those there must be a seven at the end of row two in one of those cells which actually doesn't look like it's going to be that helpful but the other thing i noticed about this is when i got the six seven pair the one now suddenly is promoted if you like it becomes more powerful it now can't go in those squares or these squares so it must be in one of those and therefore we get the eight and the one figured out um [Music] eight no not quite eights in one of these three which again i won't pencil mark um eight so two four six uh so it's the same digits look two four six seven eight two four six seven eight so what am i going to do now well first thing i'm going to do is i'm going to look along here this square now if we look along this row this square can only be five or nine so oopsie i don't mean to do that five or nine but i i'm going to look at the places where we've got sort of a lot of population density in terms of digits and so this column strikes me as immediately interesting this row i've got five digits in it this row five digits in it this column i've got five digits in so those those are the places where i'm next going to attack the puzzle and see whether there's anything that we can learn so let's look at this column first we need three five eight and nine into the gaps um so this square can't be five or nine that has to be three or eight okay okay i can't see anything else there i may well miss things by the way as we go through that often happens five seven eight nine into this row is in the gaps five seven eight nine this square c's five and seven that can only be eight and nine this square sees five and eight that can only be seven and nine this square sees eight and nine so that can only be five or seven so we've actually done quite well in row two but again and what i'm not seeing is in the cells that are now very restricted i'm not seeing any patterns and it's patterns that we love um [Music] no sorry i'm not let's look at this column we need two five eight nine we've got nothing good there nothing good there nothing oh no we have got two and eight there that's just five or nine um no that was a big disappointment column one has let us all down um now let's have a look at this row we've got one three five and nine along there one ah one one is already in one of those two squares five is here so this square is only three or nine so every time i get one of these pairs i'm sort of comparing it with things that are around trying to see whether i can spot patterns and i'm not doing a very good job um so one three five and nine this square can be lots of things i think this square can only be one or five because it sees three and nine so this row and this row yielded quite a few pairs but nothing ah no no there is something i have you now i have something here because look at look at the pattern of givens here five givens so we've got the same gaps if you like in row two and row eight exactly the same positions open but there's a five here and a five here and that's what this our pencil marks were telling us is where where is the five in row two of the grid it's only in one of the sort of flanking cells of the row where is the five in row eight of the grid it's only in one of the flanks of the row because of the fives here and the fives here and the givens being identical so that means we have a classic x-wing a sort of and this is a proper x-wing these these are x-wings but they are sort of you know a less advanced form this is the full monty because this spans boxes of the sudoku and it's much much harder to see and what does it mean well it means sort of the same thing as we saw with these these patterns because the five in row two is only in one of two places and the five in row eight is in one of two places we know in the finished grid there'll either be a five here and a five here or there'll be a five here and a five here so the thing to realize is that this restricts where five can go in the columns so in those squares these these squares although that one is a bit less important because there's already a five here so we already knew this one couldn't be five but you definitely cannot have a five in any of these now greens not that one that's definitely a five um you can't have a five in any of the green cells now you may be asking why not well it's very simple once you've got your head around it but let me explain how many if we looked at the finished solution to this puzzle how many fives are we going to find in column one of the grid it's not a trick question there's only going to be one that's the rules of sudoku there will be one five in this column how many fives are we going to find in column nine of the grid yep it's one again so in these two columns we are definitely going to find exactly two fives but how many fives are going to be contributed to those two columns by row 2 and row 8. well the answer to that is is 2 because we know that the 5 in row 2 is either in column 1 or column 9 and the 5 in row 8 is either in column 1 or column 9 so the two 5s in row 8 and row sorry and row 2 and row 8 are definitely the two fives that must exist in column one and column nine there can be no more fives so we can't go and try and put a sort of another five up here for exactly the same reason it didn't work when we tried to put an eight wherever i put it over there what will happen is in this row you'll have to put a five here and in this row you'll have to put a five here and that will most certainly give you a problem don't give yourselves problems don't put extra fives in the column we can now look at the green cells knowing they can't be fives and see what they can be so this square if we actually if we look at the column it's two five eight nine so we're just down to two eight or nine oh it can't be eight two or nine in this square can't be eight because we've got this we had the x-wing going on um again it's it's getting close to interesting things but i'm not seeing how to use that one so let's look at this one we've got so if we just have a look at the column we need one two we don't we know it's not five because of the x wings so one two six or seven into this square it can't be seven one two or six that's a bit disappointing um this one i've already looked at that's already six or seven we knew that wasn't five but it was nothing to do with the x-wing it was to do with sudoku um bobbins right let's try this one we've got so again we're looking to place two five eight nine we know it's not five so it's two eight or nine no you rotten thing okay that's this is a total red herring i'm afraid this x-wing has done nothing um [Music] oh dear oh that's very surprising okay [Music] so the best we did was this square became a two or a nine five is a bit restricted in row one now because of these given fives five can only go in one of two places both of which interrupt x swings oh that's right well this is beautiful this is absolutely beautiful good grief i do not know what the name of this pattern is but it is a pattern to me five has to be in one of the red squares in row one well if it's in this one it's interrupting our x-wing on sevens so if we put five here we know the sevens will do that but that once we place this seven it interrupts the x-wing on eights so you'd get so you'd go if you go five here let's do this slowly you have to go double seven on this x-wing and you have to go double eight on this x-wing now if on the other hand you put the 5 here you've interrupted the 8x wing so you have to go double eight there and double seven there so these three squares are always the digits five seven and eight because you're always interrupting both x-wings depending on which one you choose now that is madness and that seems fitting for today doesn't it so so this square this one this one can never be eight because of the eight x wing so this is just five or seven now and this one can't be seven because of the seven x wing so this is just five or eight and we get a five seven eight triple in the row now that might open the puzzle up because now these two squares we're only selecting from one two six and nine this one can't be one two six or nine i think can we do better than that not sure uh this one that one can't be two one six or nine i don't believe it still not it's still no good this is gorgeous though i mean i feel like this must have done something to the puzzle five seven eight nine is now restricted in this column that nine is that what it's done is it got rid of a nine got rid of a nine there used to be a nine in this square didn't there now there isn't so the nine is in nines in one of those squares in in column seven the nine is in one of those squares that gives us an x swing on nines in row seven and row nine it also means nine is locked into one of two places in box three i don't think that does anything so we've got and now we've got an swing on nines down here you could in fact use uniqueness to say this can't be a five or a nine look because if it was a five or a nine you wouldn't know how these fives and nines should be arranged they could be switched round you could put double five here double nine there or you could put double nine here double five there and you wouldn't know which was correct but i won't use uniqueness um i would in a competition um but not not in a video um so so what do we know now we now know that because of this x-wing on nines you can't have any more nines in these squares this can't be a nine so we've got nines that can't be a nine this can't be a nine either so let's check this square actually because this square also sees one four six and seven which actually i can see from the box as well so i'm not sure how good this square is two three five and eight i think are the options the x-wing doesn't end the x-ring on fives doesn't affect this square oh that five does though so we'll take that two three or eight into this square two three or eight which must be close to cracking this is it two three eight ah aha we have our old friend the bent triple here two eight nine yes oh i'm gonna get a digit this digit i'm gonna get now right let us have a look at these three squares because these three squares maybe i'll get rid of the purple highlighting as well now because these three squares if they were all in the same column we would be we would know exactly what was going on there would be a 2 8 9 triple here they are they are not in the same column but they still allow us to do some good logic because we can look at this square and ask okay what if it's two well if it's two this square is an eight if it's nine and that's the only other thing it can be this square is eight so we know for certain that one of these two cells is an eight in the finished solution and that means any cell in this grid that sees this square and this square cannot be an eight now look that means this square which we were looking at just now cannot be an eight let's remove eight from it it's two or three now but more interestingly this square can't be an eight and if this square can't be an eight where do we put the eight now in um in this box we knew from the x-wing it was in one of those two squares if it can't be in this one that must be our eight and we get an eight in the grid in fact that gives me an eight and a one straight away and that gives me a one and a six which means that square now we're down to two or nine we've now got a two nine pair here which means ah yeah yeah yeah look now we know that this square has to be a nine uh using our pencil marks so we can get rid of nine from this square nine oh we already knew nine was in one of those two positions two three and nine down here can we keep this going feel like the puzzle is now right on the cusp of cracking yeah let's have a look at row two i need to put five and seven in row two this square has to be five or seven it's c7 this square is five that gives us a seven here that's important this seven here is part of the x-wing on sevens we found so we get both of those once we place this one it interrupts the eight's x-wing so it forces the eights to be in these two squares this square's a seven obviously just to complete that chain of thought this square must be a six to complete that box we can obviously finish this square now that looks like it's a five um that means that square's a nine this square's a three a two and an eight good grief that gives us the two and the nine at the top just using this two the eight here finishes this square as a five nine nine five and all of a sudden i think the puzzle is almost cracked isn't it um what do we need to put into this box two and three yes we do three and two must go in like that this seven is fixing the seven and six that fixes the six and the one that gives us a one and a five and if i've not made an error that's a three we click tick and that's how to solve a remarkable thing it really is i mean how how can that exist and how can it be such a brilliant sudoku puzzle how many x-wings i mean it was it was beautiful to solve it was really a lot of fun it was just just perfect in terms of difficulty not nearly as barbaric as tatooine sunset was and those are the digits of pi in order it is quite sublime philip i really like that and i i have no idea how you found that but i'm very glad you did and i hope you guys enjoyed watching it let me know in the comments if you are as stunned by that as i am and we'll be back later with another pie themed sudoku for mark's edition so thanks for watching back later as i say so [Music] come down from your home leave your body alone somebody must change you are the reason i've been waiting all these years [Music] home [Music] you

Channel: Cracking The Cryptic

Views: 109,107

Rating: 4.925571 out of 5

Keywords:

Id: TkVwHx2I3F4

Length: 34min 0sec (2040 seconds)

Published: Sun Mar 14 2021

Reddit Comments

[u/MajorVacuum]

I feel like a champion and a thief at the same time. I managed to complete this sudoku in around 9 minutes, using uniqueness in the 59 pairs on boxes 8 and 9.

I know this isn’t ’ethical’ way of solving, but I just recently learned the concept of uniqueness, so I still feel good!

[u/grantmnz]

We don't see ordinary "classic" Sudoku puzzles very often on the Cracking the Cryptic channel these days, so this was a rare treat. It's a really challenging puzzle and the Pi connection(s) are mind boggling.

Try the puzzle yourself on the CTC app or on Sudoku Exchange.