The Second Best Arrow Sudoku Ever

[Music] hello and welcome to wednesday's edition of cracking the cryptic where i am assured that we are somehow going to be continuing the incredible run of puzzles we've seen on the channel over the last two or three weeks um with this puzzle which is called scorpion and it's by udacos so basically we can we immediately know it's going to be an absolutely brilliant puzzle uh just because udokosi's name is on it and i'm trying to work out why it's called scorpion i don't know it doesn't look like a scorpion to me i don't know oh now and now i'm wondering if there's a scorpion technique i might need to know to solve the puzzle that would be embarrassing because i don't think i know anything called a scorpion um but anyway this is an arrow sudoku and one of the testers um wittily described it to me as the second best arrow sudoku of all time and that's because they know that i will broke a no argument about which is the best arrow sudoku of all time i'm not going to tell you which puzzle i think that is the best aristocal full time but i do actually have a favorite and um and yeah that puzzle is completely beyond belief for me but if this really is the second best then it really should be something so we shall have a look at this in just a moment um the only other thing i've got to mention today is is for our patrons if you're a patron of the channel over on patreon do check out the quite approachable sudoku hunt we have had hundreds literally hundreds of correct entries overnight so it only came out yesterday at 4 pm um so i think we've achieved the goal of making it accessible to everybody and we've frankly been delighted with the comments so far as well so it does seem that you were all hoping for something a little bit easier than some of the hunts we've published recently and we seem to have hit the mark so thank you very much to those of you who've commented and yeah if you're a patreon channel do check it out um if anybody can get the answer to us before the 20th of february it will be eligible to well we'll have a chance of winning a prize um now all that said oh the other thing actually aren't on patreon which um uh i did release yesterday was my solve of fisting fails puzzle and i vista mapel's sequence sudoku and i've also been very pleased to read some of the uh the comments on that on that video which have been very witty and uh yeah have made me smile because of course mark solved that puzzle as well and we had somewhat uh differing styles in terms of how we went about it and i'm quite pleased to see many people now referring to mark as pencil mark or one word which amuses me greatly it does amuse him as well so i think it's fine we can just refer to him as pencil mark from now on right let's get on with scorpion by udecos the rules are as follows normal sudoku rules apply digits long an arrow must sum to the digit in that arrow circle that's all the rules so this is this is much simpler today um so how do arrows work well those three digits let's imagine these digits were one two and four one plus two plus four is seven so we would put seven into this cell here um and that's how arrows works we just make sure that whatever we put on the arrow we put the sum of those cells into the circle and that's all of the techniques we should need do have a go at the puzzle the way to play is to click the link under the video as usual now i get to play let's get cracking i mean it looks like something's going on with these this sort of cluster of circles in the middle box i can i can see something interesting immediately actually involving row six because well the first thing i guess we could have said is that these three digits would have a minimum value of one two and three one plus two plus three is six so we know that circle ab initio is at least equal to six but we can do better than that with this circle because these are sort of forming a system in the same row of the grid we can think about row six and note that these five digits here must all be different digits so even if we minimize them we're gonna have one plus two plus three plus four plus five and the triangular number for five is fifteen so this scissor g of uh planets here must add up to at least 15 and therefore this digit must be more than five because we can't make this digit 10. so that square is also six seven eight or nine and we've got similar thing well not a scissor g but we've got a one two three minimum there so that squares at least equal to six this square is at least equal to six that's um three different digits where we're summing in box three look um hang on a moment let's just see if we can see anything else that looks profitable we've got the funny sort of well arrow doing this in box one um we can yeah okay i can say that this digits has got to be at least a five and the reason for that is that what's the minimum i could put the little arms coming out of this circle well again if we made these 1 2 3 and 4 which would be the bare minimum 1 2 3 and 4 add up to 10 so 10 divided by 2 for there are two arrows is 5 so this must be 5 or more and that's worryingly about as much as i can see at first pass through the clues what we can see though is we've got some very short stubby arrows which must so those two digits have got to be the same so whatever is in these two cells must be in one of those three cells and whatever's in one of those two cells don't actually think we can do anything with at all um no right goodness me so we've gotta we've got to do something else here ordinarily i would expect i'd expect set to perhaps be an interesting thing to think about but i let me just think about that point i can see i've got a lot in row six we've already talked about that and i've got a lot in box five maybe it maybe it's so maybe i'm just going to get rid of this highlighting because i'm about to do some set highlighting so if we compare row 6 of the grid that's the set of the digits one to nine with box five of the grid that's a set of the digits one to nine and so what could we now say we can say that obviously the blue set of digits is identical to the orange set of digits therefore if i was to remove this cell which appears in both sets of digits it's both blue and orange if i remove that digit from both sets the sets must still be the same do the same here the sets must still be the same now we could use the arrows perhaps oh sorry why didn't i take that one out as well that one's got to come out as well that's got two colors on it um oh yeah no right let me re just let me just restore that last one because what what i was thinking is that i might want to i might want to try and do some mathematical trick here to help me so at the moment the blue digits are the same as the orange digits therefore if we were to sum the blue digits we would get this a number and that would be the same sum if as as the orange digits so if i remove those two digits from the orange set i could remove this digit from the blue set and say that this the the totals of both sets were the same even though the digits in them would then be different because i'd have removed two digits from orange and only one digit from blue and this is often a trick we have to do with arrow sudoku so i'm going to do that now this is where it's going to get awkward if i remove this from blue then i can remove these three from orange but this will remain in the blue set right so i'm going to do that actually that sounds like a not a silly idea so i'm going to remove these three digits from orange that digit from blue is compensation and it's still true to say that the orange digits sum to the same as the blue digits that's not actually i'm not actually learning very much at all there am i the orange so these two orange digits which must be different so they could be a maximum of 17 8 and 9 have to add up to the same as all of those digits but there are five of those digits it's not very difficult to make those add up to 17. i guess we could we can conclude from that ah okay so that's the deduction the minimum value of those five digits is 15. again it's a triangular number five they've all got to be different so the minimum value of these two squares must be 15 so they have to be at least equal to six in isolation okay what do we do now what do we do now i thought that was going to be quite helpful um so this digit no there's nothing preventing this digit from being in one of those two circles i don't think oh no ah hang on hang on if this digit is not in one of these circles then we could say it has to be in one of those four cells let's say it's this one just for the sake of argument well the implication of that is that then i can remove it from both sets um [Music] well or to put it differently the implication of this digit being here so it it yeah we can think about about this in terms of set actually it's quite nice i'll remove it from i'll remove this digit from this position and i'll replace it with this digit here because i'm saying that this is the same as this digit just for the sake of analysis then i could remove it from both sets because it's got both colors and the implication of this is that this digit is the sum of four digits in box in box five and that's impossible because these four digits would add up to at least 10 and that can't equal 10. so this is not right so i don't think this digit and by analogy this digit can live in the blue squares in box five so they must live in the orange squares so this is a pair that mimics these squares so these must add up to at least fifty well we know they add up to at least fifteen but they add they're actually actually that's a yeah that's a weird point as well isn't it because i've been working very much with sums and i've been saying that the sum of these digits is the same as the sum of the blue digits but now i'm able to go further than that and actually say that whatever that digit specifically is it must appear in one of those two cells which is not which feels a stronger constraint now where do we go from there that's the question so hang on hang on a minute these are these digits here i'm going crazy these digits here are the same as these digits here but they are also the same as blue so this so these the orange plus the blue in box five could be expressed as x plus x which is 2x the secret tells us that this box sums to 45 because it will contain all of the digits one to nine once each i normally only tell the secret to my favorite people but actually today that includes you so if this box sums to an odd number but these squares sum to 2x this 2x is even obviously that that must sum to an odd number i don't actually think that's important but uh it was a little bit of an i thought it might be an interesting thought also wondering now if i can use this arrow somehow oh that's gonna get horribly complicated i can't actually i can't work out how to do this in my head um why can't i figure that out in my head what i want to do is to put these blue cells and this what i want to do is that but then i need to i need to somehow highlight an equivalent set and i can't work out how that's going to interact with the orange cells i've already i've already got let me just think about this for a second so if i make those yellow so that's a set of the digits one to nine sorry sorry brief interruption there it was actually mark on the phone um so um i have actually been away from the puzzle now for about 10 minutes and i can't remember what i was doing what was i doing i filled in that column why on earth was i thinking about this column um let me just try and remember what we were thinking about we'd worked out that the blue squares were equal to the the blue squares were equal to the orange squares and then we worked out that these orange squares were the same as these orange squares oh yes and i know what i was thinking i was wondering whether i could use this arrow wasn't i how do we do that so if we use this arrow the problem here is that i can't quite see how to how do we obviously these colors overlap but we're getting ourselves into a world where we haven't got equal sets haven't we so what we said was that blue is equal to orange so if i now if i want to cancel these digits out i need these to be in a different set to blue just as these ones are right so i need to add this to orange so if we right so in fact i'm just going to take out the coloring there because otherwise i think this is going to get even more complicated i'm just going to remember these digits are the same as these digits but what i want to say is or would it be better to put these ones in and take these ones out that's the other question i've got for myself now hang on hang on a second i think about this um i don't know i'm not even sure it makes any difference let's stick with this so we've got orange in these two squares so at the moment all i'm saying is that the blue digits add up to the same number as the orange digits now if i add the whole of these digits to the blue side of that equation then i've got to add yeah because i want to do math so then i'm going to add 45 to the blue side of the equation so i'm now saying that blue plus 45 because that's the sum of the digits 1 to 9. so that's the sum of all the yellow cells so blue plus 45 is equal to yellow plus orange and that's going to allow me to cancel because these digits appear in yellow and blue so they can come out both sides those do digits sum to the same as that cell so they can come out of both sides so now now we know that blue plus 45 and blue is only one cell now is equal to orange plus yellow blue plus 45 is equal to orange plus yellow blue plus 45 is going to be at least 46 i mean this has to have a positive value so i need to be able to make yellow plus orange equal 46 oh and i can ah in fact there's a degree of freedom you rotten thing that's quite interesting though to be fair that is quite interesting so yellow i can max these squares out as 6 7 8 and 9. and that would be 30. and these squares would have a maximum value of 8 plus 9 that's 17 so the absolute maximum i can make orange plus yellow is 47 and therefore that square has to be a one or a two it cannot be a three or there would need to be some way of making orange plus yellow equal equal 48 which which is impossible so so now surely surely we can i need these to either equal 17 or 16 so they must have a 9 in them and they can't have a 6 in them i need these if that was 8 9 i need these to add up to at least 29 so these must must be from 5 6 7 eight and nine um but they must add up to at least twenty nine this one two is reflecting here these two oh yeah these two squares are the same as those two squares so those come out we can replace the oranges now um [Music] so just got to remember these digits here appear here at the same time as remembering that these six digits add up to that digit plus forty-five huda costs you're crazy my friend um oh wait hang on that that's on a three cell arrow so that's that's beautiful yes okay so this is on a three cell arrow so the maximum digit you can ever put on a three cell arrow is a six if you try and put seven here seven plus one plus two is at least ten so that square has to be not only does it have to be a five or a six but it has to be the low digit contributing to our sum up here you can't have two low digits you can't have a five and a six in this sum or you will never get as high as 29 so the other digits are going to have to be a 789 triple and that is rather beautiful this digit has to yes okay and this did because this is a five five plus one plus two is eight that square's got to be at least an eight eight or a nine so there's a seven eight nine triple in box eight there's a the seven of that seven eight nine triple is in one of those two squares so that square at the top is not a seven anymore this is so i mean it's so intricate isn't it it's really really cunning that square is blue because it's the same as this one so we've got a one-two pair here we've got ah yeah this domino because we're adding digits to a five or a six it must include a one because if we put a two three pair there 2 plus 3 plus 5 is 10. so these squares are from 1 2 and 3. ah yeah okay and now i'm going to do a little bit of work with blue because blue has to be in one of those two squares now by sudoku so blue is on oh blue blue is there i was about to say blues on this arrow that is true but actually it's blue sees itself in row three already so that's blue so blue is in one of those cells in box three and not on the not on the arrow so if blue is one this would have to be a 2 3 4 arrow and that would be a 9 which would make that a 9 actually because we know one of those two squares is a 9. this is lovely it's so intricate um so if but if blue is two then this could be one oh what minimum of one three four so this would this is always adding up to at least eight so that's not six or seven so this is this is eight or nine uh okay what does this mean ah ah this square limiting the value of this square in box one means that we can't make this a one two three four quadruple anymore the two arms of the circle have to be if that's a two these could be one three four five which is 13 which is okay so 13 is the minimum 13 divided by 2 is 6 and a half so there's no longer the opportunity to put 5 or 6 into this circle so so everything we've done has basically increased the values of the possibles for all of the all of the high digits we've got i wonder if i meant to highlight high digits because there are a lot of them dotted around but none of them really line up do they um [Music] there's yeah okay it's possible that that would be an orange digit one of these will have to duplicate and go over there oh seven eight nine in row eight looks a good question to ask we can't put them in there can't put them in there can you ah right look at this little short stubby arrow here this is like a i mean it's actually a beautiful short stubby arrow because it allows us to put a 789 triple in row eight because we've got seven eight nine in these three squares so in row eight those can't be seven eight nine those can't be seven eight nine and this little musical joke here this little short stubby harrow prevents that being a seven eight or a nine because if it's a seven eight nine that's a seven eight nine we've got far too many sevens eights and nines in box eight so the sevens eights and nines in that row go there that's a triple [Music] so that is a triple now we've got in column nine that digit suddenly strikes me as interesting therefore because where does that digit go in box three now it can't go here because this is a 789 triple it can't go there by sudoku you can't put an eight or a nine on a three cell arrow so it goes there so that that is an eight or a nine which means one of these three squares is an eight or a nine ah which would have been if this was a nine it would have been perfect we'd have known we'd have to put it here because you can't put nine on a two sun arrow but it could be an eight possibly in one of those oh so hang on how this cell doesn't this have to be a nine or am i going mad i think it has to be a nine because these two digits are the same so if these if these are nine you can't put nine in those two squares so the nine would go here automatically by sudoku but if these are eight oh no you could put eight in there okay sorry i'm talking rubbish absolute nonsense you just put eight in the circle but the circle can never now be seven so that is true you can't put seven here because i'm gonna have to put an eight or a nine in one of those two squares so okay um so what does that mean what does that mean actually you know what you know what would be ah yes yes yes yes here we go here we go don't look at this digit on its own simon now think about the other two high digits in column nine where do they go in box three they can't go here by sudoku and they can't go on the arrow so they go in those two squares where they are not equal to being one or two so these lose their blue their blueage ability blue hits finds itself locked in the corner these two squares have got to be seven eight or nine because they're the counterpart of these there's a seven eight nine triple in row one there's a seven eight nine triple in box three these digits now can you put now i'm wondering whether it's actually possible to put seven eight and nine on this on the little um on the little fellow here doing his arm actions i think you might be able to because i think you could put 9 8 1 7 2 or something like that so we don't we don't know um [Music] nine although actually having said that what we can we can restrict nine in this box nine in the box must go in those two squares i think because now if you put nine on the out on the arms once you add a digit to the nine you're going to get a 10 and you can't put 10 in the circle so 9 is in one of those two squares 9 is not here now whoa okay well that's rather cool okay now look at row eight where does nine go in row eight there's a nine in one of those two squares so now where what's that digit we've got an x-wing on nines now in these two rows that is that's ridiculous like this can't be how you're meant to solve this you don't hide x-wings halfway through arrow sudoku's but that is that's rather beautiful isn't it look at these nines um why am i excited about this well it tells me this digit has to be eight because um once you're able to lock a nine into or any digit in fact into two cells in a row and that you find the same thing in another row the restriction that the x-wing provides you with affects the columns let me explain that what i want to ask is how many um in the finished solution to this puzzle how many uh nines are you expecting to find in column one and column nine it's a facetious question but it's helpful because it explains the logic the answer is there's going to be one nine in column one and one nine in column nine so that's two nines but we now know that these four cells them spy themselves they contain did i say four nines please tell me i didn't i'm now wondering what i just said am i going absolutely two nines i hope i said two nines i might not have done there is going to be one nine there and one line there that's two nines i'm expecting in those two columns anyway these four cells maybe i was getting confused between four cells and two nines but these four cells also contain two nines so that means that in these columns the two nines that we know exist must be supplied by those four cells so they cannot be any more nines in these columns another way of seeing this is to just try and put a nine we know there's a nine in one of those two if we try and put it there the corollary of that is you've got to put a 9 there because you can't put a 9 here now in row 8. and if you try it the other way round you know one of these two squares is a 9 if you put the 9 here you've got to put a 9 there in row 8 and the same effect you always end up with a nine in one of those two squares you always end up with a nine in one of these two squares so you can always say there's no nine in this square this has got to be eight and that is well it's beautiful it tells us blue is two good grief because now this arrow must involve a one so that's where it's got to be a two and not only do we know that this is so clever so now now not only do we know this is a 2 but we know from our set theory earlier that that 45 plus this square which is now 2 so 47 is the sum of those squares well we couldn't make those add up to more than 47. so these are maxed out this had to add up to 30 then so that has to be a six that makes that a nine this has to be a one-two pair now and these have to be an eight nine pair because we can't even get away with a seven nine pair once we're heading towards a 47 total now our logic earlier tells me that's now an eight nine pair because they're mimicking these digits and all of a sudden the puzzle is giving it secrets to us for a smaller price now these squares add up to eight and don't use two so they're one three and four so these squares are a five six pair by sudoku which doesn't do anything that being an 8 means this is a 9 which means that's a 9 that's an 8 this is a 7 by sudoku because it sees 8 and 9 in this column that's become an 8 out of now that gives us a nine here there's eight on this arrow so there must be a one eight pair on the arrow wow wow okay this puzzle is seriously impressive um nine can be placed there by sudoku how many nines have we got in the grid some but not as oh we've got a nine eight pair here you can't put nine on an arrow so nine must go at the top there which means 9 is the yellow digit with a 7 8 pair that gets a 1 and 8 over here 7 in box 1 now can't go there by sudoku and it can't go on this little arm because it would have to have a two with it so seven goes here that's a seven which means seven is in one of those two cells and seven can't go on the arrow because if seven goes on the arrow this square would have to be an eight or a nine which we can see it can't be so seven must go at the bottom that makes that square a seven it seems that which makes that square an eight good grief um i suspect there's a lot we can do now i mean i'm seeing things like our two we can place in box eight these squares have got to be a three four five triple that can't be a three because that would have to be a one two pair and you can't be now so that's not three if it's a four it's got to be a one and a three in that specific order if it's a five it's got to be it's always got a one here and this is a three or a four um i'm not sure if we can do more than that might be able to how many eights have we got in the grid lots so there's an eight in one of these two squares there's an eight in one of those oh there's not right where does eight go in box two it's got to go here so that's another eight so we're left with i see we've got sort of an x-wing of eights in boxes three and nine that don't look like they're resolved immediately we know that those two squares add up to 11 don't we because these these circles are telling us those five cells add up to 17 17 and 17 is 34. 45 minus 34 is 11. so this is an 11 pair and it's not two nine or three eight so this is either five six or four seven that squares it ah oh okay yeah that square's a three four or a five just a complete box eight but it's also the same as that square so this is a four or a five oh dear okay so now we are we've hit the brick wall again that domino is adding up to nine it's not one eight or two seven so that's three six or four five so am i right in thinking then oh where does one go in column nine we've got sort of this pattern going on so the only place one can go is there is that useful the answer seems to be no okay we've got a 3-4 pair at the bottom of the column that gives us a 3-4 pair in row seven we've got oh lovely yeah okay look at the eight arrow here it needs a one on it and this one therefore must well it means these two can't be one so that's a one so this is either three four which looks very likely doesn't it because that would actually mimic well by sudoku it would be telling us this is a 3 4 pair or it's 2 5 sorry 2 5 here that although that might work as well okay sorry i'm not sure if we can actually do that um [Music] these three squares are three four five triple ah okay so that's a little interesting then for this circle which now is either summing 2 plus three two plus four two plus five so that's five six or a seven we seem to have too many digits here where does yeah okay where does three go in this in this box it's got to be in one of those two squares so it's not here once this isn't three this isn't five so this is now six or seven and it's c7 so it is six okay so that's six that's four that's a three five pair that's not got five in it anymore uh all six in fact so that's four and seven which means these two squares can't be one three four they are one two five okay i was not i would bet i would have bet that was one three four that's why you should never listen to me if i tip tip you any advice at a race course now these two squares are now three and six which do add up to nine we don't seem to know the order and we can we've almost actually used all the clues now so it must be possible to i mean i can see there's a six up here i think it must be possible to do better by sudoku than i've done seven is quite restricted it's got to be in one of those two cells and two three four five not oh nine there are four nines looking at this box so nine must go here which displaces a pencil mark for an eight so that's an eight that's an eight that's a seven seven goes here by sudoku how many sevens have we got now loads but not enough we still got an x-wing on sevens we've done all the eights we might have done all the nines we have those two squares are a five six pair that makes this square a four which means that's a four and that's a three and that's a four and that's a three and that's a three and that's a six and that's all good that four is giving us a four and a seven which finishes the sevens off okay this must now be about to crumble i think five six here one two there um come on simon use your brain one three and five so ah so where does one go in this column that's a sensible question it's got to go here that four tells us this is now a three which means this is a five or a six so its friend here must be a three or a four and there's a one four pair looking at it so that becomes three six that becomes six five these two squares must become four five which we know the order of these two squares must become 3 6 which we also know the order of and that square becomes a 5 by sudoku and that gives us a 5 and a 6 over on this side of the grid we know that the final digit there's a 5 i think that gives us a five and a three we must be able to put a three here this row needs four and something which i'm miss scanning is it one yes it is it's one oh lovely one and that that's a four that's a four that's a one a one a two a two or five five or six put a six in here these two squares have got to include a two and a four and that's a three five pair at the bottom and there we have done it wow wow udaca that's mad that was mad i i am far from sure that i have followed the intended line here i love the fact i discovered an x-wing in the middle of the solve that gave me that digit that was stunning and i also loved well all the set stuff at the beginning was that necessary i suspect some of it was but i'm not sure whether that bit was although that bit did give me a restriction on that cell which did give me a restriction on that cell i mean it's hella clever this it really is what did that do for me oh i know what it did once i knew this was i managed to get these to be high didn't i so that locked that digit there yeah and then there were all these seven eight not oh yes row eight with its seven eight nines this little short stubby arrow is so clever by forcing the seven eight nine there and then i got seven eight nine here somehow which gave me a seven eight nine there somehow and that seemed to have some effect over here i mean i mean how do you say this really how do you do it oodakos you know we'd like a setting video we really would he really would explain to us how you did this because i would love to know um i hope you enjoyed that i hope you had a go at it and we'll be back later with another edition of cracking the cryptic [Music] you

Channel: Cracking The Cryptic

Views: 53,711

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Id: m-TrUrKYUiw

Length: 43min 59sec (2639 seconds)

Published: Wed Feb 02 2022