The Sudoku Trick All Expert Solvers Know

[Music] hi welcome back to cracking the cryptic where we've had a few requests take a look at tuesday's new york times hard puzzle uh new york times hard sudoku is one of my favorites from the sort of the whole panoply of national newspapers sudoku's that we're faced with every day all of them are created by computer there's no handcrafted puzzles appearing in the daily press um but the new york times algorithm is is one of the better ones so if you if you need to choose a puzzle to do every day uh i suppose that would be one i'd recommend if you can't get your hands on a handcrafted puzzle um so let's take a look how we would solve this um i'm gonna go i'm gonna step through this reasonably slowly just to make sure that those of you who are new to the channel you can pick up on some of the logic that we recommend so first thing to do is to go around the grid and populate it with pencil marks as i'm doing here so all i'm doing is scanning the rows and columns and boxes and trying to identify areas where a number can only go in exactly two positions in a three by three box um and when i find such a situation i just make little pencil marks in the corners if you want to try the puzzle by the way just click on the link under the video that'll take you to our software new york times doesn't have an archive so in order that you guys can actually play the puzzle uh you're gonna have to use our software rather than theirs i'm afraid so two sevens fours ah okay now the other trick that new york times loves to do is this sort of situation have a look at this box see if you can spot anything interesting about it and the key with the new york times is very much believe it or not to focus on open flanks within three by three boxes so in this three by three box these two would be you know they're completely open all of these three cells contain no digits and they are all aligned they are all in the same row just as these three cells again all open contain no digits and all in the same column now if we have a look at these three cells here it's obvious that these three cells cannot contain the numbers two three or six um because they're already in this box therefore if we take a look at this whole row where can the numbers two and six go well given that they can't go in any of those three squares the numbers two and six only have two positions left that they can go into and that's those two so actually we can make a slightly different pencil mark so where is the pencil mark in the center of cells that's saying rather than looking at the box and identifying two positions where a number can go into i look at this pencil mark with the two and six in the center i'm saying this cell can only be a two or a six um so i do recommend two different types of pencil mark now if these two cells are two and six these cells here have got to be five eight and nine in some order well actually we're going to be able to fit in all of them because we've already got an eight and a nine in column two so this square can only be a five um now this square can't be a nine because the nine down here so that's going to be a nine this must be an eight oops so we're off to the races now these two squares can only be eights because of these two eights here and this seven obviously there can't be a seven in this square in column two so the seven must be in one of those two squares ah and this is another reason that uh we recommend the pencil marking so let's have a look at this box and this box now you can see here that we've identified that the sevens in this box must be in row eight or row nine and the sevens in this box also are in row eight or o nine so in the finished solution there'll either be a seven here and a seven here or there'll be a seven here and a seven here one of those situations must be true but in either of those cases there obviously can't be any more sevens in row eight and row nine we've got enough sevens in row eight and row nine uh however these sevens are arranged so in this three by three block over on the right hand side the seven must be in row seven because of this seven here we actually get some highlight that into one of those two squares um [Music] ah we can get a six look this six here and this six here interact on this block they lock a six into one of those two squares which means there's a six in one of these three squares in the bottom but we have a six here and a six here so in fact the six must be in that square uh what now watch now i hear you ask ah okay right interesting interesting right what we need to do now is we need to carry on pencil marking but i want to pencil mark twos i want us to go around the grid and make sure we've got all our pencil marks for twos in the grid because this two and this two interact rather nicely on this three by three block you can see that they force a two either into this square or this square and that means in this three by three block that the only positions for twos are in these two squares because obviously we've got two in either of those squares and this two up here now look at this two because this two forces the two in the top right hand three by three box to either be in this square or this square and we've got a similar thing going on to the seventh but it's just a little bit harder to spot so if we look up here down here and think about twos you can see in this three by three block the two is either in column seven or column nine and in this three by three block again the two is either in column seven or in column nine so we know that in the finished solution the two will either be here and therefore here because this square obviously can't be a 2 if this one is a 2 or here and here either way around it's not possible there to be any more 2's in column 7 or column 9 so we can rule out twos from all of those squares in this box look there's a 2 over here as well so this square can't be a 2. all of which means we actually get to get another 2 in the grid and now we've got two here and two here so that's a two looking at our earlier pencil marks now this one can't be a two anymore so this is a two oops and can we go any further than that don't know maybe but uh we've now got a lot of digits i suppose in this row let's check it we still need a one three and an eight ah okay and now we can enter in another digit so we look upwards you can see one's appearing in those two squares so where can a one go in row four well only in this position so this is now a three or an eight and this is a three or an eight ah this eight here is important isn't it where can an eight now go in the central three by three well there's only one position it's going to have to be there you can see a few things that are going to arise throughout that let's complete row 4 this must be a 3 now it must be pencil mark 3 is at the bottom here um this one means there must be a one in one of those two squares and that means there must be a one in one of these two squares and look we've got this whole pattern going on again now with once so again we've got this sort of x shape of ones exactly the same as the x shape on the sevens exactly the same as the sort of offset x shape on the twos so we've now we now cannot have any more ones in column one or column three so we're actually going to get a one seven pair now the bottom there therefore this square must be a four to complete the column four here and four here i mean this is the only candidate for four in its box which means we get to pencil mark fours at the bottom again change that to make it clearer to me that that's a one seven pair um okay so we've now got loads of stuff going on um let's have a look at this eight and this eight because actually there's only one and this eight as well there's only one place and eight can go now in this block and that's gonna be here now the moment i put this eight in look what's going to happen i'm going to take the position of a pencil mark 6 now as i know that my logic for pencil marking was that a 6 if you if i see a 6 in a cell pencil marked it means that it's one of two positions in the block that a six can go into so if i remove one of those two positions the other one which is pencil mark here must be true so the moment i put an eight here i know this must be a six and the moment i put a six here i'm taking the position of a pencil mark two look so i'm gonna be able to go six two like that therefore this must be a two i'm winding pencil marks unwind the pencil mark at the bottom and that was a good yeah that's made some real progress hasn't it so now these scales must be one eight and nine because of the you know we need those numbers to complete the box we have a one and a nine already in column nine so that one's an eight and this is a one line pair these two cells now must be what they must be there must be three and five to complete the row and we have a three here so this is a three and this is five now we have a five here and five here so this must be a five we can pencil mark fives into the corners down here because of this five and this five now if we look at this box because this is a one seven pair this must be a four eight pair to complete the box so let's put that in and highlight it now if this is four and eight we still need to put a one and a seven into these two positions that we can pencil mark one sevens into there so to complete this row we still need three five and nine so threes into one of those two squares we don't know anything really about fives and nines though do we no that's a bit frustrating so we'll have to come back to that but if we look at here because we've got a four in one of these two squares let's look over here and look we've got again we've got the same pattern going on throughout this puzzle over and over again so i know that in this three by three block i can't have a four in any of those squares and you can if you're not quite sure about that if you try it imagine there was a four here what would the implication of our pencil marking be well in this block it would be that there must be a four here and in this block it would mean there must be a four here and look we get a repeated four in row nine so oh wow i don't want to undo undo undo that's better so therefore there must be a four in one of these three squares and we have a four there so we can pencil marks and fours into this bottom box here um now let's have a look see what else we can see we've got a five here so that's going to allow us to pencil mark fives at the top which means there must be a five in one of those two squares i think this square is very restricted this must be four or a nine just wondering whether we can go do any better than that ah now when i when i put that two in if i delete that two will it actually yes let's have a look when i put that two in i wasn't careful look because in in putting the two in i actually took the position of a six that had been pencil marked so i should have gone two six and now that would also give me a five now so that was me being careless it's very easy to do but anyway i did spot it so now this five interacts down here look now there must be a five in one of these two squares because of the five here and five here these two squares have got to be uh nine and seven in some order so let's put that in and see if that helps yeah it does that means that this must be the nine in this box which means this is a one now we get to pencil mark ones at the bottom and we manage to pencil mark the ones in the same positions that the fours are pencil marked in so this is a one four pair now in this box uh this square is forced to be a seven just to complete the column obviously these two squares therefore must be three and eight so let's again let's put that in you can see hopefully if you're following the logic we've been using look we've got the pattern on eights now so we know that the eights in this uh three by three must be in the central part of it and we have an eight here and an eight here now this is going to crack the whole puzzle now because you can see the moment i put an eight into this square i'm taking the position of a four so i'm going to be able to do that that's just going to take the position of the seven that which takes position of a five bang and all of a sudden that is a serious serious uh advance in terms of the total solve so now we go four here that must be a nine therefore unwind the nine and the seven uh this now must be a seven look at the top but we still need a four i think into the top row and there's a four there so we go four and five like that this must be a five now this must be three and nine you can see the nine here allows us to resolve it this must be a three there's three points at this square so that's going to be an eight that's going to be a three this eight points over here so that all unwinds this all unwinds this must be a one now that unwinds that and all of a sudden as i'm sure you're appreciating the whole puzzle is falling we need a one and a four into these two squares this four here is going to fix that 4 1 1 7 check it's correct and that is how to do the new york times so for those of you relatively new to sort of more advanced solving of sudoku i really hope that um some of the techniques i showed you there were when interesting if they were do consider subscribing we really appreciate it and i'll be back soon with another edition of cracking the cryptic [Music] you

Channel: Cracking The Cryptic

Views: 2,673,032

Keywords: new york times sudoku tips, NYT sudoku tips, hard sudoku tips, expert sudoku tricks, sudoku tricks, sudoku trick, sudoku lesson, sudoku guide, sudoku 101, hard sudoku for dummies, solve any sudoku, difficult sudoku tricks, difficult sudoku tips, diabolical sudoku guide, sudoku strategies, sudoku expert strategies, sudoku diabolical strategies

Id: QgkVz9sdHEs

Length: 17min 53sec (1073 seconds)

Published: Thu Aug 29 2019