Tutorial #71 Sudoku. The Empty Rectangle Part 1

[Music] [Applause] hello everyone here we are again robin the sudoku guy with yet another tutorial tutorial number 71 and this one is part one of two tutorials on the same topic because it's a big topic it's called the empty rectangle now why they call it the empty rectangle i don't know if you know please tell me so anyway without further ado let me start by saying there are two fundamental things that you need to know to be able to do this particular technique and get rid of small numbers the first one is the conjugate pair now we covered this in a previous tutorial but i'm going to just quickly revise it a conjugate pair is where you have only two little numbers in a row or a column or a block but in the case of this technique it's just basically rows and columns in this particular row it only appears twice that makes it a conjugate pair now there's another thing you need to know about a conjugate pair which is very important in order to understand what i'm going to cover today if this is a 2 that will not be a2 in other words if this is true that becomes false and a vice versa if this becomes a two then this cannot be a two so that b is becomes what we can say it's true and we say that this is false with that in mind well let's push on to the second most important thing about this tutorial and that is in its empty rectangle there are several shapes that you can now identify and i'm going to show you them i think there's around five of them that can all fit in a block so let's have a look at those the first one i'm going to show you is this one i call it the big l there it is and now it can fit into this block this way these are little numbers by the way uh it can fit this way it can fit this way and it can fit this way four ways you can find it in a block now in this particular case i put little threes in each cell but you don't have to have that but you do have to have at least one of those little numbers in each arm of the of the l now here's for example i've got a three here and a three here that three is in this arm and this three is in this arm and if that's the case this will still work you'll see later let's have a look at another shape now this is what i call a little l a small l and this can be found in more than just four times in a in a block let's have a look here it is one way here it is another way here it is another way and here it is another way but you can also find it this way or this way you also find it this way or this way or this way and that way all kinds of different ways so that keep that in mind take note here we have one number little number in one arm and another little one in the other arm and in this case you've got more so there's many ways they can show up in a block when you are looking for them and you've got to look for these and after a while you get used to suddenly seeing them you've got to remember these patterns of these shapes here is my next one it's the big t now the big t is very popular um later on i'm going to actually show you being used it can be this way it can be found this way it can be found this way and it can be found this way four positions once again it can also occur this way where you only have one number down here but that number is in this arm and this number is in this arm so that's all that's needed you'll be able to solve it that way now we come to the next one which i call the little t have a look here we have a little t yep it can be that way it can be that way it can be this way it can be this way it can be this way it can be this way it can be this way and it can be just a minute this way all different positions but every one of them will work for you in this case you'll see that we have one number in the row and one number in the column that's what you have to have you can have more than that but that that is a must okay now let's go to oh i should point before i go on to the next one this is very interesting sometimes you can call that a big t you never know sometimes you could uh call it an elf no not an el no it's a t upside down to you sometimes you can call it different other names as well here we have the final one and i should have made this in red it's a it's across like the red cross and in this case it has that position that position that position or that position take your pick and uh you could have something like this and it still could be you could still consider it as a cross or you could also consider it as a little t a little t okay so there are some of the shapes that can fit into this one block config and they'll go to all blocks but there's just some of the shapes that you're going to have to learn to watch for okay i'm going to show you a lot more a little later but now i want to show you some fundamentals okay now here we have uh things that we've got to look for look for first of all a conjugate pair and here's our conjugate pair secondly we look for a pattern or a shape within a block which is part of the empty rectangle and then this is this is the most important part of all you find out if one of these arms joins up with one end of the conjugate pair that's the key this is called x x from now on will be where it joins up with a column or row in this block here and once you've found that so there's three things you find the conjugate pair you'll find the empty rectangle then you look for a conjugate pair where one end of it actually connects with the row or column in this area here and what i've done here is to show you that this in fact is in the same column as this part in here now that's what we're looking for now i'm going to tell you a secret here this is the fun part of this whole process because we can get rid of that five i'll show you how later but i want to show you how this pattern can happen all over the all over the place hold on for a second we could probably have this conjugate pair over here we could have it down here we could have it along here we could have it along there let's see what happens when we do that and we still find our x y z now i've changed the whole pattern here and we could have it over here we could have it up in here we could have it down here we could have it over here it can be all over the place it's just to show you that it doesn't just happen in that section of your puzzle so here we have on this side we have this x is there because it lines up with one of the arms of the t and it is the end of this conjugate pair of cp for short conjugate pair it's at the end of the conjugate pair so that's an x because it's the end of the conjugate pair and it lines up with the top of the t in the same row now if you have that situation and this would be you said this time now let me tell you the fun comes because that five can be removed sometimes if there's only two little numbers in there you've got a big number maybe i'll do one more now now we come to the climax of this tutorial because i'm going to show you the logic as to why we can remove that five you've probably noticed i've added a four that's that there's a reason for that you'll see in a minute let's just say let's look at this five here the xb plays a very important part in the logic of this the x can be true or false it could be a 5 or not a 5. it doesn't matter whether it is a 5 or not a 5 this still will not be a five let me explain why if this was a five these fives would be eliminated they'd all go um that leaves these two fives now if you remember rightly way back in tutorial two i talked about the exclusion rule in this particular block if that five is taken away and you're left with those two fives those two fives mean that one of those has to be a five in that block if that's the case this five can be removed okay i'll remove it okay with my red pen i'll remove it and that will make this a four big four but there's another reason why we can say that that has to go let's say this was false it didn't come out as a five and that therefore became a 5. if this was false that 5 means that this cannot be a 5 as well so in both cases if this is a 5 or not a 5 that cannot be a five and it will become a big four it's amazing how this conjugate pair helped that to happen and i'm going to show you a lot more of the examples of these in our next tutorial so don't miss out great having you on board bye for now

Channel: Sudoku Guy

Views: 64,591

Keywords: Sudoku lessons, sudoku tutorials, sudoku techniques, sudoku tricks, sudoku hints, sudoku for seniors, sudoku for the frustrated, sudoku for the family, Learn, sudoku, sudoku for beginners, sudoku for advanced, sudoku for dummies, how to solve sudoku puzzles, how solve sudoku, brain fittness game, learn sudoku step-by-step, Learn how to solve sudoku, sudoku for all levels, Advanced techniques for sudoku

Id: CsVbBB-4TCQ

Length: 12min 4sec (724 seconds)

Published: Mon Jan 11 2021