This Sudoku puzzle I was like you've got to be kidding me this can't be a valid Sudoku but it's from the Dutch master odd vandewettering so it probably is a valid Sudoku arts puzzles are always fairly minimal in terms of the number of Givens but they always have had a unique solution before so I'm sure this is no exception I'm very much looking forward to trying this because as I say a first grasp or first glance it looks absolutely mad now to be fair there are some extra constraints in this puzzle so I better tell you about those the two marked diagonals here have also got to contain the digits from 1 to 9 that's one extra constraint and there is a knight's move constraint here which means that if we look at a cell like this this one this contains a 4 now if this was a chess Knight a chess Knight could jumps us a few different squares look could go to all of those squares now that means that none of these yellow squares is allowed to contain a4 so similarly for this 8 we would be able to eliminate 8 from all of those squares as well as well as the obvious ones obviously there couldn't be an 8 in any of those squares by the normal Sudoku rules.
There's a knight's move constraint there is a diagonal constraint and there is this gray box in the middle now the gray box has to be a Magic Square and if you haven't come across a Magic Square before it's fairly simple what that means is that we have to make sure that every row every column and the two long diagonals in this 3×3 box have to add up to the same number so we're going to be able to do some arithmetic straight away actually it's work on this box I think I know some of the principles of little magic squares.
How we can make a star?
that's this is definitely where I'm going to be starting the puzzle and we'll see what we can do if you want to have a go and I definitely recommend it I mean this is this is something else isn't it when you're confronted with this is apparently a real Sudoku click on the link under the video that will take you to our webpage where you can play along frog in my throat least I hope that's all it is and yeah let's get cracking and see how we do so what can we say about this box well.
the simplest way to think about it I think is that we know the sum of this box if we add up all of the digits from 1 to 9 we get 45 now we also know that in a magic square this row this row and this row all have to add up to the same digit so let's call that X we know this will add up to X that will be 2 X that will be 3 X so 3 X has got to equal 45 so X is 15 we get that straight away now the next thing we could think about I think is central square yeah because the central square is the only square in the inner in a Magic Square with an odd number of sort of rows and columns the central square sees or needs to we need to make 15 more ways than any other cell with the central square because the central square is part of a column it's part of a row and this part of both diagonals that's the only square that meets that criteria so whatever we put in this square there have to be 4 different ways of making 15 using this square so we know actually this square therefore is a 5.
How do I know that?
well I know that there are four ways of making ten without using five so it just axiomatically it must be the only way of doing this we can use 1 9 2 8 3 7 & 4 6 add it to 5 and we're going to get 15 so and I know that it works 4 5 and it can't work for any other digit because we we know that this is the only cell that can this can make 15 and 4 different ways every other cell has to be more restricted than that so if you know if we look at this square this square has to be have to be able to make 15 once in the row twice using a column and three times using the diagonal so these squares there must be three different ways of making 15 and these squares these squares are only two different ways because this square would have to be part of a sum making 15 in this direction and part of a Sun making 15 using the 5 so let's think about 9 8 9 9 plus 5 plus 1 is 15 and 9 plus 2 plus 4 is 15 and that's the only two ways of making 15 using a 9 so 9 has to be in one of those squares as does 1 because 1 1 5.
We need to make 14 in to sell 2 cells in the only there are only 2 ways of doing that 5 & 9 & 6 & 8 so it's probably we need the of digits in these positions let's try 3 if we had 3 plus 5 plus 7 that would work and then in the row we'd have to have 3 and we couldn't use we have them so we have to make these to add up to 12 without using 5 and without using 3 so that's right that would be 4 & 8 so 3 & 7 are going to be also in these positions that's just check 7 just the sake of argument 7 plus 5 plus 3 and then seven with me these two to add up to eight without using five without using a seven so these would be two and six yeah so these must be even let's check that's right so if we had an ace in this square eight plus five plus two then these two would have to both add up to seven without using five two and there are two ways of making seven or two more ways of making seven which would be 3 4 and 1/6 so this is this is definitely working and there's a four eight here so this these can't be four and eight.
These are two and six therefore these four and eight down here and now the two actually does it allows us to place the two in the Magic Square this can't be a two so that's a two that's a six which means we know this digit that must be a seven to make 15 now this must be a three to make 15 this way this must be a four that must be an eight so we're actually going to be able to finish the Magic Square I don't know why I'm surprised by that I just am so actually although we only have four given digits we could place a five immediately because of the Magic Square and then we could use those four digits to determine another eight more digits straight away that's very nice so now we can finish this row can't we we've got one five and nine to place along here that one can't be a five because of the Knights move that one can't be a nine because of the Knights move three eight four three eight four so this these 3 squares are three four and eight and again we can do a little bit of tidying up there.
These squares must be two six and seven so these squares must be two six and seven these squares must be one five and nine so we now we can do a bit of tidying again because of these Knights move constraints look so let's do as much as we can yeah that can't be a six that can't be a seven so what do we do now this is a to that square can't be a to the two down there's lots of too so that gives us three twos in the grid ah we can place a two up here look because this to sees that Square and that square this square on the diagonal that one on the Knights move so this must be it to this to there is rules oops this two rules out that one and that one by nice moves so there must be a two in one of those squares ooh now that's rather cool because let's just have a look at this box up here where can – go now – can't go there because if we try and put a two there it rules out that Square from being a two and that one so there would be nowhere to place a two in this box Oh obviously I didn't want to do that actually we just want to delete that one so this is not – and this is not – for the same reason that rules out that one and that's one by the Knights move so – in this box is in one of those two squares that means it's not here.
Actually we're going to be able to place a 2 in this box good grief yeah because we can't now put up 2 in either of those squares in this box because if we do we can't actually put it to in either of those squares so we've got a 2 here it rules out that one and that one with the Knights move constraint same thing is true of that square so where can we put a 2 in this box we can't put it there I've got these twos ruling out those squares can't put it there for the reasons I just mentioned that to seize that square so that is a 2 which means this is a 2 so that's a 6 and that's a 7 this to see stat square by Knights move look so that's not a two this one must be a 2 that means this way it's 2 and this one isn't too and we've done all the twos all of a sudden wow wow how elegant is that so what we do next well hang on this three must be what we do next now why do I pick this number well if we look at the communication apart from twos everything is jammed into these squares so it feels to me like the diagonals must be the place we need to look for our next digit.
The most powerful digit
now the most powerful digit of that we've got here as regards these diagonals is this three now why do I say that because that's square it's ruled out and this three rules out both of those squares from the diagonal as well by the Knights move so the three must be in one of those two squares and that three sees that square yes oh that is good that does force this to be a three that means that's an eight look that's a four that's a three so now there's a three in one of those two squares now can we do anything with that no but look we've got threes here and here and that is powerful because that rules out those squares and this three sees those two squares so this is the blue which means oh nice yeah so we can continue this now these threes rule out all of those squares naturally that one by Knights move from this one here so there's another three we can place therefore up here the three is in one of two positions look oh and now we need a three on this diagonal and those threes tell us it can't be in any of those squares so it must be in one of those three squares and our pencil marking tells us it's that square and this three this is so clever isn't it.
look this three forces this to be the three purpose is that we can't have a three here or a three here because of the Knights move so that actually done all the threes as well now Wow right so now it's a fascinating puzzle this because it's it's it's very linear the way we have to go about solving it now my eyes are drawn to this six and the reason this six draws my eye is that I can see its ruling out those squares now combined with what we've just done with the two and the three this looks like it sort of meant to be doesn't it look we get a six locked up here oh yeah so now look at this the six is can't go in this these squares and this six rules out those two by a knight's move so there's an there is a six placeable six is in one of those two squares down there we don't know about this diagonal yet so on this diagonal we need 1 7 8 & 9 that one season an eight and a nine that can only be a 1 or a 7 and that can't be a 7 because if we put look let me show you but put a 7 here that's square and that's where it can't be a 7 because of the Knights move constraint.
That can't be 7 that's a 1 that's a 9 1 now can't be notice though that we can lock the 1 into one of two positions down here these squares have got to be 7 8 & 9 now the 7s rule out two of those squares so this is a 7 these two squares must be 8 & 9 7 s must be in one of those two squares these must be 1 4 5 4 rules out that 1 this is a 4 in one of those two squares for in one of these 3 squares seven sevens look in this box that must be good seven yes seven by Knights move rules out all of the yellow squares there's a seven in one of those two positions that forces this square to be a seven these squares therefore have got to be four five and nine in some order just wondering what we can eliminate so this five sees that square the four C's that square so we've got one six seven and six seven and eight to place that square can only be a 1 or an eight because it sees a six and a seven and the eighths look these eights I think they're gonna they are this eight sees that Square by a knight's move so that eights can be pencil marketing box three into those squares which means this is a 1 that means that's a 5 this is a 1 down here as well mustn't lose track of or everything we're doing here so there's a 5 here that means this is a 9 that's a 4 that's a 5 5 over here now this 5 allows us to get rid of 5 from those two squares the 4 backfires into this box and gives us a 4 and a 1 as well there's a 1 in one of those squares for in one of these 2 positions six seven and eight 6e.
Now we've got six digits in Row two so we still need to place four six and eight so we've not pencil mark sixes at all one can't be up for that one can't be an eight ones and fives a pencil mark two sevens and nines and not pencil mark but we don't know anything about them of well the nine is eliminated from that square I guess must be a five in one of those two squares looking at the column we can see we can't can't place five in those two so maybe I have to look at this diagonal I've got two three five and eight so I need one four six seven nine so that sees a six and A one so this has to be four seven or nine that's not that's not a great restriction oh no for as well here so I'm going mad one four six seven nine yeah this has to be seven or nine that is better it's still not quite resolved all this square is interesting because of course we've got this one five nine triple here so it's not possible to put a one five or a nine in this square because that would eliminate that digit entirely from those three options so this can't be one five or nine it can't be two or three can't be four can be can it be I can't be five can be six can't be seven can't be eight and it can't be nine because we just talked about that so that square is actually a naked single that is a six that means that square up there must be a four now.
On the diagonal which means there's a four down there so we've got to place one seven and nine on this diagonal still so this square can be Oh bother I think it can be anything so that can be one seven or nine this can't be seven this can be 1 or nine so forth now must be in one of those two squares OK let's look at column five we still need to place four six eight and nine so that's square can be four six or eight I think bother this one oh that's better four six and eight so this square is a nine sees a six a four and then eight by the Knights move so that square is and nine on its own so that squares are four six or an eight so look at this column we need five six seven and eight into this one that sees a five up there and an eight actually so that's got to be six or seven that's a seven in the box so this is also make it single that's a six that means that's a six so this is a seven eight pair now which means we can write that square in that's got to be a vibe to complete the column that means that's a 500 now let's not make a mistake but that seems to mean that that's a vibe which means this is a 4 that means that's a 4 and this is an 8 that means that's an 8 and that's a 6 that's a 6 and that's a 7 it's no longer be 7 up here so 7 can only go in this position on this diagonal now that must be a 7 to complete the column these two squares need to be 6 and 9 and that's resolvable these two squares can't be 6 anymore this is a 4 8 combo and what's pointing at this to resolve it that 4 is there you go so that's an 8 ounce of for these squares here needs to be 1 9 and 8 that's a 9 there forks there's a 1 and an eight up there nine one eight eight nine one nine five still looks like it's working that eight seven can be resolved here like that this is a seven now that must be a five that resolves the five and the one that results the one and the nine there you go what a beautiful puzzle that's quite startling I mean it really is that that has a unique solution is I mean something magical.