This video teaches how to solve Sudoku variants by combining standard Sudoku rules with additional constraints: cloning (shaded regions appear multiple times with identical digit positions), thermometers (digits strictly increase from bulb to tip), X symbols (cells sum to 10), V symbols (cells sum to 5), white dots (consecutive digits), and black dots (2:1 ratio). The solving process involves identifying which cells must contain the same digit through cloning, using constraint rules to eliminate possibilities, and applying logical deduction to fill the grid.
Deep Dive
Prerequisite Knowledge
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Deep Dive
Learn How To Sudoku with Cloning Working OvertimeAdded:
Hello everyone. I'm Frank and welcome to learn how to sedoku where we take a very easy variant sudoku puzzle and we break it down in detail so that you can learn how to sedoku. I don't know what where that came about. Anyways, uh today's very easy puzzle is called cloning working overtime by page. And here are the rules. My 100th puzzle. Thank you everyone for trying solving in solving my puzzles. Hope you enjoy. This is by Dolph Paige or Paige Joe. Uh um thank you actually for I've done a lot of Paige Joe's puzzles and they've always been really fun and pretty in very enjoyable in in general. So thank you for all your setting and we will have fun doing this 100th puzzle of yours.
Let's get to the real rules. We have normal sudoku rules apply which means in every cell in the grid place a single digit such that every row column and designated nine cell region contains the digits 1 through nine exactly once each.
We have clones where the four shaded cell region in grid box one is cloned four times throughout the grid.
Digits appear in exactly the same positions in each shaded clone region and clone regions do not overlap. So basically this cloned region here appears four times in this puzzle. Once is here.
Another time is here. Another time is here. And another time is here. And these shaded regions digits appear exactly in the same position in each shaded clone region. So this digit is the same as that one, which is the same as that one, which is the same as that one, which is the same as that one. And that that's the same for each of the four cells in the cloned region here.
numbers on a thermometer strictly increase as they move away from the bulb. So you could have something like say three, four, and eight here and that would be valid because it's continuously increasing from the bulb to the tip.
What you could not have though is something like say three three and eight here because it's not increasing from this cell to this cell which is not allowed on these thermometers because they must be strictly increasing as they move away from the bulb.
And that's how thermometers work. We have digits in cells joined by an X sum to 10. Digits in cells joined by a V sum to five. So for example, if the uh let's continue. Digits in cells joined by a white dot are consecutive and digits in cells joined by a black dot are in a 2:1 ratio. And not all X's, V's or dots are necessarily given.
So the X's and V's are known as X's and V's. The black and the white dots are usually known as crop key dots. So, as an example, say we had a three here.
Then this digit would have to be two and this digit would have to be seven because these two digits must add up to five and these two digits must add up to 10 because there's a v between these two and there's a x between these two. Say we had a two over here, then this would have to be 1 or 4 to maintain the 1:2 ratio between them. And if we had a six here, this would have to be five or seven because these digits must be consecutive because there's a white dot between them.
And those are all the rules. If you like to play along, there's going to be a link in the description. And now I'm going to get started. Let's learn how to sedoku.
Okay, I noticed something when I was giving examples here is okay. So these two digits add up are either 1 four adding up to five or 2 three adding up to five. If we have two and three well okay that's not that's not a good example.
Um let's look at yeah wow that automatically give gave all of those. So these are all the same. So, we'll color them as gray. These are all the same.
We'll color those as green. These are all the same. We'll color those as orange. And these are all the same.
We'll color those as yellow.
So, all the grays, all the medium grays are the same digit because it's cloned four times. And these are the clones.
All the oranges are the same. All the greens are the same. And all the yellows are the same. So the yellow must be from 1 through four because it's adding up with another digit to add up to five.
So this is 1 through four here.
And the digit that adds up to 1 through four with we'll mark as blue. So this is blue. This is blue because it adds up to five with those.
Okay.
Where is orange in this upper right hand box? Cannot be here or here because of orange is in the columns.
Can't be here or here because of orange is in the row. So the orange has to be oops the orange has to be there.
Um orange in this lower central box is one of these two.
Let's just do the ones where we have confirmed information.
So yellow in this lower left hand box cannot be here or here because of yellow in the column. Can't be here or here because of yellow in the sorry yellow in the row can't be here or here because of yellow in the column. So yellow has to be here.
Um yellow's one of these two.
So this yellow is less than sorry has to be greater than this digit.
So first of all this digit has to be less than that. So it's 1 2 or three which means the yellow cannot be one because it has a digit that's smaller than it. So yellow has to be 2 3 and four.
Um green where is green in column six?
Green cannot be here because of green's in the boxes and these are yellow and blue specifically which are different than green. So this must be green over here.
Where is green in this in row seven?
Can't be here because of green's in the row in the boxes. Can't be here because of green's in the column. So green has to be here. Interesting. So this adds up to 10 with yellow.
Where is green in row one? can't be here because of greens in the boxes. Can't be here because of green in the column. So, and this is orange definitely. So, this must be green here. And we have eight greens. We know where the last green has to be. It has to be there.
Um, yellow, green, orange, gray. So, where is gray in row six? can't be here because of grays in the boxes. This is orange and this can't be gray because of gray in the column. So gray has to be there or medium gray I should say. Where is medium gray in row three then? Can't be here because of gray is in the column or grays in the box. Can't be here because gray is in the column. And then has to be there.
Where is medium gray in column one then?
Can't be here because the gray is in the column. Can't be here because of gray in the row. And this is yellow. So, this must be medium gray there. That gives us eight grays. So, we know where the last gray has to be. It has to be there.
Okay.
Um, we've got all the greens. We got all the grays.
We have orange. Orange is consecutive with green. That's interesting.
And orange has to be less than green because so therefore um green is in a 1:2 ratio with another digit.
So this is 6, seven or eight. And green can never be seven because seven can never be in a 1:2 ratio with another digit because if you have that you get 3 and 1/2. If you get if you double it you get 14 neither of which are digits.
So all the yellows then are two and four. And if green were six, green is consecutive with orange and orange has to be less than that. So orange would necessarily have to be five. But five orange is guaranteed to be next to an another digit here which means oh sorry next to another digit. It's next to an x which means that plus another digit must add up to 10. If we had five here five only adds up to 10 10 with another five and we'd have a duplicate in that row which is not allowed. So orange can never be five. Therefore, orange has to be one less than green here because of this ratio and it shows that it's less than here because the orange is less than the green here. So that means um orange has to be seven and green has to be eight. So green is eight, orange is seven, yellow has to be two which makes this digit one. The blue digit is three. Then eight is in a 1:2 ratio with four.
Okay. So then these digits are the same. I don't know.
We'll make it red or something. Who knows?
This has to be one. We'll make that pink.
And red is four.
The reds are four.
That medium has to be less than eight.
Okay.
And medium.
Medium cannot be orange and it cannot be it has to be less than eight. So this digit has to be nine and the medium can't be 1 2 3 4 and it's this adds up to 10 with another digit.
So it cannot be five which means mediums have to be six. So this is six. Six adds up to 10 with four. It's consecutive with five or seven but this is seven. So this has to be five here.
remaining uh 7 adds up to 10 with three.
These two digits are in a 1:2 ratio and we know it cannot have 8, three or six in it. So therefore, it's two with one or two with four to be in a 1:2 ratio.
Either way, it needs a two. So two has to be there. That gives us eight twos, I think. No, it doesn't.
But it gives us enough information to get the twos, all the twos. two in row five. Obviously, these are filled.
Cannot be here or here because of twos in the column. And this is one or four here. So, therefore, neither of these can be twos. So, two in row five has to be there. We have eight twos. Now, we know where the last two is. It's there.
Um, we need and this is in a 1 to2 ratio with one and four. So the rest is probably just normal Sudoku aside from this digit. Well, it has to be because oh this has to be smaller than the six but greater than two.
So this this is four or five. So we have four or five here and this is one or four here. And now we can do just normal sudoku for the rest of the puzzle.
So remaining digits of what do we do? Um, I guess we should do maybe column three. We have 1, four, and five.
This can't be five because of five in the row. It's the same thing as this upper left hand box is 1, four, and five. And these can't be four. So, where is the four in this box? It has to be here. Which makes this one and makes that five. So, that's helpful. Remaining digits of row eight, we have four and nine. And this can't be four because a four in the column. So this is nine. That's four.
And I'm just going by order of how many digits we have available. Actually, I guess I didn't because this is three and this is five and nine is a possibility.
If five can't be here because of five in the column. So this is nine. That's five.
Um remaining digits in column 8 we have 1 4 and three.
Well this can't be four.
So it's one or three. This can't this could be 1 three or four. And it's the same with the entire box. So this is 1 three or four. This is 1 three or four.
But can't be four because a four in the column.
Remaining digits in row two, we have 1, three, and five here. That's fine.
Remaining digits in column one, we have because of the one, five pair in the column, we have three, seven, and nine.
And three cannot be either of these digits. So three has to be here. This can't be seven because of seven in the row. And it can't be three. So that's nine, which makes this seven.
Okay. Remaining digits in this box then this left central box are 1 and five and remaining digits in column two then are seven and nine.
Um remaining digits in column five we have 3 five and 7 and this can't be seven so it's three or five this can't be three that leaves us as a 5- seven pair here which eliminates 57 in the rest of the column so this can't be five here it must be three okay remaining digits in this upper central box are five and nine Okay.
Um, and the remaining digits in row one are 1, five, and nine.
Where is the four in row two? Can't be here because of four in the box. Can't be here because of four in the column.
So, four has to be here, which eliminates four from the rest of the column. This is one. Three is a pair.
Okay, remaining digits of this lower central box have to be one and four. This can't be four because of four in the row. So that makes this one which makes this four.
One eliminates one in the rest of the column. So the remaining digits in column three have to be uh sorry column four are three, five and nine.
Okay, this can't be nine because of nine in the row. So, this is three or five. We have a 1 135 triplet in row six, which eliminates 1, three, and five in the rest of the row. So, no five here. This is a four.
And remaining digits in that column are 1, five, and nine. Okay, we have a 1 3 1 pair in this right up right central box.
So, this can't be one or three. It's four. This five also eliminates five from being in the rest of the column. So remaining digits in column 7 are 1 3 and 9. And this cannot be 1 or three because of one or three in the row. So that makes this nine which makes this one and therefore this is three.
Nine eliminates nine here. So it's seven and nine. Seven eliminates seven here.
So it's five and seven.
Uh one here eliminates one in the rest of the row. So this is five and one.
Five one and five eliminate one and five here. So it's nine which eliminates nine here. So it's five which eliminates five and nine there. So it's one which leaves this as a five here. That eliminates five here. So it's three which makes this nine.
Three eliminates three in the rest of the row. So this is one and three.
Five here eliminates five here. So that's one and five. And again one in the box here eliminates one here. So that's three. That makes this five there, which leaves that as a nine. And the final digit is a one.
Um, I should probably come up with a better way of clarifying how or just what leads to what because I feel like it it becomes kind of I don't know, monotonous about the way that I I say things. Um, I don't know. I'm not sure how to make spice it up a little bit or just make it more interesting.
Um, anyways, if you guys have ideas, let me know in the comments. And I hope you enjoyed this episode of Learn How to Sodoku. And I'll see you next time on Frank Puzzles. Take care.
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