dxSudoku #11 Hidden Triple and How To Find Them 

Hidden Triples are tricky to understand. Another idea that is useful in understanding Sudoku subsets is something I call "wrapping". Wrapping is the idea where two different puzzle-solving techniques remove the same non-possible candidates from the same kill-zone. For example, say you have a house with six cells not yet set. Then what you almost always have is a Naked Triple wrapping a Hidden Triple (or you could say a Hidden Triple wrapping a Naked Triple). Here's a video on using wrapping for finding Hidden Triples which is just good to help firm up your understanding of subsets in general: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-24JewFezAgM.html

You are very welcome!

Thank you for the nice comment!

Hidden Triples are always tough to find. Especially the 2-2-2 ones. Here's a video on the concept of "wrapping": ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-24JewFezAgM.html This will help you understand subsets in general. The way wrapping works, say you have 6 open cells in a particular house. It's easier to look for a Naked Triple than it is to look for a Hidden Triple. And for a house have 7 cells left it takes practice but looking for a Naked Quad is still easer than looking for Hidden Triples. Anyway, thank you for the thank you!

Thanks! I was looking for a way to make it easier to find hidden triples. So putting the red over the possible candidate really helps see them. I use the same technique when finding Swordfish but I color out the whole row. I'm always trying to find the best way to explain the algorithm in human terms.

Thanks! I very much appreciate your feedback!

At what mark in the video?

Thank you!

Thank you for the nice comment!

@@dxsudokuchannel thanks for your quick response. Can I have your email for more information??

@@WOS1962 I spend a lot of time over on Reddit: www.reddit.com/r/sudoku/ My handle is "dxSudoku". You can send me a private message there.

@@dxsudokuchannel I wish that, but the Reddit doesn't work in my country. I prefer to contact by email if possible. anyway thanks a lot.

@@WOS1962 What is your question? I will be happy to help you.

Thank you!!

Yes it is! Nice catch! This video has been around for a long time and you are the first to find this one. Some people don't like the practice exercise but I think they help.

I did another video on Hidden Triples that you might find helpful: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-33LnPOUH6Xo.html This video shows me finding Hidden Triples with real-time video capture. I talk through the process so you can see my algorithm in better detail.

Thanks for the nice comment! If you have a pc running Java, I would use Hodoku. It is what I used to do the coloring for the slides in the video. Here is a user guide I did on Hodoku: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE--fTUFJajhSs.html If you have an Android phone I would this app: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-1lj7WI9Tcsw.html There is an interested thing I discovered about making it easier to find Hidden Triples. It is a concept I call, "wrapping". Here is a video on it: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-24JewFezAgM.html Generally, I would rather look for a Naked Quad than a Hidden Triple. But to be honest with you Hidden Triples can be tough no matter what. Especially 2-2-2 type Hidden Triples. It just takes lots of practice. Try Hodoku's Learning Mode to help you master any particular technique. Anyway, thanks again for the nice comment!

Great question!! By definition, a triple is composed of 3 cells where each cell has 2 or 3 of the same set of 3 candidates. I know this is a bit of a mouthful. When you have a triple, you have 3 candidates that must be chosen over the 3 cells or the house will be missing a 1-9 number. Keeping this in mind, when you have a single digit, this means the other 2 cells must be Naked or Hidden Pair because with a single digit, if it were part of triple, you would have to choose the single number or the cell would be blank. Since the other 2 digits being a pair, this would mean your single digit must be a hidden single. If it is a hidden single, you choose it as the value of the cell. If it's not a hidden single, then we must conclude it's not part of a triple. The hidden triple search algorithm just helps you see what's going in the house. You still have to be mindful of what is possible and what is not possible. I hope this explains it. I'm surprised no one has ever asked this question before. I think it comes down to when you have single digit, you must choose it as the value of the cell so it can't be part of triple. A little round about logic here. I guess the only way to see what I'm saying is by practicing finding them but also being mindful of hidden singles. I hope this helps. If it's not clear, reply where it's confusing and I will try again. Sorry if it's not clear. Tough question to explain.

Good point. This is a mistake. You are right. The 6 candidate should be ignored. And then by the second rule cell with the 5 can be ignored. I've changed the algorithm a bit since I did this video. When I do the Quick Video on Hidden Triples I will be using new algorithm. The new algorithm is a little easier to do. Anyway, thanks for the feedback. Your comment is greatly appreciated!

Does anyone know what software is used in these tutorials.

@@dxsudokuchannel I also noticed this. I paused it and found this triple and then resumed and saw that it was missed and hoped maybe it was mentioned in the comments because I thought I misunderstood something.

@@jonathangreene682 At what mark of the video? I'm very close to publishing a new video on the Hidden Triple. It will be titled "dxSudoku #102 Improved Hidden Triple Search Algorithm" My hope is to get this new video done by this Sunday.

Good question. Finding 2-2-2 Hidden Triples are the hardest ones to find. Think about it this way. Cells R458C5 are the only three cells having the numbers 5-6-9. There are no other cells in column 5 having the numbers 5-6-9. Say if we choose the number 3 for R4C5, this means there are only two cells remaining in the entire column where 5-6-9 can go. So whatever we choose we will be missing a 5, 6, or 9 from the values we set in column 5. This goes against the Sudoku rule of having 1 of each number in each house. So we must conclude cell R4C5 cannot have a number 3 in it. So we remove the possible 3 candidate from cell R4C5. The same logic works with the 4 in cell R5C5. This video was one of first one's I did. Here's an updated video on this same topic of finding Hidden Triples: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5pOJBMDxM04.html Hopefully, you will have an ah-ha moment and see what it means when 3 numbers must be used in 3 cells otherwise one will be missing. This video will help you understand the nature of Triples within a Sudoku puzzle: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-RLH-PcGqLA0.html If you are still frustrated please let me know. The the idea of triples is very tricky to get. I've spent a huge amount of time trying to explain it but it's not an easy topic. So please let me know what is still confusing you so I can improve how I teach it. Thanks in advance.

Here's a updated and better video on the same topic:] ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5pOJBMDxM04.html

Thank you for the thank you!

Hi, I did not find any hidden triples: imgur.com/5yv01q2 Here's a new version of this video which explains the search method of elimination for hidden triples a little better: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5pOJBMDxM04.html Remembers, when a cell just have one remaining candidate it becomes void for being in a hidden triple in all the other cells as you do the cancellations.

@@dxsudokuchannel I just followed the technique that you teach in this video. After eliminating all of the numbers in the row that occur more than 3 times (i.e., 3's and 6's) I then ignored any cell with only one possible. That left me with 24 (B8), 128 (D8), 28 (F8) and 48 (J8), indicating that 24, 28 and 48 is a hidden triple. However, when using the rules you describe in the newer video (which not only ignores the cells with only one possible, but also instructs you to eliminate all of those numbers from the remaining cells), there is no hidden triple. In other words, in this current example of column 8, after removing the 3's and 6's you would also remove the 1's and 4's from all cells, leaving no hidden triples. Therefore, if this technique that you teach in this older video is not valid, you should probably add some sort of disclaimer to this video stating that it is outdated.

@@dxsudokuchannel OK let me try this again in another example (at 14:30). Isn't there also a hidden triple in row B, columns 5, 6 and 9? This time I used your improved algorithm. You can eliminate the 3's, 4's and 9's because they occur more than 3 times in that row, followed by 8's since they appear as singles after eliminating the 3's, 4's and 9's. This leaves 267, 27 and 67 in the remaining cells, which is the hidden triple, and allows you to remove the 3, 4, 8 and 9 candidates from those cells.

1. Ignore all the candidates having more than 3 occurrences. 2. Ignore any cells having on 1 remaining candidate. 2.5 Any remaining cell having a candidate with only 1 occurrence, that candidate is not part of a triple and can be eliminated from consideration in all other cells in the house. 3. With the remaining cells and candidates look for a valid triple in the puzzle. I've recently improved the algorithm with step 2.5 above. I'm thinking of just having step 2.5 instead of step 2. When I do the Quick Video on Hidden Triples I'm going to use the latest algorithm in the video. Before I do the video I want to spend more time on this subject.

No because of the 1 and 9. Also, if you make 89-68-69 be the triple, then R3C6 becomes a 2, R3C9 becomes a 3, and we end up with a 5 in both R3C1 and R3C4. If you are not sure, pretend to set a cell to a value and then see what happens. If we get a contradiction like two 5s in the row, then our original assumption is false. Many of the advanced puzzle solving techniques use assumptions and contradictions to set values.

Here's what I believe is happening. After the 8 and 9 are disqualified because there are too many in the house to be part of the triple, it leaves a single 1 candidate in cell R4C4. When there is only one candidate in a single cell, this disqualifies the candidate from being part of a triple. This is because a triple is composed of 3 cells each having 2 or 3 candidates per cell. So having 1 candidate means the 1 is not part of a triple. After marking the 1 in red, the rest of the remaining candidates get disqualified because they become part of cells having only 1 candidate. I just created a new video showing this same algorithm with a real-time demonstration for working with cell-phone apps. Take a look at this new video and I think it will clear up any confusion you may have with this example: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-33LnPOUH6Xo.html Just post here or on the other video if you still have any questions. I hope this helps.

sorry - it is at 7:20'ish mark in the video

Hi, I'm still monitoring. I'm actually working on a video so I saw your comment popup. If I'm looking at the correct spot in the video, 7 can't be part of a triple because it's a single candidate in cell 1. And 2 can't be part of a triple because it's a single candidate part of cell 7. And 1 is can't be part of a triple because it's a single candidate in cell 9. So you are just left with 4 and 5 to fill in the 3 open cells. This is the first video I did on Hidden Triples. After getting better with doing the video's, I did a second video with a slightly improved Hidden Triple Search Algorithm. Check out this video and let me know if this explains it better: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5pOJBMDxM04.html The other thing to do is test the logic of a 457 triple. Take row 5 and turn the 457 Hidden Triple into a 457 Naked Triple. Then remove the any extra candidates on the row. You then end up with two 9's within the row which can't be right. It's always good to test out the logic by pretending values are a certain way. Again, I hope I have the right spot in the video.

@@dxsudokuchannel do you recommend a specific sudoku program/app?

@@dougtate477 For iphones, I like Sudoku Joy. For Android devices, I like Andoku 3. For PCs running Java, I like Hodoku. Sudoku Joy and Andoku 3 are built from the same code base but slightly different. Both have the ability to scan in a puzzle using your smart phone's camera. This is really cool feature. I published a puzzle book called Sudoku Toolbox which each puzzle tells you exactly which puzzle solving techniques you will need to use. It's really easy to scan in my book's puzzles with those two apps. Of the two smart phone apps, I like Andoku 3 a little better because it's Hard and Very Hard difficulty levels use puzzle-solving techniques I like to use. Sudoku Joy's difficulty levels are odd to me. If you can ever run Hodoku, it's worth every penny and here's why. Hodoku has a thing called "Learning Mode" which is the best Sudoku app feature I've ever used. With Learning Mode, you can master any puzzle solving technique. It's really amazing how it works. I feel Hodoku's Learning Mode is what brought my puzzle-solving skills several levels high over a year or two. Post a comment back and let me know how you do. I also have a website where I post lot of websites and apps in a list: dxsudoku.com/links/

@@dxsudokuchannel I also paused at that timestamp, 7:27 R5, wondering how it didn't count as a 2-2-2 hidden triple. The numbers in the single candidate cells disqualfies both the cell *as well as* the number in it as candidates for a triple. In this case the 7, the 2, and the 1. 👍

Yeah, I was not being nice. What you have with this one is a 2-2-2-2 Naked Quad wrapping a Hidden Triple. This may be one of the hardest ones to find. To be honest with you I've stopped looking for Hidden Triples. I mainly use Bivalue Elimination to flush them away: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-NOQ1Nla6ktk.html

The reason the 7 can't be used in a triple is because of the 6. The 6 has 5 possible candidates in the house making up block 6. So the 6 is disqualified as being part of a triple. When the 6 in cell R4C7 is removed, it leaves a single 7 candidate. Anytime a single candidate show up in a cell, it means it can't be part of a triple because triples are composed of 3 cells having 2 or 3 candidates not 1. I emphasize this more in the next version of this video here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5pOJBMDxM04.html And this idea of only 1 left means a candidate can't be part of a triple is shown really well in this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-33LnPOUH6Xo.html I hope this helps. Just post again if anything is not clear.

Can you tell me at what time on the video? I too am having difficulties. I think there is another rule we're not aware of.

Looking at it, I THINK it's not because 69 is in there twice. It wasn't eliminated. But there are times where there are extra numbers, and it's ok.. ARGH!!!! So confusing.

I'm not sure I'm looking at the correct example but the one I am looking at has the possible 6 candidate occurring 4 times in the same house. This means the possible 6 candidate is not currently participating in a Hidden Triple since it's located in 4 cells. I've improved the Hidden Triple search algorithm. You might find this video more helpful: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mwoy-1B4qYw.html

I've improved the Hidden Triple search algorithm. You might find this video more helpful: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mwoy-1B4qYw.html

Are you sure you meant row 4? The problem is the 8 in R4C4 prevents a Hidden Triple. I hope I am looking at the right timestamp. At the 14:00 mark I'm seeing a puzzle having a 9 in R1C3. Please confirm I am looking at the right thing.

@@dxsudokuchannel Yes, that's the right puzzle, I guess I'll have to watch the video a couple more times to better grasp the concept then ;]

@@weirdpuck921 Take a look at this video. I've improved the search algorithm for the Hidden Triple. But also, I've gotten better with the graphic animations so hopefully it will make more sense to you: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mwoy-1B4qYw.html And here is another set of Practice Exercises for the Hidden Triple: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-dMpAOkX8oXk.html And one more video. Make sure you understand the concept of wrapping: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-24JewFezAgM.html

@@dxsudokuchannel Thank you very much!

At what mark in the video?

@@dxsudokuchannel7:51 7:51

@@zepham5294 No, and here is why. A triple is composed of three cells where each of the three cells has 2 or 3 candidates from the same set of 3 numbers. I know this is a mouthful but let's consider row 6. Assume our set of 3 numbers is 5, 6, and 7 as you suggested. The problem is those three candidates occur in FIVE different cells: R6C12568. The number 1 is disqualified from being in a triple because it's the only remaining candidate in cell R6C5. So we have five cells with the numbers 5-6-7-8 which is very close to being a Hidden Quadruple except the numbers occur over five cells. It's not a Quintet because we only have four numbers in our set of 5-6-7-8. But you are very close because you are thinking in the right way. Keep practicing it. Seeing triples is like riding a bicycle. Once you experience the ah-ha moment of "balance", you forever understand how to ride a bike. Triples are the same way. Just keep in mind 3 cells where a set of 3 Candidates ONLY occur in those 3 cells.

No, the 2 occurs four times. Take a look at this video. It's an improved video showing how to find Hidden Triples: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5pOJBMDxM04.html

The possible numbers remaining that we can use to form a triple are 1, 5, 6, 7, 8. The problem is each of them shows up in three different cells. Take the 6-7 in cell R6C1 as an example. We could combine it with 5-6-7 in cell R6C8. But then we would need another cell having some combination of 5-6-7 in it (5-6, 5-7, 6-7, or 5-6-7). But there are no other cells with those numbers. In fact the 5 shows in R6C5 with the 8. For this to be a naked triple it has to be just 3 cells having some combination of 5-6-7. It's kind of tricky to explain. Check out the video I did on types of triples. But this is my latest video which includes a bit on Naked Triples which might help you understand what is and what is not a triple: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-6WnFkrUt_10.html Think of it this way. All the three numbers participating in the triple MUST only show up in exactly three cells making up the triple. It's tricky to word it.

dxSudoku Channel i think I got it.

@@nickvisic Cool! As I said it's a little tricky. I think it's easier to see with a Naked Pair. The principle idea is all the numbers are needed for just the cells having the Naked Pair or Triple. So the numbers can't exist in any other cell in the house as a possible candidate.

@@dxsudokuchannel Even my amended algorithm from my other comment identified 745 as a hidden triple here. So it failed also with this case. This makes me sad because now I have no confidence in the algorithm at all. I don't know how it can be fixed. Sigh. It would have been super useful.

@@jonathangreene682 I will take a look. At what mark in the video?

What's missing in this explanation at this point in the video is this: After coloring a candidate in dark red, if there's only one remaining candidate, then that remaining single candidate cannot be part of a triple. This is because a triple is composed of 2 or 3 cells. So when a cell as only one candidate, it can't be part of the triple. For row 5, here's the logic of my conclusion. 8 and 9 are disqualified because there are more than 3 cells having a possible 8 or 9 candidates. But now the 7 is disqualified from being in a triple because it's the only one remaining candidate in cell R5C1. The 2 is disqualified for the same reason in cell R5C7. And the 1 is disqualified for the same reason in R5C9. Since the 7 disqualified, that means there's only one candidate remaining in cell R5C8, which disqualifies the 5. With the 5 and 7 disqualified, there's only one remaining candidate in cell R5C6 which then disqualifies the 4. I've updated this video for finding Hidden Triple algorithm in the following video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5pOJBMDxM04.html RU-vid does not let you edit a video so I had to create a new video. In this updated video, I talk about disqualifying candidates when a candidate becomes the sole remaining candidate in a cell. I hope this helps.

@@dxsudokuchannel Thank you for taking the time to explain why there is no triple there. I will watch your newer video. Honestly, I still do not trust my ability to find a hidden triple in advanced puzzles. I will do my best to reason a triple in order to eliminate a candidate and if I am not sure I am correct I will check the solution to see if I was right. This of course, indicates that I'm not sure and I am guessing. I do love Suduko puzzles and want to get better. Again, thanks for your response!

@@Bergarita Sometimes it's better to understand Hidden Triples in the context of subsets. Here's a video on using Naked Triples and Naked Quads as a better way of finding Hidden Triples using a concept I call "wrapping" which is commonly known as subsets: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-24JewFezAgM.html Keep working on it. Triples are tricky and just take some practice working on them.

The problem with the three 9s in row 2, is after the 4 and 6 are eliminated because there are too many, the 9 in cell R2C8 is the only remaining candidate. This means the 9 is no longer a value candidate for being part of a triple. To be a valid triple, there must always be at least two remaining possible candidates in a cell. I've updated the Hidden Triple search algorithm over time for including this case. This tutorial demonstrates the updated Hidden Triple search algorithm: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mwoy-1B4qYw.html

@@dxsudokuchannel I'll check this out.

Yes, that's one of the harder ones. The 2-2-2 triples are always hard to find. This video is helpful in understanding what to look for: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-f-m7DlxRGXA.html And then I did an updated version of this video. See if this new version helps you: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5pOJBMDxM04.html Even after all my practice, the 2-2-2 ones can be really hard to find. There's another way to look at this example. Anytime you have 7 or 8 open cells, as in column 5 of this example has 7 open cells, if you have a hidden triple, it will be wrapped by a naked quad. Here's a video on the idea of wrapping: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-24JewFezAgM.html When I do puzzles, any time I have a house with 7 or 8 cells, I look for a Naked Quad first before looking for a Hidden Triple or Hidden Quad. I just find looking for Naked Quads to be easier. Sorry for the late reply. I was on vacation. I just got back yesterday.

Hidden Triples are one of the hardest techniques to master. Do not be too hard on yourself. And they are actually pretty rare in puzzles. After the 7-base techniques (Naked Single, Hidden Single, Naked Pair, Hidden Pair, Naked Triple, Locked Candidates, X-Wings), the next two very common occurring ones to know are the Skyscraper and the 2-String Kite. I see those ones all the time in lots of puzzles.

@@dxsudokuchannel Thank you so much. Its just me here so I do not have to worry about my time management, and and I am obsessed with Sudoku. I literally have one in my lap all my waking hours. My brain must be busy or I have severe anxiety attacks. I just got 4 of the hardest books I could find because I have been doing sudoku so long that I was breezing through ones that i previously could not. Right now I am doing a rated hard Jigsaw Sudoku but its really easy for me, by Christian Demarco, because my brain is fried from trying to figure out the hidden triples, and I am really excited to learn. Thanks again for your kindness. I feel calmer.

The way possible candidates or pencil marks are calculated is each cell participates in one row, one column, and one 3 x 3 block. So if you look at all 9 cells in house, ignore the cells already having givens or values, the remaining open cells have possible candidates. Take any number, say 2, and if 2 only occurs in three different cells then it is possible the 2 is participating in a triple. In the same cells with the 2, if there are two other numbers that only occur in the three cells then you have a triple. And here is why. In those three cells, if the three numbers only occurring in those three spots are set to some other number, then the house will be missing one of the numbers 1 through 9. This video may help you understand the concept of what is a triple: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-RLH-PcGqLA0.html&pp=sAQA And this video shows you all the different types of triples than can occur in a puzzle: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-f-m7DlxRGXA.html&pp=sAQA There is one type of triple that is really hard to spot sometimes. It's called a 2-2-2 type triple. Here's a 2-2-2 Naked Triple: imgur.com/PclrfVD And here is a 2-2-2 Hidden Triple: imgur.com/1VRxUWM Triples in a Sudoku puzzle are little like getting the concept of "balance" when riding a bicycle. Once you get it you get it. Here is a playlist on triples. Watch each video and hopefully it the idea will just pop in your head and start making sense: ru-vid.com/group/PLDT9hh28q4mw92r7d2C0WadRn_V6pDXJn You are not alone in having issues with triples. I have found triples to be one of the hardest concepts to teach and help people to understand. Let me know if it clicks for you. If you want to understand the difference between a Hidden Triple and a Naked Triple study the difference between Hidden Single and Naked Single. I hope this helps. Btw, in my recently published book I go into triples in very good detail. I had a professional editor who knew nothing about Sudoku and made me do revision after revision until the explanations made sense. I'm happy with the result but it took forever. Here is a link to my book on Amazon. It's only a $11 and so far every who sees it says good things about it: www.amazon.com/dp/1736452606?ref_=pe_3052080_397514860

@@dxsudokuchannel very informative. I'll take a look in every link you put in comment section thanks!

Take a look at cell R4C5. It has only one instance of the 5 candidate because the 8 was cancelled out. You can't have a single candidate make up a Hidden Triple. If there were an additional 4 or 7 in cell R4C5 then you would have a chance for a 4-5-7 triple. Remember, whether Hidden or Naked, a triple is composed of 3 cells having 2 or 3 candidates for a set of 3 possible candidates. Take look at this video "What makes a triple a triple" which might help you see the Hidden Triples better: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-RLH-PcGqLA0.html Hidden Triples are really tricky in general anyway.

@@dxsudokuchannel I also saw this ... I feel like following the algorithm would identify several possible triples in the 3 remaining cells. 457 being one of them. Yet it's not according to the above comment. This means the algorithm is incomplete and not reliable. :( Can it be fixed somehow? Does it need an extra step "After step 2, all cells with only 1 remaining candidate, those candidates cannot be part of the triple." Does this work? So in this case 156 can't be part of a triple? I'll need to check the other examples and see if this rule holds true.

I checked several of the other examples and I think this added rule fixes it. Like you said, "You can't have a single candidate make up a Hidden Triple" If this gets added as step 3 making a total of 4 steps, then it works in every case I've seen so far.

@@jonathangreene682 This is a very good question. So this issue was addressed in this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mwoy-1B4qYw.html Step 2 is exactly the step you are looking for in the HT algorithm used in the quick video. I'm working on an even more improved algorithm for finding Hidden Triples. This new video should be out within a few days. It will be titled, "dxSudoku #102 Improved Hidden Triple Search Algorithm" I think in this last video this horse will be thoroughly beaten to death!

Think of it this way. Assume cell R7C4 = 5. Then we have only two cells for placing a 2, 8, or 9 in block 8. Whatever values we choose for R7C56, for the house making up block 8 will be missing a 2, 8, or 9. This violates the rule of having at least one of each number 1 through 9 in each house. So assuming R7C4 = 5 leads to a contradiction of the one of each number rule, therefore, our assumption is false. Our assumption being false means R7C4 cannot be 5 and the candidate must be removed. If you are interested, here is an updated version of this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5pOJBMDxM04.html Let me know if you have anymore questions. I hope I answered what you were asking. Sorry if I misunderstood it.

@@dxsudokuchannel Ah ha! That makes sense. Thank you!!

No problem. I appreciate your sentiment. The Sudoku book I am selling on Amazon is doing pretty good. I am not really doing this for the money anyway. I just like Sudoku for the most part.

@@dxsudokuchannel What book? 😁

@@dxsudokuchannel Okay, found the book on Amazon, going to order now. 🥰🥰🥰