Thank you so much for the feature and solve Mark!! It was a nice surprise to wake up to! Good job on picking up on your error and backtracking to find where you went wrong so quickly. I sometimes do this and it takes forever to find where I went wrong. Sometimes I don’t find it and just restart. For the record I’ve lived in Australia pretty much all my life, and can confirm we have or had Australian versions of The X Factor, Australian Idol, Australia’s Got Talent and The Masked Singer, and The Voice. We do get the British and American versions of Got Talent sometimes. Though I have not watched these shows in years. Perhaps because I spend most of my time on CTC! A bit about setting this, I started with the patterns in boxes 3 and 7, and positive diagonal to see what came of it, and knew the puzzle had legs from there after it forced the 156 on the positive diagonal into box 5 and the box 3 and 7 digits, it was just a matter of how to break the symmetry. Then I did a similar factor line pattern in boxes 1 and 9 without the whispers to see where it would lead as well as the 2-cell factor lines. This is where I found that 5 in the r5c5 would not work as that puts 1 on the negative diagonal in box 5 giving two 1s in the box. I wanted the solver to discover this. I also wanted to force 6 into the middle (r5c5) somehow as that narrowed it down to only 4 (maybe 8) solutions but didn’t know how. I continued setting on the assumption that 6 was in the central cell and tried to eliminate further solutions using just whispers and factor lines but it didn’t yield a friendly solve path. So that’s when I thought of the circles. This would do the job of breaking a lot of the symmetry. So I chose a solution and added the circles in. I knew I wanted to put circles in those factor line bends in r3c9 and r7c1 that were 2 and 3 to stop the 1s from being there, forcing the 1s into their positions in these boxes and forcing it into a circle which sees r5c5. (Mark said this didn’t do much in the video, but I think it was essential to the solve). One way to proceed that Mark missed that could have saved time is asking where do the 4s go in circles? This puts 4 on the negative diagonal in box 1, forcing the 157 triple on the negative diagonal into box 9. From there we are just about home and hosed. The lines made an interesting grid with possibilities and big idea deductions, but it’s the circles that made this an interesting puzzle that a human can solve. On Logic Masters Germany, I go by the username MORISENSEIISGOD, and my first CTC feature was under this name. I changed it once I started making themed puzzles about a Japanese girl group called BEYOOOOONDS. One of which is featured on CTC (Rika’s Endless Summer). I’m not sure if I can change my name on LMD…
Thank you for setting this fascinating puzzle and for explaining your process of doing it. It was very interesting to know how you could come up with such an elegant geometry. Another way to proceed that Mark missed and that probably would have allowed him to solve in less than half an hour without mistakes would be using *placeholder digits.* They allowed me to simplify notation enough to make your intended logic crystal clear. By using them, I was able to break-in in a very short time. I explained more about this in a separate comment. Of course, this puzzle is not hard enough to unleash the full power of placeholders, but they were extremely helpful to me. I am not a very skilled solver, so simplifying notation is in most cases quite useful to me (even when notation without placeholders would not be very intricate). See my playlist if you want to learn more about this technique.
@ thank you for solving and for the kind words! I personally wouldn’t use placeholders for this puzzle as there are quite a few axes of symmetry in it. It can get confusing quite quickly. But I’m the setter so that’s easy for me to say. I find placeholders more useful for whispers puzzles where you can solve the puzzle on the assumption a certain cell is a high/low. Then if the solution is wrong, just replace each digit with 10-n.
@@MORISENSEIISGOD I am not talking about mirror symmetry. I used *180° rotational symmetry* about a single *rotation axis* which is orthogonal to the grid. It is quite unlikely to get confused if you immediately identify the *disambiguators* and colour them black, as I explained in my separate message. Yes, I know that most people are more familiar with placeholders representing *high/low parity,* associated with the transformation *y = 10 - x.* which is compatible with *German whispers,* but also with *renbans, nabners, modular lines, entropic lines,* and of course *white dots* and *Xs* (but not black dots and Vs). But that is only one type of symmetry (mirror symmetry with respect to the *digit 5* along the mono-dimensional number line...). Placeholders can be also used to represent 180° or even 90° rotation about the grid center (indeed, I believe Simon used them to represent 90° rotation in some CTC video.) They are just symbols each of which can be used to represent two or four digits, provided you know *a priori* the relationship between the digits they represent. You definitely need to know how to switch from one set of placeholders to the other (or others) by means of some function, because only one of those sets is compatible with the disambiguators. If you happen to choose the incompatible one, you need to switch quickly and elegantly to the other, without starting again from scratch. Otherwise it would be *bifurcation,* which most of us typically abhors (unless the only goal is speed.) Of course, you need to be properly trained to use placeholder digits. However, it is not difficult at all to learn. See my playlist for some examples.
It's almost as if my imploring Mark to think about 4s in circles over and over is pointless, because I don't appear to be able to influence the past. That can't be right, can it? Edit: He never did ask the question "How can I fit four 4s into these circles".
I'm not sure how the solve would change, but at 20:33 when the circles became 1,2,3,4 the number of rows containing a 4 were numbered at 4. This means r2c2 is a 4 because it's the only circle in that row.
I have an idea how that would (actually did) change the solve: make it much faster ;) I did it in less than 35 minutes, and I'm seldom faster than Mark. Here this was by a hefty margin. The two 4 on the top were my first digits, and they started to sort out corners with german whispers. Then the rest flowed pretty well.
@@dinane I feel like it's just a case of "we're all human" the puzzle was of the sort where it wasn't neccesarily obvious that was the intended next logical step. The fact that he was able to solve the puzzle without even doing that step should be more evidence of that.
Very neat puzzle 👍🏻 Finished in about 20 minutes. I know Mark admitted that there were a couple of things he was slow to spot, which definitely made a big difference (and the diversion and back-track), but for me the start was with 1s, and I'm pretty sure this is a legitimate break-in (but willing to be corrected if I've made a leap I wasn't entitled to!). After identifying the positive diagonal in box 5 as consisting of 1-5-6, next is to consider the corner boxes. Looking at boxes 1 and 9, we know that _at least one of them_ must have the 5 and/or 7 on a blue line, and therefore also a 1 on the knuckle of the blue line. Now in boxes 3 and 7, where we also know we need to put a 1 on a knuckle, if we put a 1 in either of the circles, it will force the 1-on-a-knuckle in box 1 and/or box 9 into the circle ... giving us two circled 1s, which is not allowed. This places 1s in r1c7 and r9c3.
Amazing, Mark. Especially once you have had an interruption, that you can return to the puzzle without having to spend a lot of time figuring out what you were doing!
I finished in 63 minutes exactly. This ruleset with the integer quotient was really fun to figure out in this geometry. It's really cool figuring out the meta of the rule with certain digits having to have certain partners. I think my favorite part was seeing that 1's couldn't go on the circles in boxes 3 and 7 due to it forcing too many 2's into circles. This was a clean puzzle and I enjoyed it. Great Puzzle!
Often I think of a commenter I saw forever ago saying that themselves and Mark would make one of the best sodoku teams and I can't help but agree. Mark being the intelligent solver marching only forward in logic, and myself being the buffoon reminding him of previous wisdoms (thinking this time of the 6's being restricted out of 2 rows of the puzzle and giving us the 1,2,3,4 in the circles)
@52:15, and that is also a 4 because you needed four 4's in the circles and you could put one in Row 1, one in Row 5, one if Row 9, and are only left with r2c2 as a place for a 4 in Row 2. Been that way since the moment you saw it had to be 1234 in the circles.
Glad they had the 3 cell blue lines up front, Was trying to make them 1-2-4-8 without thinking that anything divided by 1 is an integer as well as others with 2, 3, and 4.
6 in a circle on a blue line would need 2 and 3 on its sides. Since 1 has be on the other line, 4 is the only low digit available for the whisper which breaks it. There you go, Mark. Free of charge as it only took me 5 seconds to see it.
Also, 6s in circles in boxes 3 and 7, requiring 2 & 3 on both sides in those boxes, forces 236 into box 5 on the positive diagonal, but we already know those are 156.
This one just clicked for me, 29:27, I don't normally solve faster than Mark at all. Very interesting puzzle. The German Whispers force certain numbers onto the factor line, which makes German whispers difficult, which rules out numbers in the circles.
Excellent original logic. It can be elegantly solved with *placeholder digits* as it is quasi-symmetrical, but you need to understand that four of the circles break symmetry and therefore they are not compatible with placeholders. They are supposed to be used as disambiguators. Ideally, it is desirable to ignore disambiguators up tp the very end of your solve, but in this case it was not possible... I marked them in *black,* but immediately after breaking in I was forced to use them to disambiguate. In other words, I had to switch to real digits. In this puzzle, each paceholder represented either itself or the diametrically opposite digit (with respect to the center of the grid). Hence the final transformation needed to switch from a set of placeholders to the other was a *180° rotation.* Of course, there are two alternative sets of placeholder digits and only one of them is compatible with the disambiguators (i.e. it coincides with the unique set of *real digits* that solves the puzzle). See my playlist if you want to learn more about this powerful technique.
Of course, this puzzle is too easy to showcase the full power of placeholder digits, but it can be used to train this technique, which proves to be useful much more often than most people think. Believe me, even Mark and Simon dozens of times in the past got dramatically bogged down in puzzles that would have become easy if they had used placeholders to simplify their notation. I have been watching CTC every day for almost four years, and every time I try and solve before watching.
With the circles and the quotient rules playing such a powerful role throughout the solve, it would never occur to me to even _consider_ using placeholder digits in this puzzle. It isn't a remotely appropriate puzzle to think about using them in any way at all.
@@stevieinselby I would say that it did not occur to you just because you are not familiar enough with *placeholder digits.* This puzzle is rotationally quasi-symmetric, (i.e. the non-symmetric clues are minimal and can be ignored long enough to allow you to break in), hence it is *by definition* compatible with placeholder digits. This is not a matter of opinion. Sometimes, puzzles that are compatible with this notation technique are so simple that it is not worth using it. But this is a matter of *personal preference.* In this case, it was worth *for me.* It was also extremely helpful *to me,* as it allowed *me* to break-in in a very short time. And it was fun❗
Mark explained it when he went through the rules as one number must divide into the other evenly, meaning with no remainder. So 2 divides into 6 3 times (no remainder) but 2 divides into 5 2 times with a remainder of 1 - or, 2.5 times, and 2.5 is not an integer.
Thank you so much for the feature and solve Mark!! It was a nice surprise to wake up to! Good job on picking up on your error and backtracking to find where you went wrong so quickly. I sometimes do this and it takes forever to find where I went wrong. Sometimes I don’t find it and just restart.
For the record I’ve lived in Australia pretty much all my life, and can confirm we have or had Australian versions of The X Factor, Australian Idol, Australia’s Got Talent and The Masked Singer, and The Voice. We do get the British and American versions of Got Talent sometimes. Though I have not watched these shows in years. Perhaps because I spend most of my time on CTC!
A bit about setting this, I started with the patterns in boxes 3 and 7, and positive diagonal to see what came of it, and knew the puzzle had legs from there after it forced the 156 on the positive diagonal into box 5 and the box 3 and 7 digits, it was just a matter of how to break the symmetry.
Then I did a similar factor line pattern in boxes 1 and 9 without the whispers to see where it would lead as well as the 2-cell factor lines. This is where I found that 5 in the r5c5 would not work as that puts 1 on the negative diagonal in box 5 giving two 1s in the box. I wanted the solver to discover this.
I also wanted to force 6 into the middle (r5c5) somehow as that narrowed it down to only 4 (maybe 8) solutions but didn’t know how. I continued setting on the assumption that 6 was in the central cell and tried to eliminate further solutions using just whispers and factor lines but it didn’t yield a friendly solve path.
So that’s when I thought of the circles. This would do the job of breaking a lot of the symmetry. So I chose a solution and added the circles in. I knew I wanted to put circles in those factor line bends in r3c9 and r7c1 that were 2 and 3 to stop the 1s from being there, forcing the 1s into their positions in these boxes and forcing it into a circle which sees r5c5. (Mark said this didn’t do much in the video, but I think it was essential to the solve).
One way to proceed that Mark missed that could have saved time is asking where do the 4s go in circles? This puts 4 on the negative diagonal in box 1, forcing the 157 triple on the negative diagonal into box 9.
From there we are just about home and hosed.
The lines made an interesting grid with possibilities and big idea deductions, but it’s the circles that made this an interesting puzzle that a human can solve.
On Logic Masters Germany, I go by the username MORISENSEIISGOD, and my first CTC feature was under this name. I changed it once I started making themed puzzles about a Japanese girl group called BEYOOOOONDS. One of which is featured on CTC (Rika’s Endless Summer). I’m not sure if I can change my name on LMD…
Thank you for setting this fascinating puzzle and for explaining your process of doing it. It was very interesting to know how you could come up with such an elegant geometry.
Another way to proceed that Mark missed and that probably would have allowed him to solve in less than half an hour without mistakes would be using *placeholder digits.* They allowed me to simplify notation enough to make your intended logic crystal clear. By using them, I was able to break-in in a very short time. I explained more about this in a separate comment.
Of course, this puzzle is not hard enough to unleash the full power of placeholders, but they were extremely helpful to me. I am not a very skilled solver, so simplifying notation is in most cases quite useful to me (even when notation without placeholders would not be very intricate).
See my playlist if you want to learn more about this technique.
@ thank you for solving and for the kind words! I personally wouldn’t use placeholders for this puzzle as there are quite a few axes of symmetry in it. It can get confusing quite quickly. But I’m the setter so that’s easy for me to say.
I find placeholders more useful for whispers puzzles where you can solve the puzzle on the assumption a certain cell is a high/low. Then if the solution is wrong, just replace each digit with 10-n.
Thank you for the fun puzzle and taking the time to explain how you constructed the puzzle. It always fascinates me how the puzzles get made.
@@MORISENSEIISGOD I am not talking about mirror symmetry. I used *180° rotational symmetry* about a single *rotation axis* which is orthogonal to the grid.
It is quite unlikely to get confused if you immediately identify the *disambiguators* and colour them black, as I explained in my separate message.
Yes, I know that most people are more familiar with placeholders representing *high/low parity,* associated with the transformation
*y = 10 - x.*
which is compatible with *German whispers,* but also with *renbans, nabners, modular lines, entropic lines,* and of course *white dots* and *Xs* (but not black dots and Vs).
But that is only one type of symmetry (mirror symmetry with respect to the *digit 5* along the mono-dimensional number line...).
Placeholders can be also used to represent 180° or even 90° rotation about the grid center (indeed, I believe Simon used them to represent 90° rotation in some CTC video.)
They are just symbols each of which can be used to represent two or four digits, provided you know *a priori* the relationship between the digits they represent.
You definitely need to know how to switch from one set of placeholders to the other (or others) by means of some function, because only one of those sets is compatible with the disambiguators. If you happen to choose the incompatible one, you need to switch quickly and elegantly to the other, without starting again from scratch. Otherwise it would be *bifurcation,* which most of us typically abhors (unless the only goal is speed.)
Of course, you need to be properly trained to use placeholder digits.
However, it is not difficult at all to learn. See my playlist for some examples.
It's almost as if my imploring Mark to think about 4s in circles over and over is pointless, because I don't appear to be able to influence the past. That can't be right, can it?
Edit: He never did ask the question "How can I fit four 4s into these circles".
I'm not sure how the solve would change, but at 20:33 when the circles became 1,2,3,4 the number of rows containing a 4 were numbered at 4. This means r2c2 is a 4 because it's the only circle in that row.
Yes, that was the easier question to ask in the middle of the puzzle: Where do all the 4s go? And that immediately places two of them
Same. That 4 was the first digit I placed.
I have an idea how that would (actually did) change the solve: make it much faster ;) I did it in less than 35 minutes, and I'm seldom faster than Mark. Here this was by a hefty margin. The two 4 on the top were my first digits, and they started to sort out corners with german whispers. Then the rest flowed pretty well.
This is what I did and I feel bad for Mark that he missed that. He spent a lot of time stressed about symmetry long after.
@@dinane I feel like it's just a case of "we're all human" the puzzle was of the sort where it wasn't neccesarily obvious that was the intended next logical step. The fact that he was able to solve the puzzle without even doing that step should be more evidence of that.
Very neat puzzle 👍🏻 Finished in about 20 minutes. I know Mark admitted that there were a couple of things he was slow to spot, which definitely made a big difference (and the diversion and back-track), but for me the start was with 1s, and I'm pretty sure this is a legitimate break-in (but willing to be corrected if I've made a leap I wasn't entitled to!).
After identifying the positive diagonal in box 5 as consisting of 1-5-6, next is to consider the corner boxes. Looking at boxes 1 and 9, we know that _at least one of them_ must have the 5 and/or 7 on a blue line, and therefore also a 1 on the knuckle of the blue line. Now in boxes 3 and 7, where we also know we need to put a 1 on a knuckle, if we put a 1 in either of the circles, it will force the 1-on-a-knuckle in box 1 and/or box 9 into the circle ... giving us two circled 1s, which is not allowed. This places 1s in r1c7 and r9c3.
Amazing, Mark. Especially once you have had an interruption, that you can return to the puzzle without having to spend a lot of time figuring out what you were doing!
I finished in 63 minutes exactly. This ruleset with the integer quotient was really fun to figure out in this geometry. It's really cool figuring out the meta of the rule with certain digits having to have certain partners. I think my favorite part was seeing that 1's couldn't go on the circles in boxes 3 and 7 due to it forcing too many 2's into circles. This was a clean puzzle and I enjoyed it. Great Puzzle!
Often I think of a commenter I saw forever ago saying that themselves and Mark would make one of the best sodoku teams and I can't help but agree. Mark being the intelligent solver marching only forward in logic, and myself being the buffoon reminding him of previous wisdoms (thinking this time of the 6's being restricted out of 2 rows of the puzzle and giving us the 1,2,3,4 in the circles)
@52:15, and that is also a 4 because you needed four 4's in the circles and you could put one in Row 1, one in Row 5, one if Row 9, and are only left with r2c2 as a place for a 4 in Row 2. Been that way since the moment you saw it had to be 1234 in the circles.
Another very interesting and original idea, thanks, enjoyed this.
Glad they had the 3 cell blue lines up front, Was trying to make them 1-2-4-8 without thinking that anything divided by 1 is an integer as well as others with 2, 3, and 4.
6 in a circle on a blue line would need 2 and 3 on its sides. Since 1 has be on the other line, 4 is the only low digit available for the whisper which breaks it. There you go, Mark. Free of charge as it only took me 5 seconds to see it.
Also, 6s in circles in boxes 3 and 7, requiring 2 & 3 on both sides in those boxes, forces 236 into box 5 on the positive diagonal, but we already know those are 156.
Damn Mark, I feel for you. The 4 in the circle in box 1 would have spared you half an hour of mental frustrations.
This one just clicked for me, 29:27, I don't normally solve faster than Mark at all. Very interesting puzzle. The German Whispers force certain numbers onto the factor line, which makes German whispers difficult, which rules out numbers in the circles.
00:32:49 for me. Wonderful puzzle. Not sure if I solved it in the most efficient way, but fully enjoyed it! Kind comment.
25:21 finish. A fun puzzle, but those thick blue lines made it difficult to read the pencil marks.
“Quotient” is the new word of the week.
19:46 for me. Nice puzzle!
Great puzzle.
i think he got that 4 in box 1 the hard way
Excellent original logic. It can be elegantly solved with *placeholder digits* as it is quasi-symmetrical, but you need to understand that four of the circles break symmetry and therefore they are not compatible with placeholders. They are supposed to be used as disambiguators.
Ideally, it is desirable to ignore disambiguators up tp the very end of your solve, but in this case it was not possible... I marked them in *black,* but immediately after breaking in I was forced to use them to disambiguate. In other words, I had to switch to real digits.
In this puzzle, each paceholder represented either itself or the diametrically opposite digit (with respect to the center of the grid).
Hence the final transformation needed to switch from a set of placeholders to the other was a *180° rotation.*
Of course, there are two alternative sets of placeholder digits and only one of them is compatible with the disambiguators (i.e. it coincides with the unique set of *real digits* that solves the puzzle).
See my playlist if you want to learn more about this powerful technique.
Of course, this puzzle is too easy to showcase the full power of placeholder digits, but it can be used to train this technique, which proves to be useful much more often than most people think.
Believe me, even Mark and Simon dozens of times in the past got dramatically bogged down in puzzles that would have become easy if they had used placeholders to simplify their notation.
I have been watching CTC every day for almost four years, and every time I try and solve before watching.
With the circles and the quotient rules playing such a powerful role throughout the solve, it would never occur to me to even _consider_ using placeholder digits in this puzzle. It isn't a remotely appropriate puzzle to think about using them in any way at all.
@@stevieinselby I would say that it did not occur to you just because you are not familiar enough with *placeholder digits.*
This puzzle is rotationally quasi-symmetric, (i.e. the non-symmetric clues are minimal and can be ignored long enough to allow you to break in), hence it is *by definition* compatible with placeholder digits. This is not a matter of opinion.
Sometimes, puzzles that are compatible with this notation technique are so simple that it is not worth using it. But this is a matter of *personal preference.* In this case, it was worth *for me.* It was also extremely helpful *to me,* as it allowed *me* to break-in in a very short time.
And it was fun❗
Just WOW
I don’t understand the quotient rule.
Mark explained it when he went through the rules as one number must divide into the other evenly, meaning with no remainder. So 2 divides into 6 3 times (no remainder) but 2 divides into 5 2 times with a remainder of 1 - or, 2.5 times, and 2.5 is not an integer.
Once there could not be 4's in boxes 3 and 7, to put the four 4's there should be two of them in boxes 1 and 2
😊
24:38 today. took me about 15 minutes to break in. once that was done it was just filling.