## January 20, 2019

Post puzzles for others to solve here.

### January 20, 2019

Code: Select all
` *-----------* |219|485|.7.| |863|917|524| |7..|.3.|891| |---+---+---| |.96|7..|48.| |3.8|.9.|..7| |.27|..8|..9| |---+---+---| |981|.7.|.45| |672|...|938| |.3.|8.9|71.| *-----------*`

Play/Print this puzzle online
dan

ArkieTech

Posts: 3355
Joined: 29 May 2006
Location: NW Arkansas USA

### Re: January 20, 2019

What! Really? This is too easy.
"Output from my solver": Show
Dense subset: In row 9, r9c1 r9c3 have identical candidates: 4 5
- Removing candidate 4 from r9c5
- Removing candidate 5 from r9c5
Dense subset: In block 6, r5c8 r6c8 have identical candidates: 5 6
- Removing candidate 6 from r5c7 r6c7
X-wing: In columns 5 & 9, digit 2 must go in row 4 or 9
Therefore candidate 2 can be removed from all other cells in rows 4 & 9
Removing candidate 2 from r4c6
XY-wing: Interdependent cells r4c6 r4c9 r5c7 each have two out of the three candidates 1 2 3.
Depending on the value of pivot cell r4c9, either r4c6 or r5c7 must have the value 1.
Therefore candidate 1 can be eliminated from cells which intersect r4c6 and r5c7.
- Eliminating candidate 1 from cell r5c4
- Eliminating candidate 1 from cell r5c6
* Cell r5c7 is the only valid location in row 5 for digit 1
- Removing candidate 1 from r6c7
* Cell r6c7 now has only one possible value: 3
- Removing candidate 3 from r6c4 r1c7 r4c9
* Cell r1c7 now has only one possible value: 6
- Removing candidate 6 from r1c9 r7c7
* Cell r1c9 now has only one possible value: 3
* Cell r7c7 now has only one possible value: 2
- Removing candidate 2 from r7c4 r7c6 r9c9
* Cell r9c9 now has only one possible value: 6
- Removing candidate 6 from r9c5
* Cell r9c5 now has only one possible value: 2
- Removing candidate 2 from r4c5
* Cell r4c5 now has only one possible value: 5
- Removing candidate 5 from r4c1 r6c5 r8c5 r5c4 r6c4
* Cell r4c1 now has only one possible value: 1
- Removing candidate 1 from r4c6 r6c1
* Cell r4c6 now has only one possible value: 3
- Removing candidate 3 from r7c6
* Cell r7c6 now has only one possible value: 6
- Removing candidate 6 from r7c4 r3c6 r5c6
* Cell r7c4 now has only one possible value: 3
* Cell r3c6 now has only one possible value: 2
- Removing candidate 2 from r3c4 r5c6
* Cell r3c4 now has only one possible value: 6
- Removing candidate 6 from r5c4 r6c4
* Cell r5c4 now has only one possible value: 2
* Cell r6c4 now has only one possible value: 1
- Removing candidate 1 from r8c4
* Cell r8c4 now has only one possible value: 5
* Cell r5c6 now has only one possible value: 4
- Removing candidate 4 from r5c2 r8c6 r6c5
* Cell r5c2 now has only one possible value: 5
- Removing candidate 5 from r5c8 r3c2 r6c1
* Cell r5c8 now has only one possible value: 6
- Removing candidate 6 from r6c8
* Cell r6c8 now has only one possible value: 5
* Cell r3c2 now has only one possible value: 4
- Removing candidate 4 from r3c3
* Cell r3c3 now has only one possible value: 5
- Removing candidate 5 from r9c3
* Cell r9c3 now has only one possible value: 4
- Removing candidate 4 from r9c1
* Cell r9c1 now has only one possible value: 5
* Cell r6c1 now has only one possible value: 4
* Cell r8c6 now has only one possible value: 1
* Cell r6c5 now has only one possible value: 6
* Cell r8c5 now has only one possible value: 4
* Cell r4c9 now has only one possible value: 2
RSW

Posts: 77
Joined: 01 December 2018
Location: Western Canada

### Re: January 20, 2019

Code: Select all
`+-----------------+---------------------+----------------+| 2      1     9  | 4       8      5    | 36    7     36 || 8      6     3  | 9       1      7    | 5     2     4  || 7      45    45 | 26      3      26   | 8     9     1  |+-----------------+---------------------+----------------+|e15     9     6  | 7      f25     123  | 4     8    b23 || 3      45    8  | 1256    9      1246 | 12    56    7  ||d145    2     7  | 1356    456    8    |c13    56    9  |+-----------------+---------------------+----------------+| 9      8     1  | 236     7      236  | 26    4     5  || 6      7     2  | 15      45     14   | 9     3     8  || 45     3     45 | 8      g2-6    9    | 7     1    a26 |+-----------------+---------------------+----------------+`

(6=2)r9c9 - (2=3)r4c9- (3=1)r6c7 - r6c1 = (1-5)r4c1 = (5-2)r4c5 = (2)r9c5 => - 6r9c5; stte

Clement
Ngisa

Posts: 1194
Joined: 18 November 2012

### Re: January 20, 2019

Code: Select all
`.----------------.-------------------.--------------.|   2     1   9  | 4      8     5    |  36  7    36 ||   8     6   3  | 9      1     7    |  5   2    4  ||   7     45  45 | 26     3     26   |  8   9    1  |:----------------+-------------------+--------------:| a(1)-5  9   6  | 7     c2(5)  123  |  4   8   c23 ||   3     45  8  | 1256   9     1246 |  12  56   7  ||  a145   2   7  | 1356   456   8    | b13  56   9  |:----------------+-------------------+--------------:|   9     8   1  | 236    7     236  |  26  4    5  ||   6     7   2  | 15     45    14   |  9   3    8  ||   45    3   45 | 8      26    9    |  7   1    26 |'----------------'-------------------'--------------'`

1r(4=6)c1 - (1=3)r6c7 - (3=25)r4c95 => -5 r4c1; stte
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2617
Joined: 22 May 2017

### Re: January 20, 2019

RSW wrote:What! Really? This is too easy.

If you find it so easy, perhaps you could start playing by the rules conventions already? Almost all of these are trivial to solve with more than one step, so we're not normally interested in those solutions (especially if presented as software-produced puke). It's quite all right to use multi-steps as training wheels, but don't expect anyone to be very impressed. I've also explained the presentation conventions to you a couple of times already, but it seems that you're not making any effort to follow any of them. It's not that hard
Last edited by SpAce on Mon Jan 21, 2019 12:41 am, edited 1 time in total.

SpAce

Posts: 2617
Joined: 22 May 2017

### Re: January 20, 2019

Code: Select all
` *-----------------------------------------------------------* | 2     1     9     | 4     8     5     | 36    7     36    | | 8     6     3     | 9     1     7     | 5     2     4     | | 7     45    45    | 26    3     26    | 8     9     1     | *-------------------+-------------------+-------------------| |d15    9     6     | 7    b25   c123   | 4     8    c23    | | 3     5-4   8     | 1256  9    a1246  | 12    56    7     | |d145   2     7     | 1356 b56-4   8     |c13    56    9     | *-------------------+-------------------+-------------------| | 9     8     1     | 236   7     236   | 26    4     5     | | 6     7     2     | 15   b45    14    | 9     3     8     | | 45    3     45    | 8     26    9     | 7     1     26    | *-----------------------------------------------------------*`

4r5c6 = (245)r468c5 - (2=13)(r4c69)&(b6p37) - (1=45)r46c1 => -4 r4c2,r6c5 ; stte

Or:

Code: Select all
` *-----------------------------------------------------------* | 2     1     9     | 4     8     5     | 36    7     36    | | 8     6     3     | 9     1     7     | 5     2     4     | | 7     45    45    | 26    3     26    | 8     9     1     | *-------------------+-------------------+-------------------| |c15    9     6     | 7     5-2  c123   | 4     8   ac23    | | 3     45    8     | 1256  9     1246  | 12    56    7     | |b145   2     7     | 1356  456   8     |a13    56    9     | *-------------------+-------------------+-------------------| | 9     8     1     | 236   7     236   | 26    4     5     | | 6     7     2     | 15    45    14    | 9     3     8     | | 45    3     45    | 8     26    9     | 7     1     26    | *-----------------------------------------------------------*`

(2=13)b6p37 - 1r6c1 = (123)r4c169 => -2 r4c5 ; stte
Last edited by SteveG48 on Sun Jan 20, 2019 7:25 pm, edited 1 time in total.
Steve

SteveG48
2019 Supporter

Posts: 3066
Joined: 08 November 2013
Location: Orlando, Florida

### Re: January 20, 2019

SpAce wrote:
RSW wrote:What! Really? This is too easy.

If you find it so easy, perhaps you could start playing by the rules already? Almost all of these are trivial to solve with more than one step, so we're not normally interested in those solutions (especially if presented as software-produced puke). It's quite all right to use multi-steps as training wheels, but don't expect anyone to be very impressed. I've also explained the presentation conventions to you a couple of times already, but it seems that you're not making any effort to follow any of them. It's not that hard

what? there are no defined rules in this forum (other than arguably that engine solutions are discouraged as they are against the spirit of a players' forum) and if someone thinks that a multi step solution is neat by itself, or otherwise easier to find than a single step solution, then they shouldn't be discouraged from posting it.

besides I looked through the solver output and it looks exactly like a one step solution. it's how I would have solved it myself as the xy wing is arguably simpler than any of the labelled chains in the other solutions since it has a well defined name. other than that it's computer generated I see nothing wrong with it

i wouldn't say it's "too easy", as sometimes having an easier puzzle thrown into the mix is nice, and i think having tiered difficulty levels in rotation like andrew stuart's dailies would be lovely!
Covid-19 is FAKE and it doesn't exist! It's all a CONSPIRACY by the world's governments to control your lives, take your jobs, avoid paying you, crash stocks on purpose to buy them cheap, raise taxes to make you pay for the economic impact of this fake pandemic, and sell you a fake vaccine that does nothing! Death counts are RIGGED and include deaths from cancer and car crashes! Hospitals are financially compensated to make up the death counts! The 2009 swine flu killed 500000 people and there were no lockdowns anywhere! Get them to admit it! Don't let them tell you what to do! End this disgusting social experiment! Stop buying into the government's lies and slander! #covid1984 #plandemic #endtheconspiracy #scamdemic #buybitcoins
Pat wrote:prenyast
999_Springs

Posts: 527
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

### Re: January 20, 2019

SpAce wrote:
Code: Select all
`.----------------.-------------------.--------------.|   2     1   9  | 4      8     5    |  36  7    36 ||   8     6   3  | 9      1     7    |  5   2    4  ||   7     45  45 | 26     3     26   |  8   9    1  |:----------------+-------------------+--------------:| a(1)-5  9   6  | 7     c2(5)  123  |  4   8   c23 ||   3     45  8  | 1256   9     1246 |  12  56   7  ||  a145   2   7  | 1356   456   8    | b13  56   9  |:----------------+-------------------+--------------:|   9     8   1  | 236    7     236  |  26  4    5  ||   6     7   2  | 15     45    14   |  9   3    8  ||   45    3   45 | 8      26    9    |  7   1    26 |'----------------'-------------------'--------------'`
1r(4=6)c1 - (1=3)r6c7 - (3=25)r4c95 => -5 r4c1; stte

FWIW, one can add two fins (in 5s) to SpAce's [reversed] chain to solve a simple kraken 1-Fish c5\r4 + rfr68c5 => -5 r4c1
5r68c5 - [(52=3)r4c95 - (3=1)r6c7 - 1r(6=4)c1] - 5r4c1

SteveC
Sudtyro2

Posts: 730
Joined: 15 April 2013

### Re: January 20, 2019

999_Springs wrote:what? there are no defined rules in this forum (other than arguably that engine solutions are discouraged as they are against the spirit of a players' forum) and if someone thinks that a multi step solution is neat by itself, or otherwise easier to find than a single step solution, then they shouldn't be discouraged from posting it.

You're right that there are no rules. There are conventions, however, and most of us prefer to comply with them because it makes solutions comparable and easy to read. Those conventions are explained here, and I clarified them here. For example:

Leren wrote:The challenge for a responder is to solve the puzzle with one non-basic move, if possible.

That's a pretty clear goal for most of us. Sometimes a multi-step solution is more elegant, however, especially if it's very clever or the alternative is an unreadable net or something otherwise overly complex. Yet most of the time there are relatively simple one-steppers available, which makes multi-steppers seem inferior. However, there's no rule that says they can't be used anyway (and I've made that clear myself as well):

Leren wrote:You are also quite free to respond with a multiple non basic move solution if you want to, because, as I said, there are no "rules" to stop you doing this. The whole idea of this convention is just to have fun solving puzzles.

Just to be clear: in this particular case I didn't have a problem with the multi-step solution itself but the lazy way it was presented (and the bit of undeserved arrogance accompanying it). It's disrespectful for the other participants who make an effort to comply with the conventions and present their solutions so that others can easily see what's going on without loading them into a software solver and tracking the steps there.

besides I looked through the solver output and it looks exactly like a one step solution. it's how I would have solved it myself as the xy wing is arguably simpler than any of the labelled chains in the other solutions since it has a well defined name.

What are you talking about? It clearly has two non-basic steps: an X-Wing and an XY-Wing, but because it's presented as software puke including basics, it's not immediately obvious how many non-basic moves it has. That's exactly what I'm complaining about. I don't think Dan would post a puzzle solvable with just an XY-Wing anyway. That would be way too easy.

other than that it's computer generated I see nothing wrong with it

I don't really see the computer generation as a problem, as long as the program was written by the poster (as is the case here). As far as I know, several regulars use or have used their own programs to produce neat solutions. One of these days I might do that too if I ever get around to programming my own solver, but until then I have to stick to manual solving (I do use Hodoku to clear basics, and in some rare cases to report backdoors if finding one-steppers proves to be difficult otherwise).

i wouldn't say it's "too easy", as sometimes having an easier puzzle thrown into the mix is nice, and i think having tiered difficulty levels in rotation like andrew stuart's dailies would be lovely!

Yeah, it's nice to have puzzles of varying difficulty, as it produces a larger variance in solution techniques. Mostly I like the level here because daily puzzles shouldn't take too much time. Sometimes they're perhaps a bit too easy for the first poster, like this one, but once the trivial solution is used up, others have to come up with something different (or more correctly, it's just another convention), which may not be as easy.

(Btw, if you look at the timestamps of the previously mentioned puzzle, you'll see that the whole process of solving, verifying, documenting, and posting my solution took at most 14 minutes (and probably less). Even though it was a trivial example with a large percentage of documentation overhead, one should be able to conclude that proper presentation doesn't take a whole lot of absolute time and effort even in more complex cases. Therefore I see no excuse to skip that part.)

SpAce

Posts: 2617
Joined: 22 May 2017

### Re: January 20, 2019

SpAce wrote:You're right that there are no rules. There are conventions, however, and most of us prefer to comply with them because it makes solutions comparable and easy to read. Those conventions are explained here, and I clarified them here. For example: ...

thanks for clarifying what the conventions are exactly, for a long time i had thought these conventions were only unwritten hivemind rules (that may change over time) that allowed players to understand each other's solutions, rather than being well defined. i'm surprised they were documented, however it's each person's choice as to whether they want to stick to them and you can never make someone follow these conventions (as a trivial example i don't stick to conventions about starting sentences with capital letters)

Just to be clear: in this particular case I didn't have a problem with the multi-step solution itself but the lazy way it was presented (and the bit of undeserved arrogance accompanying it). It's disrespectful for the other participants who make an effort to comply with the conventions and present their solutions so that others can easily see what's going on without loading them into a software solver and tracking the steps there.

i agree with you in principle but in this particular puzzle i think disrespectful is too strong a word to use - i can see where the user is coming from here, as it is the only puzzle i've seen where dan has left the singles/basics up to the sticking point in the starting position meaning that the written solution isn't too hard to follow if you refer to dan's original grid. I mean obviously it would be much clearer to see with the full pm grid, and work from there, and it saves a lot of effort for others if the key step(s) were highlighted and the rest taken out, but for this particular puzzle it is not necessary to load such a solution into a software solver (perhaps only because dan just made a mistake with the original puzzle). maybe the user concluded that it wasn't a big deal in this particular case. now if someone posted "software puke" like that for every puzzle they encountered i'm sure their posts would be blanked very quickly

What are you talking about?

this is where i disagree with your conventions. to me, an x-wing is a basic move, always has been, and nothing will ever change my mind on this. i was shocked to hear that you and leren (and maybe dan) think otherwise. i think the choice of basic moves is really arbitrary and each person can interpret it how they want. i also don't count quads as basics as they're so rare and hard for humans to spot, but i can see the case for including them. the speedsolver community (as an example) have been through this debate on what techniques are valid several times because of people's wildly differing opinions

besides space i read somewhere you're a big fan of nr and nc space to solve puzzles, if you allow locked sets in rc space why not allow them in the other spaces? i know you're only following what you think the conventions are without setting them, but it seems arbitrary

something otherwise overly complex

says the guy who posted that bug+23 or whatever it is i think it's hilarious, creative liberties are fun sometimes

I don't really see the computer generation as a problem, as long as the program was written by the poster (as is the case here). As far as I know, several regulars use or have used their own programs to produce neat solutions. One of these days I might do that too if I ever get around to programming my own solver, but until then I have to stick to manual solving (I do use Hodoku to clear basics, and in some rare cases to report backdoors if finding one-steppers proves to be difficult otherwise).

i think this sort of kills the point of posting or doing daily puzzles to put them through a computer solver like that but of course anyone can solve puzzles however they want
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Pat wrote:prenyast
999_Springs

Posts: 527
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

### Re: January 20, 2019

999_Springs wrote:to me, an x-wing is a basic move, always has been, and nothing will ever change my mind on this. i was shocked to hear that you and leren (and maybe dan) think otherwise.

I consider Locked Cells and Locked Sets to be basic moves.
dan

ArkieTech

Posts: 3355
Joined: 29 May 2006
Location: NW Arkansas USA

### Re: January 20, 2019

999_Springs wrote:this is where i disagree with your conventions. to me, an x-wing is a basic move, always has been, and nothing will ever change my mind on this.

What difference does it make? If we're going to play the "one step" game, it helps if we all use the same starting point. Whether an x-wing is called a basic move or not, we've informally agreed to not use it in getting to the starting point. <shrug>
Steve

SteveG48
2019 Supporter

Posts: 3066
Joined: 08 November 2013
Location: Orlando, Florida

### Re: January 20, 2019

999_Springs wrote:thanks for clarifying what the conventions are exactly, for a long time i had thought these conventions were only unwritten hivemind rules (that may change over time) that allowed players to understand each other's solutions, rather than being well defined. i'm surprised they were documented,

At first I didn't know about them either, but then someone raised a question about it some months ago. Incidentally it was about the same thing: someone thought basic fishes were or should be considered basic moves here. They're not; end of story.

however it's each person's choice as to whether they want to stick to them and you can never make someone follow these conventions

Sure. It's also each person's choice how they react to those who don't.

(as a trivial example i don't stick to conventions about starting sentences with capital letters)

Have you asked yourself why you choose to do so? While it's totally your prerogative, such a style makes anyone's text (slightly) less readable. Not a big deal, of course, as your writing is otherwise good and easy to read. But why? Most conventions exist for a good reason.

I mean obviously it would be much clearer to see with the full pm grid, and work from there, and it saves a lot of effort for others if the key step(s) were highlighted and the rest taken out, but for this particular puzzle it is not necessary to load such a solution into a software solver (perhaps only because dan just made a mistake with the original puzzle).

I don't think there was any mistake on Dan's part. It was on the easier side, of course, but still all right as long as the one-stepper convention was followed. The conventions are there partly to make things interesting, even when the puzzle is otherwise very easy. As I said in my original reply, most of these are quite trivial if you resort to multiple steps. Most (but not all -- like today's puzzle) are pretty easy as one-steppers too. Sometimes adding an extra rule can make a trivial puzzle more interesting, like when I posted one with an explicit stte-rule (otherwise it would have been solvable with just an X-Wing and a triple).

maybe the user concluded that it wasn't a big deal in this particular case.

I don't think his skill set yet supports making such conclusions. He could have used the easy opportunity to learn something new, if he'd tried to solve it as a one-stepper instead of posting the trivial two-stepper -- or at least used the opportunity to learn to present his solution properly. He chose to do neither, which to me seems like a wasted learning opportunity (among other things). It would be different if we all knew he could do both already, but there's no evidence of that.

now if someone posted "software puke" like that for every puzzle they encountered i'm sure their posts would be blanked very quickly

That's the thing. It would have been different had it been someone who usually follows conventions or posts especially interesting solutions (which gives more freedom in the presentation department, as far as I'm concerned). This was a newcomer who had been advised about the conventions a couple of times already (in a very friendly way) but chose to repeatedly ignore them anyway.

It would be nice to at least say thanks if someone bothers to explain the conventions in detail, but I don't think my previous attempts received any reaction at all (and neither has this, unfortunately, because I hate talking about people in third person). I can't help if I find that a bit arrogant or whatever. I don't think anyone ever told me about the conventions, but I picked them up by observing for quite a while before I started posting any of my own solutions here. Since then I've broken a few conventions myself but rarely because I didn't know better.

this is where i disagree with your conventions. to me, an x-wing is a basic move, always has been, and nothing will ever change my mind on this. i was shocked to hear that you and leren (and maybe dan) think otherwise. i think the choice of basic moves is really arbitrary and each person can interpret it how they want. i also don't count quads as basics as they're so rare and hard for humans to spot, but i can see the case for including them. the speedsolver community (as an example) have been through this debate on what techniques are valid several times because of people's wildly differing opinions

Yeah, but it's totally irrelevant what you or I or anyone else considers basic moves in their own solving. You're right that it's completely arbitrary. That doesn't change the fact that here X-Wings are considered non-basic moves, period. The same division is used by SudokuWiki and Hodoku, for example.

besides space i read somewhere you're a big fan of nr and nc space to solve puzzles, if you allow locked sets in rc space why not allow them in the other spaces? i know you're only following what you think the conventions are without setting them, but it seems arbitrary

Good point. If someone starts posting solutions in those spaces, then the concept of basic moves might need to be reconsidered. Somehow I doubt that.

I wrote:something otherwise overly complex

says the guy who posted that bug+23 or whatever it is i think it's hilarious, creative liberties are fun sometimes

Well, the BUG+23 was both a joke and a proof of concept. Glad if you liked it! There was no need for it, of course, but I just wanted to do it because I could. It's a fun reference when someone has trouble understanding how BUGs work. Sometimes, like today, I'm actually forced to post a regrettably complex solution because I can't find anything else (or don't want to spend more time looking for one). As Cenoman seems to have demonstrated, today was a good day to use two moves.

i think this sort of kills the point of posting or doing daily puzzles to put them through a computer solver like that but of course anyone can solve puzzles however they want

I guess I should see it that way too since I don't do it myself, but I just don't. I have nothing against it if someone writes an effective human-style solver that produces interesting and well-presented solutions. I presume that they must have a pretty solid understanding of various solving techniques to be able to code them, so what difference does it make if they let the computer do the heavy lifting? I think I understand where you're coming from, though, because from what I've seen you're most likely an exceptionally good manual solver.

SpAce

Posts: 2617
Joined: 22 May 2017

### Re: January 20, 2019

I apologize for my poor choice of words in my earlier post. Clearly, this puzzle is not "too easy". Actually, I was just surprised that my solver was able to solve it completely. It's rarely able to do that with these puzzles. Normally, I use the solver with the advanced techniques switched off just to do the initial grunt work so that I can then try to finish by hand. This time, I forgot to do that, and was surprised that it came up with a complete solution. So, I was a bit overenthusiastic in my post. Anyway, if it stimulated a lively discussion, I guess it wasn't all bad.
RSW

Posts: 77
Joined: 01 December 2018
Location: Western Canada

### Re: January 20, 2019

RSW wrote:I apologize for my poor choice of words in my earlier post. Clearly, this puzzle is not "too easy". Actually, I was just surprised that my solver was able to solve it completely. It's rarely able to do that with these puzzles. Normally, I use the solver with the advanced techniques switched off just to do the initial grunt work so that I can then try to finish by hand. This time, I forgot to do that, and was surprised that it came up with a complete solution. So, I was a bit overenthusiastic in my post. Anyway, if it stimulated a lively discussion, I guess it wasn't all bad.

Ok, good, and thanks for your response. Nothing wrong with being enthusiastic about your discoveries. I still wish you would at least acknowledge the conventions used here, though. I'm sure we'd all like you to participate, but it's more fun if everyone plays the same game and presents their results in roughly similar format. We're happy to help with both aspects, and no one expects perfection, but it would be nice to see some effort or even interest in learning on your part as well. I've already shown you twice how you could have presented your previous solutions in a compliant way, but received no acknowledgement or follow-up questions from you, which I tend to interpret as lack of interest. With this puzzle you had an easy opportunity to try it yourself -- and you could still do it. It's not a skill problem, I'm sure of it.

SpAce

Posts: 2617
Joined: 22 May 2017

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