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 no-op puzzle - is this reasoning correct? - newbie alert 
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Posted on: Sat Mar 10, 2018 10:18 am




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Joined: Wed Mar 07, 2018 11:59 am
 no-op puzzle - is this reasoning correct? - newbie alert
In a no-op puzzle I see 2 fields that could contain 1 and 2 (and more). Can I disregard this combination because there is no way for me to know if it should be "2x1" or "2/1" ?
Same for 2,4 (could be 4/2 and 4-2).

In other words: when there are two possible operators, does this result in a puzzle with more than one solution (so: the combination is invalid) or is it a "don't care" situation?


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Posted on: Sat Mar 10, 2018 11:15 am




Posts: 556
Location: Ladysmith, BC, Canada
Joined: Fri May 13, 2011 1:37 am
Post Re: no-op puzzle - is this reasoning correct? - newbie alert
There is always one solution only for each puzzle......if you cannot make up your mind on that problem, then go to some of the other more obvious ones........get solutions for those and soon you will end up back at your questionable solutions and the real answer will show itself.........once you get a number of these, you should find that they get a little easier as certain combinations become more obvious.........they are (in my opinion) somewhat of a challenge to begin with but now I look forward to seeing them.......just like the puzzles that are +3 to -3.......I used to spend a lot of time on each of them and now am disappointed if they take longer than 8-10 minutes......good luck and enjoy this site(been on it for 8 years now).......maybe clm can help.......as he has helped a lot of us with these irritants when they show up


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Posted on: Sat Mar 10, 2018 11:38 am




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Joined: Thu May 12, 2011 11:58 pm
Post Re: no-op puzzle - is this reasoning correct? - newbie alert
In case this helps: the operator does not have to be unique (which is impossible anyway,
for many combinations multiple operators are valid, e.g. a cage that has "5" as a target,
and you find it must have a 1 and 5: x and : both work)


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Posted on: Sat Mar 10, 2018 12:28 pm




Posts: 368
Joined: Tue Mar 01, 2016 10:03 pm
Post Re: no-op puzzle - is this reasoning correct? - newbie alert
bogie2820 wrote:
In other words: when there are two possible operators, does this result in a puzzle with more than one solution (so: the combination is invalid) or is it a "don't care" situation?


I remember having the same issue when I first starting using this site a couple of years ago. But it was explained to me that the "unique solution" requirement only applies to the numbers, not the operators. I actually think it would be almost impossible to produce a no-op puzzle that had unique operators. I certainly don't recall ever seeing one, but then again I wasn't particularly checking to see if this was the case.

Perhaps Patrick can enlighten us. I would imagine any puzzle with unique operators would have to contain very few two cell cages.


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Posted on: Sat Mar 10, 2018 12:51 pm




Posts: 368
Joined: Tue Mar 01, 2016 10:03 pm
Post Re: no-op puzzle - is this reasoning correct? - newbie alert
I remember giving this a bit of thought when I first did no-op puzzles and there are three possible operator combinations.

: and x

Example 15 (as given by Patrick)

: and -

Example 126

+ and x

Example 123


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Posted on: Sat Mar 10, 2018 11:06 pm




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Joined: Fri May 13, 2011 6:51 pm
Post Re: no-op puzzle - is this reasoning correct? - newbie alert
beaker wrote:
There is always one solution only for each puzzle......


Long time ago, when the no-ops were introduced in the site, IIRC we kept a long debate (with sneaklyfox and other puzzlers) with respect to this subject. The final conclusion was that as long the unicity of the solution is produced (the position of the numbers and the value - final result - of the cages) the operator itself is in some way "indifferent" and does not create any problem in finding the solution.

Actually the no-op puzzles appear on Sundays (extra 6x6) and some times in the bonus puzzles (up to 7x7), these no-ops usually with natural numbers, I can not remember having seen them "from 0". The important thing, as you say, is to determine (imagine) the numbers, and later to assign an operator. In the case of the 6x6's, prime numbers like 7, 11, 13, 17, in a cage, must always be a sum. A "0" (three or more cells), or a "1" 2-cell cage, must always be a subtraction cage. In the case of the 6x6's, a 14 (in three cells, for instance), being not prime, must also be a sum, since a 7 cann't be present in the grid, while a 15 or a 16 could be a x or a + (the 15 could also be the result of a 2-cell cage, being obviously 3 and 5 the operands).

But my opinion is that it is possible to obtain the unicity of the operator too (though the difficulty of the puzzle would probably vary, the software should be modified to assign a different result of the cage anytime it detects there is not unicity for the operator).

For instance, for 123 (x or + if the result is 6) we could set a "0" (0-) instead of the result 6. For 24 (with an operator of - or : for a result of 2) we could assign an "8" (8x), and for 15 or 115 L-shape, for instance, with a result of 5, where we can set a x or a :, we could, respectively, modify the result of the cage to "4" (4-) or "7" (7+). Obviously now the no-op puzzle could be considered "different", but with the numbers in the same positions, and the uncertainty of the operators eliminated.


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Posted on: Sat Mar 10, 2018 11:30 pm




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Joined: Wed Mar 07, 2018 11:59 am
Post Re: no-op puzzle - is this reasoning correct? - newbie alert
Thanks most of you, you did understand my question.

It was my first time I encountered such a puzzle and got no heads up. In fact it took me quite a few seconds to realize I had to fill in the operators :)

I now know why my attempts to complete the puzzle failed. I had a choice between 1,2 and 4,6 (or so, don't remember exactly) and then I discounted 1,2 as invalid.

My reasoning: 1,2 cannot be a single solution (is it 2x1 or 2/1) so it has to be 6-4=2.

Of course then you will eventually get stuck and wonder where you went wrong...

Thanks for explaining in such detail. Yes, 1,5 is also a good example, exactly what I mean. I would have flagged this combination as wrong and if I would end up in having to fill in 1 and 5, I would have thought I made a mistake earlier on, and restart the puzzle.

I now know only the numbers are important, and I did complete that bonus puzzle.

cheers


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Posted on: Sun Mar 11, 2018 12:42 am




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Post Re: no-op puzzle - is this reasoning correct? - newbie alert
My longstanding grump is that, since the operators aren't unique, we shouldn't need to spend time filling them in. I think Patrick has said that the programming would be arduous to make that happen, though.


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Posted on: Sun Mar 11, 2018 1:57 pm




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Post Re: no-op puzzle - is this reasoning correct? - newbie alert
sjs34 wrote:
My longstanding grump is that, since the operators aren't unique, we shouldn't need to spend time filling them in. I think Patrick has said that the programming would be arduous to make that happen, though.

It's possible to do: every time a cage is full, the code needs to check every operator to see if there is at least one that leads to the target.

I feel it would be helping the puzzler though..


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Posted on: Sun Mar 11, 2018 2:01 pm




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Joined: Sun May 22, 2016 2:17 pm
Post Re: no-op puzzle - is this reasoning correct? - newbie alert
Well, if the puzzler filled out all of the numbers correctly, they already know what operations each cage would be performing. It just removes a tedious and annoying part of no-ops.

Along the same line, we don't need to put in operators when submitting no-op book puzzles, so why only on the website itself?


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