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No-op puzzle
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Posted on: Mon Dec 05, 2011 4:43 am

Posts: 422
Joined: Fri May 13, 2011 2:43 am
No-op puzzle
I thought we'd start a new thread on this. I just made one and I believe it has a unique solution:

Operators: +,-,x,:

Any comments? Trivial? Easy? Medium? Hard?

Posted on: Mon Dec 05, 2011 5:34 am

Posts: 422
Joined: Fri May 13, 2011 2:43 am
Re: No-op puzzle
If you're not sure what no op means, it means that the operator isn't specified. For example, "2" for a two-cell cage can mean...
2+ (no possibility)
2- (3,1 or 4,2 or 5,3)
2x (1,2)
2: (1,2 or 2,4)

Posted on: Mon Dec 05, 2011 6:23 am

Posts: 175
Joined: Fri May 13, 2011 2:11 am
Re: No-op puzzle
Seemed pretty easy, solved in paint. Probably was about comparable to the easier difficult 5x5's or the harder medium 5x5's. I believe the solution to be unique as well, based off the positioning of the 2's. Was, however, not what I'd consider to be a "hard puzzle."

Posted on: Mon Dec 05, 2011 10:41 am

Posts: 246
Location: Lisbon, Portugal
Joined: Sun Sep 18, 2011 5:40 pm
Re: No-op puzzle
Interesting variant! But it's unnecessary to make it much harder. It must be limited to the 4 elementary operations and to the 6x6 size at most.
Why Patrick doesn't create a new page ( weekly ) with these no usual puzzles from the ideas of Sneaklyfox, Clm, Giulio,and others?

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Posted on: Mon Dec 05, 2011 11:53 am

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: No-op puzzle
sneaklyfox wrote:
I thought we'd start a new thread on this. I just made one and I believe it has a unique solution:

Operators: +,-,x,:

Any comments? Trivial? Easy? Medium? Hard?

Very interesting, between easy and medium, difficult for beginners, solution unique in my opinion. But I have observed a curiosity, the cages "2" (c1-c2), "3" (a3-a4), "5" (c3-c4) and "2" (d3-e3), once the puzzle is solved show some type of "uncertainty" with respect to the operation, two different operations may be applied in all four cages. To make it absolutely unique (that is to have also the unicity of the operations, satisfying the "purist" kenken players, though most people would probably prefer that the type of arithmetic operation be considered irrelevant) and with more or less the same level of difficulty I suggest a variation as below (I believe also with a unique solution):

Posted on: Tue Dec 06, 2011 1:05 am

Posts: 175
Joined: Fri May 13, 2011 2:11 am
Re: No-op puzzle
In my opinion, the solution is sufficiently unique if no other arrangement of numbers satisfies all the requirements. In this case, I believe that to be true even without the changes.

Posted on: Fri Dec 09, 2011 10:06 pm

Posts: 422
Joined: Fri May 13, 2011 2:43 am
Re: No-op puzzle
I think a puzzle is fine as long as the solution is unique. Making it so that the operators also have to be unique makes the puzzle even easier because it limits the operators and so also limits the possibilities.

Posted on: Sat Dec 10, 2011 12:24 am

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: No-op puzzle
sneaklyfox wrote:
I think a puzzle is fine as long as the solution is unique. Making it so that the operators also have to be unique makes the puzzle even easier because it limits the operators and so also limits the possibilities.

Yes, the no-op puzzle in 5x5 (or 6x6 or even 7x7) is a very nice type of puzzle anyway, but I wanted to underline that curious situation, really both possibilities could be considered at the time of creating them, that is, with the unicity of the operations or regardless of this, in fact it would be more interesting to let the generator free, without a previously defined target in that sense (without that restriction) because, really, the puzzlers are generally more interested in finding a solution (having the certainty that the position of the numbers found is unique) than in observing the unicity of the operations.

Other subject is if the puzzle itself is going to be easy with that unicity, I am not very sure about that, the complexity may depend more on the size of the puzzle or on the size of the cages and other factors, etc., I believe that even with that unicity of the operations a very difficult puzzle could be conceived, even starting in 6x6.

Posted on: Sat Dec 10, 2011 1:51 pm

Posts: 246
Location: Lisbon, Portugal
Joined: Sun Sep 18, 2011 5:40 pm
Re: No-op puzzle
sneaklyfox wrote:
I think a puzzle is fine as long as the solution is unique. Making it so that the operators also have to be unique makes the puzzle even easier because it limits the operators and so also limits the possibilities.

I also agree with Sneaklyfox about the unicity of the numbers. It is, of course, the condition number 1 for a puzzle be a puzzle.
But I don't understand when she talks about " the unicity of operators ":
If "2-cage"=[1,2] maybe 2x1 or 2:1 and it looks like the unicity of the operators is an utopia! If a cage has an operation -, :,x it is many times possible to impute another operation.
For a "3-cage"=[1,2,6] "3-" =6-2-1 and "3:"=6:2:1 !

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Posted on: Sat Dec 10, 2011 7:46 pm

Posts: 422
Joined: Fri May 13, 2011 2:43 am
Re: No-op puzzle
clm wrote:
Other subject is if the puzzle itself is going to be easy with that unicity, I am not very sure about that, the complexity may depend more on the size of the puzzle or on the size of the cages and other factors, etc., I believe that even with that unicity of the operations a very difficult puzzle could be conceived, even starting in 6x6.

It does probably depend more on the size of the puzzle and/or other factors, but limiting the unicity of the operations makes it easier in my mind. Let's take the 5x5 puzzle. For example, if you have a "2" cage with two cells, you will automatically know the numbers cannot be 1,2 because then it could be 1x2 or 2:1 in essence ruling out possibilities. More possibilities make puzzles harder.

jomapil wrote:
But I don't understand when she talks about " the unicity of operators ":
If "2-cage"=[1,2] maybe 2x1 or 2:1 and it looks like the unicity of the operators is an utopia! If a cage has an operation -, :,x it is many times possible to impute another operation.
For a "3-cage"=[1,2,6] "3-" =6-2-1 and "3:"=6:2:1 !

The unicity of operators or unicity of operations is something clm brought up. It means you can't be ambiguous about operators. As mentioned above, you could never have a "2" cage with the solution consisting of a 1 and 2 because the operator is ambiguous... is it multiplication or division? Either is possible. I think you got the idea anyway. Like the "3" three-cell cage [1,2,6] that you mentioned. Operator can be - or :. If operator must be unique then the only possibility I see would be [1,1,5] (L-shaped cage in a 6x6 puzzle) as only 3- satisfies the cage.

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