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No-op puzzle
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Posted on: Sat Dec 10, 2011 8:44 pm

Posts: 699
Joined: Fri May 13, 2011 6:51 pm
Re: No-op puzzle
sneaklyfox wrote:
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.

Well, in order to have some additional fun I have gone one step more and developped this no-op 6x6 (+, -, x, :, numbers 1 to 6). I believe it has a unique solution (though there is not unicity in the operators ). Unfortunately, Patrick has not (for the moment) the solver prepared for the no-op puzzles so we cann't verify these unicities with the computer, it would have been interesting to see a "solver rating" for this type of puzzles (this 6x6 is not difficult, in my opinion).

sneaklyfox wrote:
... 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.

But in a "3" three-cell cage (L-shaped in a 6x6 puzzle) [1,1,3] could be another solution with the ":" operator, we go to a different situation, the cage "3" itself would admit several combinations, but the ambiguity we are talking about refers to the situation with the same operands, like with the [1,2,6] in "3", when the "-" and the ":" can be applied indifferently, as jomapil mentions and as you mention with the pair [1,2] in a "2" cage, otherwise, sneaklyfox, we could create additional confusion in this discussion.

Posted on: Sat Dec 10, 2011 11:32 pm

Posts: 422
Joined: Fri May 13, 2011 2:43 am
Re: No-op puzzle
clm wrote:
But in a "3" three-cell cage (L-shaped in a 6x6 puzzle) [1,1,3] could be another solution with the ":" operator, we go to a different situation, the cage "3" itself would admit several combinations, but the ambiguity we are talking about refers to the situation with the same operands, like with the [1,2,6] in "3", when the "-" and the ":" can be applied indifferently, as jomapil mentions and as you mention with the pair [1,2] in a "2" cage, otherwise, sneaklyfox, we could create additional confusion in this discussion.

In the "3" three-cell cage (L-shaped in 6x6), [1,1,3] would not be a possibility if we want to retain operator unicity because it could be done using the : operator or x operator. I'm just arguing for not having operator unicity as I think it limits possibilities.

Posted on: Sun Dec 11, 2011 1:45 am

Posts: 699
Joined: Fri May 13, 2011 6:51 pm
Re: No-op puzzle
sneaklyfox wrote:
clm wrote:
But in a "3" three-cell cage (L-shaped in a 6x6 puzzle) [1,1,3] could be another solution with the ":" operator, we go to a different situation, the cage "3" itself would admit several combinations, but the ambiguity we are talking about refers to the situation with the same operands, like with the [1,2,6] in "3", when the "-" and the ":" can be applied indifferently, as jomapil mentions and as you mention with the pair [1,2] in a "2" cage, otherwise, sneaklyfox, we could create additional confusion in this discussion.

In the "3" three-cell cage (L-shaped in 6x6), [1,1,3] would not be a possibility if we want to retain operator unicity because it could be done using the : operator or x operator. I'm just arguing for not having operator unicity as I think it limits possibilities.

Yes, you are right, for the unicity of the operator the only possibility is, in your example, "3" = [1, 1, 5] I had probably the mind in other place, all this interesting discussion has been useful in some way clarifying that it is better for this type of puzzle not forcing the unicity of the operator so that in a case like that, for a "3" cage (3-cell L-shape), we may consider "3" = [1, 1, 3], [1, 1, 5], [1, 2, 6] and forget the operator so arranging the numbers according to the rest of the puzzle. In the normal puzzles we imagine which numbers produce the result shown in the cage with that defined operator, in the no-op puzzle we must think in the possible numbers together with any possible operator that may produce that "blind" result. I am thinking too that increasing the number of the operators, using not only the arithmetic but the full set we have till the moment (that is, including the bitwise OR, the mod, the exponentiation, ... and even starting the numbers in 0) we may obtain very complex, diverse and difficult puzzles.

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