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 And a pseudohybrid 7x7 puzzle (with AND and XOR operators) 
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Posted on: Sat Dec 03, 2011 8:53 pm




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Post And a pseudohybrid 7x7 puzzle (with AND and XOR operators)
And a pseudohybrid 7x7 puzzle (with AND and XOR operators).

Hi, Patrick:

I have developped this other “pseudohybrid” 7x7 puzzle (arithmetic and logic only) containing two “new” logic operators, the AND and the XOR (Note *). I have solved the puzzle, in the usual way, and found that apparently it has only one solution. The puzzle contains the four conventional arithmetic operations (8 cages “-“, 1 cage “+”, 2 cages “x” and 2 cages “:”), the well known bitwise OR (3 cages), the AND (2 cages) and the XOR (3 cages). It seems to be not difficult. If you have the possibility of including these “new” operations in the solver, then if you give me a symbol for them, I would send you the code in order to confirm the unicity of the solution and to obtain the “solver rating”.

I have “painted” in yellow colour the new 2 cages AND, and in blue colour the new 3 cages XOR.

Note *: For those who are not very familiarized with Logic Operators, just to remind that these operate at bit level, like the bitwise OR, and that the “truth table” for both operations is:

AND
0 an 0 produce a 0
0 and 1 produce a 0
1 and 0 produce a 0
1 and 1 produce a 1. For instance:
011 (= 3)
101 (= 5)
------------
001 (= 1), that is, 3 AND 5 = 1 (“1and”).

XOR
0 an 0 produce a 0
0 and 1 produce a 1
1 and 0 produce a 1
1 and 1 produce a 0. For instance:
010 (= 2)
110 (= 6)
------------
100 (= 4), that is, 2 XOR 6 = 4 (“4xor”).

Image


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Posted on: Sat Dec 03, 2011 10:00 pm




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Joined: Thu May 12, 2011 11:58 pm
Post Re: And a pseudohybrid 7x7 puzzle (with AND and XOR operator
hi clm,

cool puzzle :-)

clm wrote:
If you have the possibility of including these “new” operations in the solver, then if you give me a symbol for them, I would send you the code in order to confirm the unicity of the solution and to obtain the “solver rating”

For XOR use ^,
and for AND use &.

Patrick


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Posted on: Sun Dec 04, 2011 12:51 am




Posts: 694
Joined: Fri May 13, 2011 6:51 pm
Post Re: And a pseudohybrid 7x7 puzzle (with AND and XOR operator
pnm wrote:

... For XOR use ^,
and for AND use &.

Patrick


Thank you, here is the code for the 7x7 pseudohybrid puzzle (arithmetic and logic operators), however I have observed that you are using the same symbol, ^, for the operation XOR than for the exponentiation (previous topic 7x7 hybrid with all operators), I assume it's Ok:

7
4,&,a1a2
1,^,b1b2
2,+,c1
7,|,d1e1
6,-,f1g1
3,-,c2d2
2,:,e2f2
3,-,g2g3
3,|,a3b3
1,-,c3c4
5,-,d3e3
5,+,f3
2,-,a4b4
15,x,d4c5d5
24,x,e4e5f5
7,|,f4g4
2,&,a5b5
3,-,g5g6
2,:,a6a7b7
5,+,b6
5,+,c6d6
5,^,e6f6
3,^,c7d7
2,-,e7f7
2,+,g7


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Posted on: Sun Dec 04, 2011 1:43 am




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Joined: Thu May 12, 2011 11:58 pm
Post Re: And a pseudohybrid 7x7 puzzle (with AND and XOR operator
clm wrote:
Thank you, here is the code for the 7x7 pseudohybrid puzzle (arithmetic and logic operators), however I have observed that you are using the same symbol, ^, for the operation XOR than for the exponentiation (previous topic 7x7 hybrid with all operators), I assume it's Ok:

Hm, you're right, I'll have to figure something out.

The ^ for XOR is borrowed from C, the ^ for exponentiation from LaTeX ..

Patrick


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Posted on: Sun Dec 04, 2011 7:30 am




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Post Re: And a pseudohybrid 7x7 puzzle (with AND and XOR operator
Very interesting.

clm (or anyone)... can you make a puzzle with no specified operator?


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Posted on: Sun Dec 04, 2011 9:37 am




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Joined: Fri May 13, 2011 6:51 pm
Post Re: And a pseudohybrid 7x7 puzzle (with AND and XOR operator
sneaklyfox wrote:
Very interesting.

clm (or anyone)... can you make a puzzle with no specified operator?


Yes, sneaklyfox, it is easy to prepare it but I think that, at least, the type of operations must be specified, if these are the four conventional arithmetic operations, etc. (since the Patrick Min's Calcudoku uses special operations that nobody else uses), otherwise I think it would be almost impossible to solve it.

Meanwhile, take a look at this "mathmojo" 9x9 kenken with blank cages and try to solve it (before checking the solution... those terrible 26 steps and 28 graphics [crying] ):

http://www.mathmojo.com/chronicles/kenken/

(Note: Reedited just to correct a typo error)


Last edited by clm on Sun Dec 04, 2011 1:05 pm, edited 1 time in total.



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Posted on: Sun Dec 04, 2011 10:14 am




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Joined: Fri May 13, 2011 2:11 am
Post Re: And a pseudohybrid 7x7 puzzle (with AND and XOR operator
clm wrote:
sneaklyfox wrote:
Very interesting.

clm (or anyone)... can you make a puzzle with no specified operator?


Yes, sneaklyfox, it is easy to prepare it but I think that, at least, the [b]type/b] of operations must be specified, if these are the four conventional arithmetic operations, etc. (since the Patrick Min's Calcudoku uses special operations that nobody else uses), otherwise I think it would be almost impossible to solve it.

Meanwhile, take a look at this "mathmojo" 9x9 kenken with blank cages and try to solve it (before checking the solution... those terrible 26 steps and 28 graphics [crying] ):

http://www.mathmojo.com/chronicles/kenken/

Did they manage to avoid the usual solution no-ops do where there are usually multiple solutions? I really dislike no-ops because they almost never do.


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Posted on: Sun Dec 04, 2011 1:22 pm




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Post Re: And a pseudohybrid 7x7 puzzle (with AND and XOR operator
starling wrote:
clm wrote:
sneaklyfox wrote:
Very interesting.

clm (or anyone)... can you make a puzzle with no specified operator?


Yes, sneaklyfox, it is easy to prepare it but I think that, at least, the type of operations must be specified, if these are the four conventional arithmetic operations, etc. (since the Patrick Min's Calcudoku uses special operations that nobody else uses), otherwise I think it would be almost impossible to solve it.

Meanwhile, take a look at this "mathmojo" 9x9 kenken with blank cages and try to solve it (before checking the solution... those terrible 26 steps and 28 graphics [crying] ):

http://www.mathmojo.com/chronicles/kenken/

Did they manage to avoid the usual solution no-ops do where there are usually multiple solutions? I really dislike no-ops because they almost never do.


I am not sure I am understanding you very well this time, starling (my English...! [crying] ), but I am in your group, I do not like them very much, though they can be built with a unique solution I believe (in this case the computer will elapse more time to insure the unicity consequently increasing the difficulty level) but they are a curious type of calcudokus anyway (the possibility of building them with a reduced number of solutions may be considered in some circumstances though the general philosophy for all type of puzzles "politically correct", sudokus, kakuros, kenkens, ... is that they have a unique solution, and this is easier at the time of publishing the solutions I think..., this is an absolute target in the case of Patrick's calcudokus).


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Posted on: Sun Dec 04, 2011 11:36 pm




Posts: 175
Joined: Fri May 13, 2011 2:11 am
Post Re: And a pseudohybrid 7x7 puzzle (with AND and XOR operator
clm wrote:
starling wrote:
Did they manage to avoid the usual solution no-ops do where there are usually multiple solutions? I really dislike no-ops because they almost never do.


I am not sure I am understanding you very well this time, starling (my English...! [crying] ), but I am in your group, I do not like them very much, though they can be built with a unique solution I believe (in this case the computer will elapse more time to insure the unicity consequently increasing the difficulty level) but they are a curious type of calcudokus anyway (the possibility of building them with a reduced number of solutions may be considered in some circumstances though the general philosophy for all type of puzzles "politically correct", sudokus, kakuros, kenkens, ... is that they have a unique solution, and this is easier at the time of publishing the solutions I think..., this is an absolute target in the case of Patrick's calcudokus).

Nah, it's not your English, for some reason I wrote the word solution where I meant problem in the bolded place. That post was written at the end of an 8 hours stretch studying for finals, and I wasn't exactly thinking completely straight (Finals wouldn't be so bad if my teachers weren't deliberately trying to screw my grades over because I never go to class. I actually explicitly had one teacher tell me that none of my answers on past tests are wrong, but he wouldn't be giving me credit back).

Anyhow, basically, it's between hard and impossible to write a difficult no-op that doesn't have multiple solutions. If it has one solution, it's probably easy. If it's hard, it probably has multiple solutions.


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Posted on: Sun Dec 04, 2011 11:46 pm




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Post Re: And a pseudohybrid 7x7 puzzle (with AND and XOR operator
starling wrote:
Anyhow, basically, it's between hard and impossible to write a difficult no-op that doesn't have multiple solutions. If it has one solution, it's probably easy. If it's hard, it probably has multiple solutions.

It is possible to modify my solver so it'll accept cages without an operation, but it'll be quite a job.
Once done, it should be possible to control the level of difficulty "as normal", i.e. to create a difficult
puzzle with a single solution.

Patrick


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