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Old 2019-01-05, 12:46   #34
science_man_88
 
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here's another thing you all may have noticed neither A or B can have more than 2 values mod 4 within them.
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Old 2019-01-05, 17:06   #35
henryzz
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Have found plenty of 4+3 solutions but no 4+4 yet. Not sure I can search much further
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Old 2019-01-07, 09:57   #36
henryzz
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Quote:
Originally Posted by henryzz View Post
Have found plenty of 4+3 solutions but no 4+4 yet. Not sure I can search much further
Turns out I had a bug. 4+4 solutions found.

Something I hadn't realized is that if A=[a,b,c,d] and B=[e,f,g,h] is a solution then A=[a-1,b-1,c-1,d-1] and B=[e+1,f+1,g+1,h+1] is a solution. I think this means that you can set a=1 and generate all solutions based on this.
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Old 2019-01-07, 10:44   #37
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Quote:
Originally Posted by henryzz View Post
I think this means that you can set a=1 and generate all solutions based on this.
Or set a=0. This way, all the entries in the other set will be squares.
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Old 2019-01-07, 12:47   #38
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Unfortunately I have found a bug that invalidates my solutions.

@axn that is potentially a useful idea.
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Old 2019-01-13, 07:46   #39
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Eight days ago, I have found a 4+4 solution and a few hours later a 4+5 solution - sufficient for a "*". But the search for a 4+6 solution - [a1,a2,a3,a4] and [b1,b2,b3,b4,b5,b6] with ai+bj = square number seems to be difficult. Until now I have only three “quasi-solutions” with 23 of 24 fulfilled conditions:
cij: = ai +bj = a square number is correct for i = 1 to 4 and j = 1 to 6; only
a4 + b6 is no square number.
I would like to know which sort of solutions other people with “*” have sent to the puzzle master.

Last fiddled with by Dieter on 2019-01-13 at 07:49
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Old 2019-01-13, 17:04   #40
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Quote:
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I would like to know which sort of solutions other people with “*” have sent to the puzzle master.
I've found a 4+6 solution.
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Old 2019-01-13, 20:20   #41
petrw1
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Default The age old binary question: 1 or 0

Just curious if you are having more luck if a1=1 or a1=0?
I found a (4,3) solution quite easily with a1=1.

I guess the third option could be: a1 != {0,1}
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Old 2019-01-14, 07:50   #42
Dieter
 
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[QUOTE=petrw1;505800]Just curious if you are having more luck if a1=1 or a1=0?
I found a (4,3) solution quite easily with a1=1.


That's no question for me, because I don't use ai and bj as parameters. My parameters for the search are the square numbers cij = ai + bj.


I don't know, if I am allowed to write more here.
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Old 2019-01-14, 11:44   #43
henryzz
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Quote:
Originally Posted by petrw1 View Post
Just curious if you are having more luck if a1=1 or a1=0?
I found a (4,3) solution quite easily with a1=1.

I guess the third option could be: a1 != {0,1}
The value for a1 shouldn't make a difference. If you add 1 onto all As and subtract 1 from all Bs then you have a new solution. As such something needs to be fixed. This can be 0 or 1.
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Old 2019-01-14, 16:03   #44
petrw1
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Quote:
Originally Posted by henryzz View Post
The value for a1 shouldn't make a difference. If you add 1 onto all As and subtract 1 from all Bs then you have a new solution. As such something needs to be fixed. This can be 0 or 1.
Good point .... or if you have a 4X4 solution put a zero in one list.
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