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 2019-01-05, 12:46 #34 science_man_88     "Forget I exist" Jul 2009 Dumbassville 100000110000002 Posts here's another thing you all may have noticed neither A or B can have more than 2 values mod 4 within them.
 2019-01-05, 17:06 #35 henryzz Just call me Henry     "David" Sep 2007 Liverpool (GMT/BST) 25×11×17 Posts Have found plenty of 4+3 solutions but no 4+4 yet. Not sure I can search much further
2019-01-07, 09:57   #36
henryzz
Just call me Henry

"David"
Sep 2007
Liverpool (GMT/BST)

598410 Posts

Quote:
 Originally Posted by henryzz 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.

2019-01-07, 10:44   #37
axn

Jun 2003

23·233 Posts

Quote:
 Originally Posted by henryzz 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.

 2019-01-07, 12:47 #38 henryzz Just call me Henry     "David" Sep 2007 Liverpool (GMT/BST) 25×11×17 Posts Unfortunately I have found a bug that invalidates my solutions. @axn that is potentially a useful idea.
 2019-01-13, 07:46 #39 Dieter   Oct 2017 22×31 Posts 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
2019-01-13, 17:04   #40
uau

Jan 2017

2×3×23 Posts

Quote:
 Originally Posted by Dieter 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.

 2019-01-13, 20:20 #41 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 143D16 Posts 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}
 2019-01-14, 07:50 #42 Dieter   Oct 2017 22×31 Posts [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.
2019-01-14, 11:44   #43
henryzz
Just call me Henry

"David"
Sep 2007
Liverpool (GMT/BST)

135408 Posts

Quote:
 Originally Posted by petrw1 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.

2019-01-14, 16:03   #44
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

3·11·157 Posts

Quote:
 Originally Posted by henryzz 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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