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 2019-04-02, 15:14 #1 Xyzzy     Aug 2002 864010 Posts April 2019
 2019-04-03, 13:45 #2 bsquared     "Ben" Feb 2007 22·941 Posts Easy to find solutions. I wonder what "elegant" looks like for this puzzle; mine surely are not.
 2019-04-03, 14:35 #3 bsquared     "Ben" Feb 2007 22·941 Posts Found a solution for 4x4
2019-04-03, 14:50   #4
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

45108 Posts

Quote:
 Originally Posted by bsquared Found a solution for 4x4
I stopped after 21x21. It seems pointless going further up.

2019-04-03, 14:59   #5
bsquared

"Ben"
Feb 2007

22·941 Posts

Quote:
 Originally Posted by a1call I stopped after 21x21. It seems pointless going further up.

Are all of your averages integers? I.e., all row/col/diag sums are 0 mod 21 as well as prime? If so then you have a much better search algorithm than me.

2019-04-03, 15:13   #6
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

23·33·11 Posts

Quote:
 Originally Posted by bsquared Are all of your averages integers? I.e., all row/col/diag sums are 0 mod 21 as well as prime? If so then you have a much better search algorithm than me.
Well shouldn't spoil the challenge at this point but there is a simple algorithm as a factor of number of rows as is obvious with the great number of solutions submitted this early.

 2019-04-03, 16:46 #7 lukerichards     "Luke Richards" Jan 2018 Birmingham, UK 25·32 Posts Thanks for sharing. My year 10 class (aged 14-15) had great fun with this today.
 2019-04-03, 17:55 #8 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 123128 Posts Yes quite easy indeed. ...
 2019-04-07, 20:36 #9 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 1001010010002 Posts Well, I did a 101x101 matrix because I found it interesting to write a code to generate a code to solve the large matrix. Otherwise it would have been prohibitively too much work to type the code to check all the 101+101+2 averages. ETA Again, I wished someone would write a "foreach" style function for the PARI-GP vectors/matrices or add a few decent numeric examples to the forvec loop documentation. Last fiddled with by a1call on 2019-04-07 at 20:59
2019-04-08, 15:01   #10
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

24×643 Posts

Quote:
 Originally Posted by bsquared all <...> sums are 0 mod 21 as well as prime?
now yafu is very angry with his daddy...

2019-04-09, 13:35   #11
bsquared

"Ben"
Feb 2007

22·941 Posts

Quote:
 Originally Posted by LaurV now yafu is very angry with his daddy...
Not sure I get it...

Anyway, I picked this back up and figured out a few more things, but I don't think I'll bother to progress much beyond 6x6.

 Similar Threads Thread Thread Starter Forum Replies Last Post Xyzzy Puzzles 74 2019-04-09 13:34 Xyzzy Puzzles 6 2019-04-04 16:32 Xyzzy Puzzles 17 2019-03-07 21:05 miroslavkures Number Theory Discussion Group 2 2018-12-27 08:59

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