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 2019-05-05, 04:56 #12 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2,333 Posts Looks like it's gonna be a quiet weekend. So I will post here. 176 correct submissions and no solutions posted yet. I assume the challenge is closed. No clue what the May challenge is talking about. Looks like they have decided to raise the bar this month.
 2019-05-06, 11:55 #13 Xyzzy     Aug 2002 23·1,069 Posts
2019-05-08, 00:57   #14
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

233310 Posts

Quote:
 Originally Posted by a1call ... because I found it interesting to write a code to generate a code to solve the large matrix.
FWIW & FTR:

You can run the following code in Pari-GP and then Copy & Paste the output (between the Markings) in Pari-GP to solve any (arbitrary speaking) positive odd number of Rows=Columns except for 19, 1 (and incidentally 0 ).

For larger Matrices you would need to modify the code so that it outputs to a file rather than the screen.

The algorithm is to populate all the Matrix with a prime number (19 in this case) and then increment all cells except for the central one by 6*(number of rows) until a prime is found that restores the prime average criteria. It doesn't take long to get a solution.

Code:
\\CTI-100-A by Rashid Naimi
\\ Run once in Pari-GP and the Copy the result between the markings and Paste in Pari-GP
\\ https://pari.math.u-bordeaux.fr/

allocatemem()
theSize = 101 \\\\\Enter an odd number other than 19 (dimension for the number of Rows/Columns)
theSize = theSize\2*2+1
{
theString =Str("
\\\\\\\\\\\\\\\\\\\\\\\\\\\Start copying from here.\\\\\\\\\\\\\\\\\\\\\\\\\\\
theSize = ",theSize ,"
a=matrix(theSize ,theSize )
for(i=1,theSize ,{
for(j=1,theSize ,
a[i,j]=19;
);
})
a
largestPrime =19;
for(i=1,theSize ,{
for(j=1,theSize ,
if(i==theSize\\2+1  && j==theSize\\2+1 ,next());
a[i,j]=largestPrime +theSize *6;
while(
!isprime(a[i,j]) || !isprime((a[i,1]");\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
for(k=2,theSize ,theString =Str(theString,"+a[i,",k,"]"));
theString =Str(theString,")/theSize )
||
!isprime((a[1,j]");\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
for(k=2,theSize ,theString =Str(theString,"+a[",k,",j]"));
theString =Str(theString,")/theSize )
||
!isprime((a[1,1]");\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
for(k=2,theSize ,theString =Str(theString,"+a[",k,",",k,"]"));
theString =Str(theString,")/theSize )
||
!isprime((a[1,",theSize ,"]");\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
for(k=2,theSize ,theString =Str(theString,"+a[",k,",",theSize-k+1,"]"));
theString =Str(theString,")/theSize )
,a[i,j]=a[i,j]+theSize *6;
);
largestPrime =a[i,j];
);
})
for(i=1,theSize ,print(a[i,]))
\\\\\\\\\\\\\\\\\\\\\\\\\\\End copying here & Paste in Pari-GP\\\\\\\\\\\\\\\\\\\\\\\\\\\

");
}
print(theString );
a 9 x 9 solution:

Code:
[   127    397    829    991   1747   3259   3529   4339   5419]

[  5527   7417   7741   8929  11251  13411  14437  15787  16651]

[ 16759  22051  25939  29017  29989  32257  34039  35227  39979]

[ 42409  44029  47809  59149  60337  61687  62929  64171  65413]

[ 65629  65899  70867  73459     19  74377  76213  78427  79399]

[ 82531  83773  84691 108991 109639 114661 116443 121789 125353]

[129457 130699 148573 149059 149113 153271 158293 158563 162829]

[163909 172009 172171 174763 176383 177949 179947 189019 190261]

[212239 214129 216829 217369 227251 229249 229897 231409 247609]
a 101 x 101 Solution is attached.
Attached Files
 101.txt (112.4 KB, 197 views)

 2019-05-08, 03:47 #15 Kebbaj     "Kebbaj Reda" May 2018 Casablanca, Morocco 11000112 Posts Hi Rachid Naimi, The question is like this: Find a b c d e f g h i Such the squre : a b c d e f g h i (a+b+c)/3 is prime (d+e+f)/3 prime (g+h+i)/3 prime (a+d+g)/3 prime (b+e+h)/3 prime (c+f+i)/3 prime (a+e+i)/3 prime (c+e+g)/3 prime All a,b,c,d,e,f,g,h,i are primes numbers. It's easy 3x3. Your 9×9 is Fauls: Example: First line 127+397+829+991+1747+3259+3529+4339+5419= 17378 The average is 17378/9 is not integer. Not Prime. Reda Kebbaj.
 2019-05-08, 04:19 #16 Kebbaj     "Kebbaj Reda" May 2018 Casablanca, Morocco 32×11 Posts There is a lot of 4X4, 5X5 solution. Here is one from Professor Barry O'Sulivan,MRIA: 4x4 19 37 31 29 97 17 11 23 43 7 13 109 5 103 61 3 Rows: 29.0 37.0 43.0 43.0 Cols: 41.0 41.0 29.0 41.0 Up: 13.0 Down: 2.0 5x5 29 61 41 31 23 127 17 43 19 89 59 67 3 37 199 83 13 79 11 229 7 107 139 47 5 Rows: 37.0 59.0 73.0 83.0 61.0 Cols: 61.0 53.0 61.0 29.0 109.0 Up: 13.0 Down: 2.0 Thanks to Serge Batalov who made me discover by a post on this forum the first time the sit IBM Ponther This. Reda Kebbaj.
2019-05-08, 04:48   #17
axn

Jun 2003

124748 Posts

Quote:
 Originally Posted by Kebbaj Your 9×9 is Fauls: Example: First line 127+397+829+991+1747+3259+3529+4339+5419= 17378 The average is 17378/9 is not integer. Not Prime.
Check again. 127+397+829+991+1747+3259+3529+4339+5419 = 20637. The average is 2293 which is a prime.

 2019-05-08, 23:55 #18 Kebbaj     "Kebbaj Reda" May 2018 Casablanca, Morocco 32×11 Posts Well seen axn!!

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