April 2019

[a1call]

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.

[Xyzzy]

http://www.research.ibm.com/haifa/po...April2019.html

[a1call]

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.

\\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:

[   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.

[Kebbaj]

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.

[Kebbaj]

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.

[axn]

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.

[Kebbaj]

Well seen axn!!