Magic Squares

Magic Squares

Suppose there is a NxN matrix. We want to fill the matrix with numbers from 1 to N*N( only once is used) and every row's/column's total is same.

Here is an example. N=5

1	7	13	19	25	65
14	20	21	2	8	65
22	3	9	15	16	65
10	11	17	23	4	65
18	24	5	6	12	65
65	65	65	65	65

It's really hard to write a program for any number N but if we can except the even numbers and take only odd numbers we can write a program to generate such matrices.

The Algorithm

C Source Code

#include<stdio.h>

int main(void)
{
    int i, j, n, k1, k2, z1, z2, Dizi[10000], A[30][30], B[30][30], D[30][30];

    printf("Enter the number (below 30 and odd): ");scanf("%d",&n);
    if ((n&1) == 0)
    {
       printf("ERROR! Must be ODD number");
       return 0;
    }
    for(i=0;i<n;i++)
    {
       Dizi[i] = i;
    }
    z1 = k1 = n/2 + 1 - 1;
    z2 = k2 = n/2 + 2 - 1;
    for(i=0;i<n;i++)
    {
       A[0][i] = i;
       B[0][i] = i;
    }
    for(i=1;i<n;i++)
    {
       for(j=0;j<n;j++)
       {
          A[i][j] = Dizi[z1];
          B[i][j] = Dizi[z2];
          z1++;
          z2++;
          if(z1>=n)
          {
                      z1 = 0;
          }
          if(z2>=n)
          {
                      z2 = 0;
          }
       }
       z1 = A[i][k1];
       z2 = B[i][k2];
    }
    for(i=0;i<n;i++)
    {
        for(j=0;j<n;j++)
        {
            D[i][j] = n * (A[i][j]+1 - 1) + B[i][j]+1;
        }
    }
    printf("Magic Square:\n");
    for(i=0;i<n;i++)
    {
       for(j=0;j<n;j++)
       {
          printf("%3d ", D[i][j]);
       }
       z1 = 0;
       for(j=0;j<n;j++)
          z1 += D[i][j];
       printf("= [%d]\n", z1);
    }
    printf("+__");
    for(i=1;i<n;i++)
                printf("___");
    printf("\n");
    for(j=0;j<n;j++)
    {
       z1 = 0;
       for(i=0;i<n;i++)
                  z1 += D[i][j];
       printf("%3d ", z1);
    }

    return 0;
}

Sample Execution

Enter the number (below 30 and odd): 5

Magic Square:

1	7	13	19	25	65
14	20	21	2	8	65
22	3	9	15	16	65
10	11	17	23	4	65
18	24	5	6	12	65
65	65	65	65	65

------------------------------------------------------------------------------------

Enter the number (below 30 and odd): 7

Magic Square:

1	9	17	25	33	41	49	175
26	34	42	43	2	10	18	175
44	3	11	19	27	35	36	175
20	28	29	37	45	4	12	175
38	46	5	13	21	22	30	175
14	15	23	31	39	47	6	175
32	40	48	7	8	16	24	175
175	175	175	175	175	175	175

------------------------------------------------------------------------------------

Enter the number (below 30 and odd): 11

Magic Square:

1	13	25	37	49	61	73	85	97	109	121	671
62	74	86	98	110	111	2	14	26	38	50	671
112	3	15	27	39	51	63	75	87	99	100	671
52	64	76	88	89	101	113	4	16	28	40	671
102	114	5	17	29	41	53	65	77	78	90	671
42	54	66	67	79	91	103	115	6	18	30	671
92	104	116	7	19	31	43	55	56	68	80	671
32	44	45	57	69	81	93	105	117	8	20	671
82	94	106	118	9	21	33	34	46	58	70	671
22	23	35	47	59	71	83	95	107	119	10	671
72	84	96	108	120	11	12	24	36	48	60	671
671	671	671	671	671	671	671	671	671	671	671