Magic squares of singly even order
A magic square of singly even order has a size that is a multiple of 4, plus 2 (e.g. 6, 10, 14). This means that the subsquares have an odd size, which plays a role in the construction.
The task: create a magic square of 6 x 6.
- Cf.
- See also
Java
<lang java>public class MagicSquareSinglyEven {
public static void main(String[] args) {
int n = 6;
for (int[] row : magicSquareSinglyEven(n)) {
for (int x : row)
System.out.printf("%2s ", x);
System.out.println();
}
System.out.printf("\nMagic constant: %d ", (n * n + 1) * n / 2);
}
public static int[][] magicSquareOdd(final int n) {
if (n < 3 || n % 2 == 0)
throw new IllegalArgumentException("base must be odd and > 2");
int value = 0;
int gridSize = n * n;
int c = n / 2, r = 0;
int[][] result = new int[n][n];
while (++value <= gridSize) {
result[r][c] = value;
if (r == 0) {
if (c == n - 1) {
r++;
} else {
r = n - 1;
c++;
}
} else if (c == n - 1) {
r--;
c = 0;
} else if (result[r - 1][c + 1] == 0) {
r--;
c++;
} else {
r++;
}
}
return result;
}
static int[][] magicSquareSinglyEven(final int n) {
if (n < 6 || (n - 2) % 4 != 0)
throw new IllegalArgumentException("base must be a positive "
+ "multiple of 4 plus 2");
int size = n * n;
int halfN = n / 2;
int subSquareSize = size / 4;
int[][] subSquare = magicSquareOdd(halfN);
int[] quadrantFactors = {0, 2, 3, 1};
int[][] result = new int[n][n];
for (int r = 0; r < n; r++) {
for (int c = 0; c < n; c++) {
int quadrant = (r / halfN) * 2 + (c / halfN);
result[r][c] = subSquare[r % halfN][c % halfN];
result[r][c] += quadrantFactors[quadrant] * subSquareSize;
}
}
int nColsLeft = halfN / 2;
int nColsRight = nColsLeft - 1;
for (int r = 0; r < halfN; r++)
for (int c = 0; c < n; c++) {
if (c < nColsLeft || c >= n - nColsRight
|| (c == nColsLeft && r == nColsLeft)) {
if (c == 0 && r == nColsLeft)
continue;
int tmp = result[r][c];
result[r][c] = result[r + halfN][c];
result[r + halfN][c] = tmp;
}
}
return result; }
}</lang>
35 1 6 26 19 24 3 32 7 21 23 25 31 9 2 22 27 20 8 28 33 17 10 15 30 5 34 12 14 16 4 36 29 13 18 11 Magic constant: 111
Perl 6
See Magic squares/Perl 6 for a general magic square generator. Note that it produces a magic square, not the magic square. The output is different each time.
- Output:
With a parameter of 6:
26 35 1 19 6 24 17 8 28 10 33 15 12 30 5 14 34 16 13 4 36 18 29 11 21 3 32 23 7 25 22 31 9 27 2 20 The magic number is 111
With a parameter of 10:
78 46 37 44 53 94 96 35 12 10 97 45 31 38 72 13 95 29 6 79 22 70 56 63 47 88 20 54 81 4 90 33 49 26 65 76 83 42 24 17 84 27 43 50 59 100 77 36 18 11 9 52 68 75 34 25 2 61 93 86 91 39 30 32 66 82 89 48 5 23 16 64 55 57 41 7 14 73 80 98 15 58 74 51 40 1 8 67 99 92 3 71 62 69 28 19 21 60 87 85 The magic number is 505
zkl
<lang zkl>class MagicSquareSinglyEven{
fcn init(n){ var result=magicSquareSinglyEven(n) }
fcn toString{
sink,n:=Sink(String),result.len(); // num collumns
fmt:="%2s ";
foreach row in (result)
{ sink.write(row.apply('wrap(n){ fmt.fmt(n) }).concat(),"\n") }
sink.write("\nMagic constant: %d".fmt((n*n + 1)*n/2));
sink.close();
}
fcn magicSquareOdd(n){
if (n<3 or n%2==0) throw(Exception.ValueError("base must be odd and > 2"));
value,gridSize,c,r:=0, n*n, n/2, 0;
result:=n.pump(List(),n.pump(List(),0).copy); // array[n,n] of zero
while((value+=1)<=gridSize){
result[r][c]=value; if(r==0){ if(c==n-1) r+=1;
else{ r=n-1; c+=1; }
} else if(c==n-1){ r-=1; c=0; } else if(result[r-1][c+1]==0){ r-=1; c+=1; } else r+=1;
}
result;
}
fcn magicSquareSinglyEven(n){
if (n<6 or (n-2)%4!=0)
throw(Exception.ValueError("base must be a positive multiple of 4 +2"));
size,halfN,subSquareSize:=n*n, n/2, size/4;
subSquare:=magicSquareOdd(halfN);
quadrantFactors:=T(0, 2, 3, 1);
result:=n.pump(List(),n.pump(List(),0).copy); // array[n,n] of zero
foreach r,c in (n,n){
quadrant:=(r/halfN)*2 + (c/halfN);
result[r][c]=subSquare[r%halfN][c%halfN]; result[r][c]+=quadrantFactors[quadrant]*subSquareSize;
}
nColsLeft,nColsRight:=halfN/2, nColsLeft-1;
foreach r,c in (halfN,n){
if ( c<nColsLeft or c>=(n-nColsRight) or
(c==nColsLeft and r==nColsLeft) ){
if(c==0 and r==nColsLeft) continue; tmp:=result[r][c]; result[r][c]=result[r+halfN][c]; result[r+halfN][c]=tmp; }
}
result
}
}</lang> <lang zkl>MagicSquareSinglyEven(6).println();</lang>
- Output:
35 1 6 26 19 24 3 32 7 21 23 25 31 9 2 22 27 20 8 28 33 17 10 15 30 5 34 12 14 16 4 36 29 13 18 11 Magic constant: 111