An implementation of Dabbaghian & Wu's algorithm of constructing non-cyclic pandiagonal Latin squares for the order 13

the algorithm from:

Dabbaghian V, Wu T. Constructing non-cyclic pandiagonal Latin squares of prime orders. Journal of Discrete Algorithms. 2015;30:70–7.

https://doi.org/10.1016/j.jda.2014.12.001

The implementation was inspired by N.V. Makarova 2021

https://doi.org/10.5281/zenodo.4695879

import numpy as np

a_b = ((1,4),(1,10),(2,7),(2,8),(3,4),(3,12),(5,7),(5,11),(6,8),(6,11),(9,10),(9,12))
u = (4, 9, 1, 12, 1, 12)
lam1 = ( lambda a, b: (b - a) % 13,
        lambda a, b: (a - b) % 13,
        lambda a, b: (a + b) % 13,
        lambda a, b: (a + b) % 13,
        lambda a, b: (- b) % 13,
        lambda a, b: b % 13,
        lambda a, b: (a ** 2) % 13
       )
lam2 = ( lambda a, b, i: ((a + b) * i) % 13,
        lambda a, b, i: ((a + b) * i) % 13,
        lambda a, b, i: ((b - a) * i) % 13,
        lambda a, b, i: ((a - b) * i) % 13,
        lambda a, b, i: (a * i) % 13,
        lambda a, b, i: (a * i) % 13,
        lambda a, b, i: ((a + b) * i) % 13
       )


def findLam(a: int, b: int, j: int) -> int:
    for i in range(13):
        if lam1[j](a, b) == lam2[j](a, b, i):
            return i
    raise Exception('Failure to find lambda_L for j %d' % j)

    
def buildSquare(lam: int) -> np.ndarray:
    matrix = np.zeros((13, 13),dtype='int')
    for i in range(13):
        for j in range(13):
            matrix[i,j] = (lam * i + j) % 13
    return matrix


def shift(m: np.ndarray, u: int, a: int, b: int) -> None:
    l = findLam(a=a, b=b, j=6)
    for i in range(13):
        m[i, (i*u+a)%13], m[i, (i*u)%13], m[i, (i*u+b)%13], m[i, (i*u+b+l)%13], m[i, (i*u+l)%13], m[i, (i*u+l+b-a)%13] = m[i, (i*u)%13], m[i, (i*u+b)%13], m[i, (i*u+a)%13],  m[i, (i*u+l)%13], m[i, (i*u+b-a+l)%13], m[i, (i*u+b+l)%13]


def pandiagonal(matrix: np.ndarray) -> bool:
    matrix_ = matrix.copy()
    for i in range(1,13):
        matrix_[i,:] = matrix_[i,np.mod(np.arange(13) + i, 13)]
    for i in range(13):
        if np.unique(matrix_[:,i]).size < 13:
            print(np.unique(matrix_[:,i]).size)
            return False
    matrix_ = matrix.copy()
    for i in range(1,13):
        matrix_[i,:] = matrix_[i,np.mod(np.arange(13) - i, 13)]
    for i in range(13):
        if np.unique(matrix_[:,i]).size < 13:
            print(np.unique(matrix_[:,i]).size)
            return False
    return True

for n in range(12):
    for k in range(6):
        lamL = findLam(*a_b[n], k)
        square = buildSquare(lamL + 13)
        shift(square, u[k], *a_b[n])
        if(pandiagonal(square)):
            print('\n********************************************\n\tThe pandiagonal Latin square\n********************************************\n')
            print(square)
        else:
            print('\n++++++++++++++++++++++++++++++++++++++++++++\n\tTHE NON-PANDIAGONAL LATIN SQUARE\n++++++++++++++++++++++++++++++++++++++++++++\n')
            print(square)
            

********************************************
	The pandiagonal Latin square
********************************************

[[ 4  0  2  3  1  5  6  7 11  9 10 12  8]
 [11 12  1 10  6  2  4  5  3  7  8  9  0]
 [ 9 10 11  2  0  1  3 12  8  4  6  7  5]
 [ 6  8  9  7 11 12  0  4  2  3  5  1 10]
 [ 5  7  3 12  8 10 11  9  0  1  2  6  4]
 [ 3  4  8  6  7  9  5  1 10 12  0 11  2]
 [ 1  2  0  4  5  6 10  8  9 11  7  3 12]
 [ 0  9  5  1  3  4  2  6  7  8 12 10 11]
 [10  1 12  0  2 11  7  3  5  6  4  8  9]
 [ 8  6 10 11 12  3  1  2  4  0  9  5  7]
 [ 2 11  7  9 10  8 12  0  1  5  3  4  6]
 [ 7  5  6  8  4  0  9 11 12 10  1  2  3]
 [12  3  4  5  9  7  8 10  6  2 11  0  1]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 4  0  2  3  1  5  6  7 11  9 10 12  8]
 [12  3  4  5  9  7  8 10  6  2 11  0  1]
 [ 7  5  6  8  4  0  9 11 12 10  1  2  3]
 [ 2 11  7  9 10  8 12  0  1  5  3  4  6]
 [ 8  6 10 11 12  3  1  2  4  0  9  5  7]
 [10  1 12  0  2 11  7  3  5  6  4  8  9]
 [ 0  9  5  1  3  4  2  6  7  8 12 10 11]
 [ 1  2  0  4  5  6 10  8  9 11  7  3 12]
 [ 3  4  8  6  7  9  5  1 10 12  0 11  2]
 [ 5  7  3 12  8 10 11  9  0  1  2  6  4]
 [ 6  8  9  7 11 12  0  4  2  3  5  1 10]
 [ 9 10 11  2  0  1  3 12  8  4  6  7  5]
 [11 12  1 10  6  2  4  5  3  7  8  9  0]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 4  0  2  3  1  5  6  7 11  9 10 12  8]
 [ 2 11  7  9 10  8 12  0  1  5  3  4  6]
 [ 0  9  5  1  3  4  2  6  7  8 12 10 11]
 [ 5  7  3 12  8 10 11  9  0  1  2  6  4]
 [11 12  1 10  6  2  4  5  3  7  8  9  0]
 [ 7  5  6  8  4  0  9 11 12 10  1  2  3]
 [10  1 12  0  2 11  7  3  5  6  4  8  9]
 [ 3  4  8  6  7  9  5  1 10 12  0 11  2]
 [ 9 10 11  2  0  1  3 12  8  4  6  7  5]
 [12  3  4  5  9  7  8 10  6  2 11  0  1]
 [ 8  6 10 11 12  3  1  2  4  0  9  5  7]
 [ 1  2  0  4  5  6 10  8  9 11  7  3 12]
 [ 6  8  9  7 11 12  0  4  2  3  5  1 10]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 4  0  2  3  1  5  6  7 11  9 10 12  8]
 [ 6  8  9  7 11 12  0  4  2  3  5  1 10]
 [ 1  2  0  4  5  6 10  8  9 11  7  3 12]
 [ 8  6 10 11 12  3  1  2  4  0  9  5  7]
 [12  3  4  5  9  7  8 10  6  2 11  0  1]
 [ 9 10 11  2  0  1  3 12  8  4  6  7  5]
 [ 3  4  8  6  7  9  5  1 10 12  0 11  2]
 [10  1 12  0  2 11  7  3  5  6  4  8  9]
 [ 7  5  6  8  4  0  9 11 12 10  1  2  3]
 [11 12  1 10  6  2  4  5  3  7  8  9  0]
 [ 5  7  3 12  8 10 11  9  0  1  2  6  4]
 [ 0  9  5  1  3  4  2  6  7  8 12 10 11]
 [ 2 11  7  9 10  8 12  0  1  5  3  4  6]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 4  0  2  3  1  5  6  7 11  9 10 12  8]
 [ 5  1 10 12  0 11  2  3  4  8  6  7  9]
 [ 6  2 11  7  9 10  8 12  0  1  5  3  4]
 [ 1  3 12  8  4  6  7  5  9 10 11  2  0]
 [10 11  0  9  5  1  3  4  2  6  7  8 12]
 [ 9  7  8 10  6  2 11  0  1 12  3  4  5]
 [ 2  6  4  5  7  3 12  8 10 11  9  0  1]
 [11 12  3  1  2  4  0  9  5  7  8  6 10]
 [ 7  8  9  0 11 12  1 10  6  2  4  5  3]
 [ 0  4  5  6 10  8  9 11  7  3 12  1  2]
 [12 10  1  2  3  7  5  6  8  4  0  9 11]
 [ 8  9  7 11 12  0  4  2  3  5  1 10  6]
 [ 3  5  6  4  8  9 10  1 12  0  2 11  7]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 4  0  2  3  1  5  6  7 11  9 10 12  8]
 [ 3  5  6  4  8  9 10  1 12  0  2 11  7]
 [ 8  9  7 11 12  0  4  2  3  5  1 10  6]
 [12 10  1  2  3  7  5  6  8  4  0  9 11]
 [ 0  4  5  6 10  8  9 11  7  3 12  1  2]
 [ 7  8  9  0 11 12  1 10  6  2  4  5  3]
 [11 12  3  1  2  4  0  9  5  7  8  6 10]
 [ 2  6  4  5  7  3 12  8 10 11  9  0  1]
 [ 9  7  8 10  6  2 11  0  1 12  3  4  5]
 [10 11  0  9  5  1  3  4  2  6  7  8 12]
 [ 1  3 12  8  4  6  7  5  9 10 11  2  0]
 [ 6  2 11  7  9 10  8 12  0  1  5  3  4]
 [ 5  1 10 12  0 11  2  3  4  8  6  7  9]]

********************************************
	The pandiagonal Latin square
********************************************

[[10  0  3  6  4  5  2  7  8  9  1 11 12]
 [ 2  7  4  5  3  6  9 12 10 11  8  0  1]
 [ 4  1  6  7  8  0 10 11  9 12  2  5  3]
 [ 5  8 11  9 10  7 12  0  1  6  3  4  2]
 [12  9 10  8 11  1  4  2  3  0  5  6  7]
 [ 6 11 12  0  5  2  3  1  4  7 10  8  9]
 [ 0  3  1  2 12  4  5  6 11  8  9  7 10]
 [ 1  2  0  3  6  9  7  8  5 10 11 12  4]
 [ 3  4  5 10  7  8  6  9 12  2  0  1 11]
 [ 8  6  7  4  9 10 11  3  0  1 12  2  5]
 [ 7  5  8 11  1 12  0 10  2  3  4  9  6]
 [ 9 10  2 12  0 11  1  4  7  5  6  3  8]
 [11 12  9  1  2  3  8  5  6  4  7 10  0]]

********************************************
	The pandiagonal Latin square
********************************************

[[10  0  3  6  4  5  2  7  8  9  1 11 12]
 [11 12  9  1  2  3  8  5  6  4  7 10  0]
 [ 9 10  2 12  0 11  1  4  7  5  6  3  8]
 [ 7  5  8 11  1 12  0 10  2  3  4  9  6]
 [ 8  6  7  4  9 10 11  3  0  1 12  2  5]
 [ 3  4  5 10  7  8  6  9 12  2  0  1 11]
 [ 1  2  0  3  6  9  7  8  5 10 11 12  4]
 [ 0  3  1  2 12  4  5  6 11  8  9  7 10]
 [ 6 11 12  0  5  2  3  1  4  7 10  8  9]
 [12  9 10  8 11  1  4  2  3  0  5  6  7]
 [ 5  8 11  9 10  7 12  0  1  6  3  4  2]
 [ 4  1  6  7  8  0 10 11  9 12  2  5  3]
 [ 2  7  4  5  3  6  9 12 10 11  8  0  1]]

********************************************
	The pandiagonal Latin square
********************************************

[[10  0  3  6  4  5  2  7  8  9  1 11 12]
 [ 7  5  8 11  1 12  0 10  2  3  4  9  6]
 [ 1  2  0  3  6  9  7  8  5 10 11 12  4]
 [12  9 10  8 11  1  4  2  3  0  5  6  7]
 [ 2  7  4  5  3  6  9 12 10 11  8  0  1]
 [ 9 10  2 12  0 11  1  4  7  5  6  3  8]
 [ 3  4  5 10  7  8  6  9 12  2  0  1 11]
 [ 6 11 12  0  5  2  3  1  4  7 10  8  9]
 [ 4  1  6  7  8  0 10 11  9 12  2  5  3]
 [11 12  9  1  2  3  8  5  6  4  7 10  0]
 [ 8  6  7  4  9 10 11  3  0  1 12  2  5]
 [ 0  3  1  2 12  4  5  6 11  8  9  7 10]
 [ 5  8 11  9 10  7 12  0  1  6  3  4  2]]

********************************************
	The pandiagonal Latin square
********************************************

[[10  0  3  6  4  5  2  7  8  9  1 11 12]
 [ 5  8 11  9 10  7 12  0  1  6  3  4  2]
 [ 0  3  1  2 12  4  5  6 11  8  9  7 10]
 [ 8  6  7  4  9 10 11  3  0  1 12  2  5]
 [11 12  9  1  2  3  8  5  6  4  7 10  0]
 [ 4  1  6  7  8  0 10 11  9 12  2  5  3]
 [ 6 11 12  0  5  2  3  1  4  7 10  8  9]
 [ 3  4  5 10  7  8  6  9 12  2  0  1 11]
 [ 9 10  2 12  0 11  1  4  7  5  6  3  8]
 [ 2  7  4  5  3  6  9 12 10 11  8  0  1]
 [12  9 10  8 11  1  4  2  3  0  5  6  7]
 [ 1  2  0  3  6  9  7  8  5 10 11 12  4]
 [ 7  5  8 11  1 12  0 10  2  3  4  9  6]]

********************************************
	The pandiagonal Latin square
********************************************

[[10  0  3  6  4  5  2  7  8  9  1 11 12]
 [ 3  1  4  7 10  8  9  6 11 12  0  5  2]
 [ 6  7  5  8 11  1 12  0 10  2  3  4  9]
 [ 0 10 11  9 12  2  5  3  4  1  6  7  8]
 [12  4  1  2  0  3  6  9  7  8  5 10 11]
 [ 2  3  8  5  6  4  7 10  0 11 12  9  1]
 [ 5  6  7 12  9 10  8 11  1  4  2  3  0]
 [ 4  9 10 11  3  0  1 12  2  5  8  6  7]
 [11  8  0  1  2  7  4  5  3  6  9 12 10]
 [ 1  2 12  4  5  6 11  8  9  7 10  0  3]
 [ 7  5  6  3  8  9 10  2 12  0 11  1  4]
 [ 8 11  9 10  7 12  0  1  6  3  4  2  5]
 [ 9 12  2  0  1 11  3  4  5 10  7  8  6]]

********************************************
	The pandiagonal Latin square
********************************************

[[10  0  3  6  4  5  2  7  8  9  1 11 12]
 [ 9 12  2  0  1 11  3  4  5 10  7  8  6]
 [ 8 11  9 10  7 12  0  1  6  3  4  2  5]
 [ 7  5  6  3  8  9 10  2 12  0 11  1  4]
 [ 1  2 12  4  5  6 11  8  9  7 10  0  3]
 [11  8  0  1  2  7  4  5  3  6  9 12 10]
 [ 4  9 10 11  3  0  1 12  2  5  8  6  7]
 [ 5  6  7 12  9 10  8 11  1  4  2  3  0]
 [ 2  3  8  5  6  4  7 10  0 11 12  9  1]
 [12  4  1  2  0  3  6  9  7  8  5 10 11]
 [ 0 10 11  9 12  2  5  3  4  1  6  7  8]
 [ 6  7  5  8 11  1 12  0 10  2  3  4  9]
 [ 3  1  4  7 10  8  9  6 11 12  0  5  2]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 7  1  0  3  6  5 12  2  8  9 10 11  4]
 [ 2  3  4 10  0  7  6  9 12 11  5  8  1]
 [ 4 11  1  7  8  9 10  3  6  0 12  2  5]
 [ 6  5  8 11 10  4  7  0  1  2  3  9 12]
 [ 8  9  2  5 12 11  1  4  3 10  0  6  7]
 [ 3  6 12  0  1  2  8 11  5  4  7 10  9]
 [10  0  3  2  9 12  5  6  7  8  1  4 11]
 [ 1  7 10  4  3  6  9  8  2  5 11 12  0]
 [11  4  5  6  7  0  3 10  9 12  2  1  8]
 [ 5  8  7  1  4 10 11 12  0  6  9  3  2]
 [12  2  9  8 11  1  0  7 10  3  4  5  6]
 [ 9 10 11 12  5  8  2  1  4  7  6  0  3]
 [ 0 12  6  9  2  3  4  5 11  1  8  7 10]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 7  1  0  3  6  5 12  2  8  9 10 11  4]
 [ 0 12  6  9  2  3  4  5 11  1  8  7 10]
 [ 9 10 11 12  5  8  2  1  4  7  6  0  3]
 [12  2  9  8 11  1  0  7 10  3  4  5  6]
 [ 5  8  7  1  4 10 11 12  0  6  9  3  2]
 [11  4  5  6  7  0  3 10  9 12  2  1  8]
 [ 1  7 10  4  3  6  9  8  2  5 11 12  0]
 [10  0  3  2  9 12  5  6  7  8  1  4 11]
 [ 3  6 12  0  1  2  8 11  5  4  7 10  9]
 [ 8  9  2  5 12 11  1  4  3 10  0  6  7]
 [ 6  5  8 11 10  4  7  0  1  2  3  9 12]
 [ 4 11  1  7  8  9 10  3  6  0 12  2  5]
 [ 2  3  4 10  0  7  6  9 12 11  5  8  1]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 7  1  0  3  6  5 12  2  8  9 10 11  4]
 [12  2  9  8 11  1  0  7 10  3  4  5  6]
 [ 1  7 10  4  3  6  9  8  2  5 11 12  0]
 [ 8  9  2  5 12 11  1  4  3 10  0  6  7]
 [ 2  3  4 10  0  7  6  9 12 11  5  8  1]
 [ 9 10 11 12  5  8  2  1  4  7  6  0  3]
 [11  4  5  6  7  0  3 10  9 12  2  1  8]
 [ 3  6 12  0  1  2  8 11  5  4  7 10  9]
 [ 4 11  1  7  8  9 10  3  6  0 12  2  5]
 [ 0 12  6  9  2  3  4  5 11  1  8  7 10]
 [ 5  8  7  1  4 10 11 12  0  6  9  3  2]
 [10  0  3  2  9 12  5  6  7  8  1  4 11]
 [ 6  5  8 11 10  4  7  0  1  2  3  9 12]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 7  1  0  3  6  5 12  2  8  9 10 11  4]
 [ 6  5  8 11 10  4  7  0  1  2  3  9 12]
 [10  0  3  2  9 12  5  6  7  8  1  4 11]
 [ 5  8  7  1  4 10 11 12  0  6  9  3  2]
 [ 0 12  6  9  2  3  4  5 11  1  8  7 10]
 [ 4 11  1  7  8  9 10  3  6  0 12  2  5]
 [ 3  6 12  0  1  2  8 11  5  4  7 10  9]
 [11  4  5  6  7  0  3 10  9 12  2  1  8]
 [ 9 10 11 12  5  8  2  1  4  7  6  0  3]
 [ 2  3  4 10  0  7  6  9 12 11  5  8  1]
 [ 8  9  2  5 12 11  1  4  3 10  0  6  7]
 [ 1  7 10  4  3  6  9  8  2  5 11 12  0]
 [12  2  9  8 11  1  0  7 10  3  4  5  6]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 7  1  0  3  6  5 12  2  8  9 10 11  4]
 [ 8 11  5  4  7 10  9  3  6 12  0  1  2]
 [ 6 12  2  9  8 11  1  0  7 10  3  4  5]
 [ 9 10  3  6  0 12  2  5  4 11  1  7  8]
 [12  0  1  7 10  4  3  6  9  8  2  5 11]
 [ 2  3  4  5 11  1  8  7 10  0 12  6  9]
 [ 0  6  7  8  9  2  5 12 11  1  4  3 10]
 [ 1  4 10 11 12  0  6  9  3  2  5  8  7]
 [11  5  8  1  2  3  4 10  0  7  6  9 12]
 [ 3  2  9 12  5  6  7  8  1  4 11 10  0]
 [ 4  7  6  0  3  9 10 11 12  5  8  2  1]
 [ 5  8 11 10  4  7  0  1  2  3  9 12  6]
 [10  9 12  2  1  8 11  4  5  6  7  0  3]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 7  1  0  3  6  5 12  2  8  9 10 11  4]
 [10  9 12  2  1  8 11  4  5  6  7  0  3]
 [ 5  8 11 10  4  7  0  1  2  3  9 12  6]
 [ 4  7  6  0  3  9 10 11 12  5  8  2  1]
 [ 3  2  9 12  5  6  7  8  1  4 11 10  0]
 [11  5  8  1  2  3  4 10  0  7  6  9 12]
 [ 1  4 10 11 12  0  6  9  3  2  5  8  7]
 [ 0  6  7  8  9  2  5 12 11  1  4  3 10]
 [ 2  3  4  5 11  1  8  7 10  0 12  6  9]
 [12  0  1  7 10  4  3  6  9  8  2  5 11]
 [ 9 10  3  6  0 12  2  5  4 11  1  7  8]
 [ 6 12  2  9  8 11  1  0  7 10  3  4  5]
 [ 8 11  5  4  7 10  9  3  6 12  0  1  2]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 8  1  0  9  4  5  6  7  2 11 10  3 12]
 [ 0 12  5  1 10  3  2 11  6  7  8  9  4]
 [ 9 10 11  6  2  1  7  3 12  5  4  0  8]
 [ 7  6  2 10 11 12  0  8  4  3  9  5  1]
 [ 5 11  7  3  9  8  4 12  0  1  2 10  6]
 [ 3  4 12  8  7  0  9  5 11 10  6  1  2]
 [12  8  3  4  5  6  1 10  9  2 11  7  0]
 [ 4  0  9  2  1 10  5  6  7  8  3 12 11]
 [10  5  1  0  6  2 11  4  3 12  7  8  9]
 [ 1  9 10 11 12  7  3  2  8  4  0  6  5]
 [ 6  2  8  7  3 11 12  0  1  9  5  4 10]
 [11  7  6 12  8  4 10  9  5  0  1  2  3]
 [ 2  3  4  5  0  9  8  1 10  6 12 11  7]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 8  1  0  9  4  5  6  7  2 11 10  3 12]
 [ 2  3  4  5  0  9  8  1 10  6 12 11  7]
 [11  7  6 12  8  4 10  9  5  0  1  2  3]
 [ 6  2  8  7  3 11 12  0  1  9  5  4 10]
 [ 1  9 10 11 12  7  3  2  8  4  0  6  5]
 [10  5  1  0  6  2 11  4  3 12  7  8  9]
 [ 4  0  9  2  1 10  5  6  7  8  3 12 11]
 [12  8  3  4  5  6  1 10  9  2 11  7  0]
 [ 3  4 12  8  7  0  9  5 11 10  6  1  2]
 [ 5 11  7  3  9  8  4 12  0  1  2 10  6]
 [ 7  6  2 10 11 12  0  8  4  3  9  5  1]
 [ 9 10 11  6  2  1  7  3 12  5  4  0  8]
 [ 0 12  5  1 10  3  2 11  6  7  8  9  4]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 8  1  0  9  4  5  6  7  2 11 10  3 12]
 [ 6  2  8  7  3 11 12  0  1  9  5  4 10]
 [ 4  0  9  2  1 10  5  6  7  8  3 12 11]
 [ 5 11  7  3  9  8  4 12  0  1  2 10  6]
 [ 0 12  5  1 10  3  2 11  6  7  8  9  4]
 [11  7  6 12  8  4 10  9  5  0  1  2  3]
 [10  5  1  0  6  2 11  4  3 12  7  8  9]
 [ 3  4 12  8  7  0  9  5 11 10  6  1  2]
 [ 9 10 11  6  2  1  7  3 12  5  4  0  8]
 [ 2  3  4  5  0  9  8  1 10  6 12 11  7]
 [ 1  9 10 11 12  7  3  2  8  4  0  6  5]
 [12  8  3  4  5  6  1 10  9  2 11  7  0]
 [ 7  6  2 10 11 12  0  8  4  3  9  5  1]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 8  1  0  9  4  5  6  7  2 11 10  3 12]
 [ 7  6  2 10 11 12  0  8  4  3  9  5  1]
 [12  8  3  4  5  6  1 10  9  2 11  7  0]
 [ 1  9 10 11 12  7  3  2  8  4  0  6  5]
 [ 2  3  4  5  0  9  8  1 10  6 12 11  7]
 [ 9 10 11  6  2  1  7  3 12  5  4  0  8]
 [ 3  4 12  8  7  0  9  5 11 10  6  1  2]
 [10  5  1  0  6  2 11  4  3 12  7  8  9]
 [11  7  6 12  8  4 10  9  5  0  1  2  3]
 [ 0 12  5  1 10  3  2 11  6  7  8  9  4]
 [ 5 11  7  3  9  8  4 12  0  1  2 10  6]
 [ 4  0  9  2  1 10  5  6  7  8  3 12 11]
 [ 6  2  8  7  3 11 12  0  1  9  5  4 10]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 8  1  0  9  4  5  6  7  2 11 10  3 12]
 [ 9  5 11 10  6  1  2  3  4 12  8  7  0]
 [10  6  2  8  7  3 11 12  0  1  9  5  4]
 [ 1  7  3 12  5  4  0  8  9 10 11  6  2]
 [12 11  4  0  9  2  1 10  5  6  7  8  3]
 [ 0  9  8  1 10  6 12 11  7  2  3  4  5]
 [ 2 10  6  5 11  7  3  9  8  4 12  0  1]
 [11 12  7  3  2  8  4  0  6  5  1  9 10]
 [ 7  8  9  4  0 12  5  1 10  3  2 11  6]
 [ 3  4  5  6  1 10  9  2 11  7  0 12  8]
 [ 5  0  1  2  3 11  7  6 12  8  4 10  9]
 [ 6  2 10 11 12  0  8  4  3  9  5  1  7]
 [ 4  3 12  7  8  9 10  5  1  0  6  2 11]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 8  1  0  9  4  5  6  7  2 11 10  3 12]
 [ 4  3 12  7  8  9 10  5  1  0  6  2 11]
 [ 6  2 10 11 12  0  8  4  3  9  5  1  7]
 [ 5  0  1  2  3 11  7  6 12  8  4 10  9]
 [ 3  4  5  6  1 10  9  2 11  7  0 12  8]
 [ 7  8  9  4  0 12  5  1 10  3  2 11  6]
 [11 12  7  3  2  8  4  0  6  5  1  9 10]
 [ 2 10  6  5 11  7  3  9  8  4 12  0  1]
 [ 0  9  8  1 10  6 12 11  7  2  3  4  5]
 [12 11  4  0  9  2  1 10  5  6  7  8  3]
 [ 1  7  3 12  5  4  0  8  9 10 11  6  2]
 [10  6  2  8  7  3 11 12  0  1  9  5  4]
 [ 9  5 11 10  6  1  2  3  4 12  8  7  0]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 4  1  2  0  3  6  9  7  8  5 10 11 12]
 [11  3  4  5 10  7  8  6  9 12  2  0  1]
 [ 5  8  6  7  4  9 10 11  3  0  1 12  2]
 [ 6  7  5  8 11  1 12  0 10  2  3  4  9]
 [ 8  9 10  2 12  0 11  1  4  7  5  6  3]
 [ 0 11 12  9  1  2  3  8  5  6  4  7 10]
 [12 10  0  3  6  4  5  2  7  8  9  1 11]
 [ 1  2  7  4  5  3  6  9 12 10 11  8  0]
 [ 3  4  1  6  7  8  0 10 11  9 12  2  5]
 [ 2  5  8 11  9 10  7 12  0  1  6  3  4]
 [ 7 12  9 10  8 11  1  4  2  3  0  5  6]
 [ 9  6 11 12  0  5  2  3  1  4  7 10  8]
 [10  0  3  1  2 12  4  5  6 11  8  9  7]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 4  1  2  0  3  6  9  7  8  5 10 11 12]
 [10  0  3  1  2 12  4  5  6 11  8  9  7]
 [ 9  6 11 12  0  5  2  3  1  4  7 10  8]
 [ 7 12  9 10  8 11  1  4  2  3  0  5  6]
 [ 2  5  8 11  9 10  7 12  0  1  6  3  4]
 [ 3  4  1  6  7  8  0 10 11  9 12  2  5]
 [ 1  2  7  4  5  3  6  9 12 10 11  8  0]
 [12 10  0  3  6  4  5  2  7  8  9  1 11]
 [ 0 11 12  9  1  2  3  8  5  6  4  7 10]
 [ 8  9 10  2 12  0 11  1  4  7  5  6  3]
 [ 6  7  5  8 11  1 12  0 10  2  3  4  9]
 [ 5  8  6  7  4  9 10 11  3  0  1 12  2]
 [11  3  4  5 10  7  8  6  9 12  2  0  1]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 4  1  2  0  3  6  9  7  8  5 10 11 12]
 [ 7 12  9 10  8 11  1  4  2  3  0  5  6]
 [ 1  2  7  4  5  3  6  9 12 10 11  8  0]
 [ 8  9 10  2 12  0 11  1  4  7  5  6  3]
 [11  3  4  5 10  7  8  6  9 12  2  0  1]
 [ 9  6 11 12  0  5  2  3  1  4  7 10  8]
 [ 3  4  1  6  7  8  0 10 11  9 12  2  5]
 [ 0 11 12  9  1  2  3  8  5  6  4  7 10]
 [ 5  8  6  7  4  9 10 11  3  0  1 12  2]
 [10  0  3  1  2 12  4  5  6 11  8  9  7]
 [ 2  5  8 11  9 10  7 12  0  1  6  3  4]
 [12 10  0  3  6  4  5  2  7  8  9  1 11]
 [ 6  7  5  8 11  1 12  0 10  2  3  4  9]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 4  1  2  0  3  6  9  7  8  5 10 11 12]
 [ 6  7  5  8 11  1 12  0 10  2  3  4  9]
 [12 10  0  3  6  4  5  2  7  8  9  1 11]
 [ 2  5  8 11  9 10  7 12  0  1  6  3  4]
 [10  0  3  1  2 12  4  5  6 11  8  9  7]
 [ 5  8  6  7  4  9 10 11  3  0  1 12  2]
 [ 0 11 12  9  1  2  3  8  5  6  4  7 10]
 [ 3  4  1  6  7  8  0 10 11  9 12  2  5]
 [ 9  6 11 12  0  5  2  3  1  4  7 10  8]
 [11  3  4  5 10  7  8  6  9 12  2  0  1]
 [ 8  9 10  2 12  0 11  1  4  7  5  6  3]
 [ 1  2  7  4  5  3  6  9 12 10 11  8  0]
 [ 7 12  9 10  8 11  1  4  2  3  0  5  6]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 4  1  2  0  3  6  9  7  8  5 10 11 12]
 [ 3  8  5  6  4  7 10  0 11 12  9  1  2]
 [ 6  7 12  9 10  8 11  1  4  2  3  0  5]
 [ 9 10 11  3  0  1 12  2  5  8  6  7  4]
 [ 8  0  1  2  7  4  5  3  6  9 12 10 11]
 [ 2 12  4  5  6 11  8  9  7 10  0  3  1]
 [ 5  6  3  8  9 10  2 12  0 11  1  4  7]
 [11  9 10  7 12  0  1  6  3  4  2  5  8]
 [12  2  0  1 11  3  4  5 10  7  8  6  9]
 [ 0  3  6  4  5  2  7  8  9  1 11 12 10]
 [ 1  4  7 10  8  9  6 11 12  0  5  2  3]
 [ 7  5  8 11  1 12  0 10  2  3  4  9  6]
 [10 11  9 12  2  5  3  4  1  6  7  8  0]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 4  1  2  0  3  6  9  7  8  5 10 11 12]
 [10 11  9 12  2  5  3  4  1  6  7  8  0]
 [ 7  5  8 11  1 12  0 10  2  3  4  9  6]
 [ 1  4  7 10  8  9  6 11 12  0  5  2  3]
 [ 0  3  6  4  5  2  7  8  9  1 11 12 10]
 [12  2  0  1 11  3  4  5 10  7  8  6  9]
 [11  9 10  7 12  0  1  6  3  4  2  5  8]
 [ 5  6  3  8  9 10  2 12  0 11  1  4  7]
 [ 2 12  4  5  6 11  8  9  7 10  0  3  1]
 [ 8  0  1  2  7  4  5  3  6  9 12 10 11]
 [ 9 10 11  3  0  1 12  2  5  8  6  7  4]
 [ 6  7 12  9 10  8 11  1  4  2  3  0  5]
 [ 3  8  5  6  4  7 10  0 11 12  9  1  2]]

********************************************
	The pandiagonal Latin square
********************************************

[[12  1  2  0  4  5  6 10  8  9 11  7  3]
 [11  0  9  5  1  3  4  2  6  7  8 12 10]
 [ 9 10  1 12  0  2 11  7  3  5  6  4  8]
 [ 7  8  6 10 11 12  3  1  2  4  0  9  5]
 [ 6  2 11  7  9 10  8 12  0  1  5  3  4]
 [ 3  7  5  6  8  4  0  9 11 12 10  1  2]
 [ 1 12  3  4  5  9  7  8 10  6  2 11  0]
 [ 8  4  0  2  3  1  5  6  7 11  9 10 12]
 [ 0 11 12  1 10  6  2  4  5  3  7  8  9]
 [ 5  9 10 11  2  0  1  3 12  8  4  6  7]
 [10  6  8  9  7 11 12  0  4  2  3  5  1]
 [ 4  5  7  3 12  8 10 11  9  0  1  2  6]
 [ 2  3  4  8  6  7  9  5  1 10 12  0 11]]

********************************************
	The pandiagonal Latin square
********************************************

[[12  1  2  0  4  5  6 10  8  9 11  7  3]
 [ 2  3  4  8  6  7  9  5  1 10 12  0 11]
 [ 4  5  7  3 12  8 10 11  9  0  1  2  6]
 [10  6  8  9  7 11 12  0  4  2  3  5  1]
 [ 5  9 10 11  2  0  1  3 12  8  4  6  7]
 [ 0 11 12  1 10  6  2  4  5  3  7  8  9]
 [ 8  4  0  2  3  1  5  6  7 11  9 10 12]
 [ 1 12  3  4  5  9  7  8 10  6  2 11  0]
 [ 3  7  5  6  8  4  0  9 11 12 10  1  2]
 [ 6  2 11  7  9 10  8 12  0  1  5  3  4]
 [ 7  8  6 10 11 12  3  1  2  4  0  9  5]
 [ 9 10  1 12  0  2 11  7  3  5  6  4  8]
 [11  0  9  5  1  3  4  2  6  7  8 12 10]]

********************************************
	The pandiagonal Latin square
********************************************

[[12  1  2  0  4  5  6 10  8  9 11  7  3]
 [10  6  8  9  7 11 12  0  4  2  3  5  1]
 [ 8  4  0  2  3  1  5  6  7 11  9 10 12]
 [ 6  2 11  7  9 10  8 12  0  1  5  3  4]
 [11  0  9  5  1  3  4  2  6  7  8 12 10]
 [ 4  5  7  3 12  8 10 11  9  0  1  2  6]
 [ 0 11 12  1 10  6  2  4  5  3  7  8  9]
 [ 3  7  5  6  8  4  0  9 11 12 10  1  2]
 [ 9 10  1 12  0  2 11  7  3  5  6  4  8]
 [ 2  3  4  8  6  7  9  5  1 10 12  0 11]
 [ 5  9 10 11  2  0  1  3 12  8  4  6  7]
 [ 1 12  3  4  5  9  7  8 10  6  2 11  0]
 [ 7  8  6 10 11 12  3  1  2  4  0  9  5]]

********************************************
	The pandiagonal Latin square
********************************************

[[12  1  2  0  4  5  6 10  8  9 11  7  3]
 [ 7  8  6 10 11 12  3  1  2  4  0  9  5]
 [ 1 12  3  4  5  9  7  8 10  6  2 11  0]
 [ 5  9 10 11  2  0  1  3 12  8  4  6  7]
 [ 2  3  4  8  6  7  9  5  1 10 12  0 11]
 [ 9 10  1 12  0  2 11  7  3  5  6  4  8]
 [ 3  7  5  6  8  4  0  9 11 12 10  1  2]
 [ 0 11 12  1 10  6  2  4  5  3  7  8  9]
 [ 4  5  7  3 12  8 10 11  9  0  1  2  6]
 [11  0  9  5  1  3  4  2  6  7  8 12 10]
 [ 6  2 11  7  9 10  8 12  0  1  5  3  4]
 [ 8  4  0  2  3  1  5  6  7 11  9 10 12]
 [10  6  8  9  7 11 12  0  4  2  3  5  1]]

********************************************
	The pandiagonal Latin square
********************************************

[[12  1  2  0  4  5  6 10  8  9 11  7  3]
 [ 0  9 11 12 10  1  2  3  7  5  6  8  4]
 [ 1 10  6  8  9  7 11 12  0  4  2  3  5]
 [ 2 11  7  3  5  6  4  8  9 10  1 12  0]
 [10 12  8  4  0  2  3  1  5  6  7 11  9]
 [ 6  7  9  5  1 10 12  0 11  2  3  4  8]
 [ 5  3  4  6  2 11  7  9 10  8 12  0  1]
 [11  2  0  1  3 12  8  4  6  7  5  9 10]
 [ 7  8 12 10 11  0  9  5  1  3  4  2  6]
 [ 3  4  5  9  7  8 10  6  2 11  0  1 12]
 [ 9  0  1  2  6  4  5  7  3 12  8 10 11]
 [ 8  6 10 11 12  3  1  2  4  0  9  5  7]
 [ 4  5  3  7  8  9  0 11 12  1 10  6  2]]

********************************************
	The pandiagonal Latin square
********************************************

[[12  1  2  0  4  5  6 10  8  9 11  7  3]
 [ 4  5  3  7  8  9  0 11 12  1 10  6  2]
 [ 8  6 10 11 12  3  1  2  4  0  9  5  7]
 [ 9  0  1  2  6  4  5  7  3 12  8 10 11]
 [ 3  4  5  9  7  8 10  6  2 11  0  1 12]
 [ 7  8 12 10 11  0  9  5  1  3  4  2  6]
 [11  2  0  1  3 12  8  4  6  7  5  9 10]
 [ 5  3  4  6  2 11  7  9 10  8 12  0  1]
 [ 6  7  9  5  1 10 12  0 11  2  3  4  8]
 [10 12  8  4  0  2  3  1  5  6  7 11  9]
 [ 2 11  7  3  5  6  4  8  9 10  1 12  0]
 [ 1 10  6  8  9  7 11 12  0  4  2  3  5]
 [ 0  9 11 12 10  1  2  3  7  5  6  8  4]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 7  3  2  8  4  0  6  5  1  9 10 11 12]
 [11 12  0  1  9  5  4 10  6  2  8  7  3]
 [ 4 10  9  5  0  1  2  3 11  7  6 12  8]
 [ 9  8  1 10  6 12 11  7  2  3  4  5  0]
 [ 5  6  7  2 11 10  3 12  8  1  0  9  4]
 [ 3  2 11  6  7  8  9  4  0 12  5  1 10]
 [ 1  7  3 12  5  4  0  8  9 10 11  6  2]
 [12  0  8  4  3  9  5  1  7  6  2 10 11]
 [ 8  4 12  0  1  2 10  6  5 11  7  3  9]
 [ 0  9  5 11 10  6  1  2  3  4 12  8  7]
 [ 6  1 10  9  2 11  7  0 12  8  3  4  5]
 [10  5  6  7  8  3 12 11  4  0  9  2  1]
 [ 2 11  4  3 12  7  8  9 10  5  1  0  6]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 7  3  2  8  4  0  6  5  1  9 10 11 12]
 [ 2 11  4  3 12  7  8  9 10  5  1  0  6]
 [10  5  6  7  8  3 12 11  4  0  9  2  1]
 [ 6  1 10  9  2 11  7  0 12  8  3  4  5]
 [ 0  9  5 11 10  6  1  2  3  4 12  8  7]
 [ 8  4 12  0  1  2 10  6  5 11  7  3  9]
 [12  0  8  4  3  9  5  1  7  6  2 10 11]
 [ 1  7  3 12  5  4  0  8  9 10 11  6  2]
 [ 3  2 11  6  7  8  9  4  0 12  5  1 10]
 [ 5  6  7  2 11 10  3 12  8  1  0  9  4]
 [ 9  8  1 10  6 12 11  7  2  3  4  5  0]
 [ 4 10  9  5  0  1  2  3 11  7  6 12  8]
 [11 12  0  1  9  5  4 10  6  2  8  7  3]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 7  3  2  8  4  0  6  5  1  9 10 11 12]
 [ 6  1 10  9  2 11  7  0 12  8  3  4  5]
 [12  0  8  4  3  9  5  1  7  6  2 10 11]
 [ 5  6  7  2 11 10  3 12  8  1  0  9  4]
 [11 12  0  1  9  5  4 10  6  2  8  7  3]
 [10  5  6  7  8  3 12 11  4  0  9  2  1]
 [ 8  4 12  0  1  2 10  6  5 11  7  3  9]
 [ 3  2 11  6  7  8  9  4  0 12  5  1 10]
 [ 4 10  9  5  0  1  2  3 11  7  6 12  8]
 [ 2 11  4  3 12  7  8  9 10  5  1  0  6]
 [ 0  9  5 11 10  6  1  2  3  4 12  8  7]
 [ 1  7  3 12  5  4  0  8  9 10 11  6  2]
 [ 9  8  1 10  6 12 11  7  2  3  4  5  0]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 7  3  2  8  4  0  6  5  1  9 10 11 12]
 [ 9  8  1 10  6 12 11  7  2  3  4  5  0]
 [ 1  7  3 12  5  4  0  8  9 10 11  6  2]
 [ 0  9  5 11 10  6  1  2  3  4 12  8  7]
 [ 2 11  4  3 12  7  8  9 10  5  1  0  6]
 [ 4 10  9  5  0  1  2  3 11  7  6 12  8]
 [ 3  2 11  6  7  8  9  4  0 12  5  1 10]
 [ 8  4 12  0  1  2 10  6  5 11  7  3  9]
 [10  5  6  7  8  3 12 11  4  0  9  2  1]
 [11 12  0  1  9  5  4 10  6  2  8  7  3]
 [ 5  6  7  2 11 10  3 12  8  1  0  9  4]
 [12  0  8  4  3  9  5  1  7  6  2 10 11]
 [ 6  1 10  9  2 11  7  0 12  8  3  4  5]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 7  3  2  8  4  0  6  5  1  9 10 11 12]
 [ 9  4  0 12  5  1 10  3  2 11  6  7  8]
 [ 5  6  1 10  9  2 11  7  0 12  8  3  4]
 [ 1  2  3 11  7  6 12  8  4 10  9  5  0]
 [10 11 12  0  8  4  3  9  5  1  7  6  2]
 [12  7  8  9 10  5  1  0  6  2 11  4  3]
 [ 0  9  4  5  6  7  2 11 10  3 12  8  1]
 [11 10  6  1  2  3  4 12  8  7  0  9  5]
 [ 2  8  7  3 11 12  0  1  9  5  4 10  6]
 [ 3 12  5  4  0  8  9 10 11  6  2  1  7]
 [ 4  0  9  2  1 10  5  6  7  8  3 12 11]
 [ 8  1 10  6 12 11  7  2  3  4  5  0  9]
 [ 6  5 11  7  3  9  8  4 12  0  1  2 10]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 7  3  2  8  4  0  6  5  1  9 10 11 12]
 [ 6  5 11  7  3  9  8  4 12  0  1  2 10]
 [ 8  1 10  6 12 11  7  2  3  4  5  0  9]
 [ 4  0  9  2  1 10  5  6  7  8  3 12 11]
 [ 3 12  5  4  0  8  9 10 11  6  2  1  7]
 [ 2  8  7  3 11 12  0  1  9  5  4 10  6]
 [11 10  6  1  2  3  4 12  8  7  0  9  5]
 [ 0  9  4  5  6  7  2 11 10  3 12  8  1]
 [12  7  8  9 10  5  1  0  6  2 11  4  3]
 [10 11 12  0  8  4  3  9  5  1  7  6  2]
 [ 1  2  3 11  7  6 12  8  4 10  9  5  0]
 [ 5  6  1 10  9  2 11  7  0 12  8  3  4]
 [ 9  4  0 12  5  1 10  3  2 11  6  7  8]]

********************************************
	The pandiagonal Latin square
********************************************

[[11  1  4  3 10  0  6  7  8  9  2  5 12]
 [ 2  8 11  5  4  7 10  9  3  6 12  0  1]
 [12  5  6  7  8  1  4 11 10  0  3  2  9]
 [ 6  9  8  2  5 11 12  0  1  7 10  4  3]
 [ 0  3 10  9 12  2  1  8 11  4  5  6  7]
 [10 11 12  0  6  9  3  2  5  8  7  1  4]
 [ 1  0  7 10  3  4  5  6 12  2  9  8 11]
 [ 8  2  1  4  7  6  0  3  9 10 11 12  5]
 [ 3  4  5 11  1  8  7 10  0 12  6  9  2]
 [ 5 12  2  8  9 10 11  4  7  1  0  3  6]
 [ 7  6  9 12 11  5  8  1  2  3  4 10  0]
 [ 9 10  3  6  0 12  2  5  4 11  1  7  8]
 [ 4  7  0  1  2  3  9 12  6  5  8 11 10]]

********************************************
	The pandiagonal Latin square
********************************************

[[11  1  4  3 10  0  6  7  8  9  2  5 12]
 [ 4  7  0  1  2  3  9 12  6  5  8 11 10]
 [ 9 10  3  6  0 12  2  5  4 11  1  7  8]
 [ 7  6  9 12 11  5  8  1  2  3  4 10  0]
 [ 5 12  2  8  9 10 11  4  7  1  0  3  6]
 [ 3  4  5 11  1  8  7 10  0 12  6  9  2]
 [ 8  2  1  4  7  6  0  3  9 10 11 12  5]
 [ 1  0  7 10  3  4  5  6 12  2  9  8 11]
 [10 11 12  0  6  9  3  2  5  8  7  1  4]
 [ 0  3 10  9 12  2  1  8 11  4  5  6  7]
 [ 6  9  8  2  5 11 12  0  1  7 10  4  3]
 [12  5  6  7  8  1  4 11 10  0  3  2  9]
 [ 2  8 11  5  4  7 10  9  3  6 12  0  1]]

********************************************
	The pandiagonal Latin square
********************************************

[[11  1  4  3 10  0  6  7  8  9  2  5 12]
 [ 7  6  9 12 11  5  8  1  2  3  4 10  0]
 [ 8  2  1  4  7  6  0  3  9 10 11 12  5]
 [ 0  3 10  9 12  2  1  8 11  4  5  6  7]
 [ 2  8 11  5  4  7 10  9  3  6 12  0  1]
 [ 9 10  3  6  0 12  2  5  4 11  1  7  8]
 [ 3  4  5 11  1  8  7 10  0 12  6  9  2]
 [10 11 12  0  6  9  3  2  5  8  7  1  4]
 [12  5  6  7  8  1  4 11 10  0  3  2  9]
 [ 4  7  0  1  2  3  9 12  6  5  8 11 10]
 [ 5 12  2  8  9 10 11  4  7  1  0  3  6]
 [ 1  0  7 10  3  4  5  6 12  2  9  8 11]
 [ 6  9  8  2  5 11 12  0  1  7 10  4  3]]

********************************************
	The pandiagonal Latin square
********************************************

[[11  1  4  3 10  0  6  7  8  9  2  5 12]
 [ 6  9  8  2  5 11 12  0  1  7 10  4  3]
 [ 1  0  7 10  3  4  5  6 12  2  9  8 11]
 [ 5 12  2  8  9 10 11  4  7  1  0  3  6]
 [ 4  7  0  1  2  3  9 12  6  5  8 11 10]
 [12  5  6  7  8  1  4 11 10  0  3  2  9]
 [10 11 12  0  6  9  3  2  5  8  7  1  4]
 [ 3  4  5 11  1  8  7 10  0 12  6  9  2]
 [ 9 10  3  6  0 12  2  5  4 11  1  7  8]
 [ 2  8 11  5  4  7 10  9  3  6 12  0  1]
 [ 0  3 10  9 12  2  1  8 11  4  5  6  7]
 [ 8  2  1  4  7  6  0  3  9 10 11 12  5]
 [ 7  6  9 12 11  5  8  1  2  3  4 10  0]]

********************************************
	The pandiagonal Latin square
********************************************

[[11  1  4  3 10  0  6  7  8  9  2  5 12]
 [ 3  2  5  8  7  1  4 10 11 12  0  6  9]
 [ 0  7  6  9 12 11  5  8  1  2  3  4 10]
 [ 1  4 11 10  0  3  2  9 12  5  6  7  8]
 [12  5  8  2  1  4  7  6  0  3  9 10 11]
 [ 2  3  9 12  6  5  8 11 10  4  7  0  1]
 [ 5  6  7  0  3 10  9 12  2  1  8 11  4]
 [ 8  9 10 11  4  7  1  0  3  6  5 12  2]
 [ 6 12  0  1  2  8 11  5  4  7 10  9  3]
 [ 7 10  3  4  5  6 12  2  9  8 11  1  0]
 [ 4 11  1  7  8  9 10  3  6  0 12  2  5]
 [ 9  8  2  5 11 12  0  1  7 10  4  3  6]
 [10  0 12  6  9  2  3  4  5 11  1  8  7]]

********************************************
	The pandiagonal Latin square
********************************************

[[11  1  4  3 10  0  6  7  8  9  2  5 12]
 [10  0 12  6  9  2  3  4  5 11  1  8  7]
 [ 9  8  2  5 11 12  0  1  7 10  4  3  6]
 [ 4 11  1  7  8  9 10  3  6  0 12  2  5]
 [ 7 10  3  4  5  6 12  2  9  8 11  1  0]
 [ 6 12  0  1  2  8 11  5  4  7 10  9  3]
 [ 8  9 10 11  4  7  1  0  3  6  5 12  2]
 [ 5  6  7  0  3 10  9 12  2  1  8 11  4]
 [ 2  3  9 12  6  5  8 11 10  4  7  0  1]
 [12  5  8  2  1  4  7  6  0  3  9 10 11]
 [ 1  4 11 10  0  3  2  9 12  5  6  7  8]
 [ 0  7  6  9 12 11  5  8  1  2  3  4 10]
 [ 3  2  5  8  7  1  4 10 11 12  0  6  9]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 8  1  2  3  4 10  0  7  6  9 12 11  5]
 [ 2  5  4 11  1  7  8  9 10  3  6  0 12]
 [ 9 12  6  5  8 11 10  4  7  0  1  2  3]
 [ 6  7  8  9  2  5 12 11  1  4  3 10  0]
 [10  9  3  6 12  0  1  2  8 11  5  4  7]
 [ 4 11 10  0  3  2  9 12  5  6  7  8  1]
 [12  0  1  7 10  4  3  6  9  8  2  5 11]
 [ 1  8 11  4  5  6  7  0  3 10  9 12  2]
 [ 3  2  5  8  7  1  4 10 11 12  0  6  9]
 [ 5  6 12  2  9  8 11  1  0  7 10  3  4]
 [ 0  3  9 10 11 12  5  8  2  1  4  7  6]
 [ 7 10  0 12  6  9  2  3  4  5 11  1  8]
 [11  4  7  1  0  3  6  5 12  2  8  9 10]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 8  1  2  3  4 10  0  7  6  9 12 11  5]
 [11  4  7  1  0  3  6  5 12  2  8  9 10]
 [ 7 10  0 12  6  9  2  3  4  5 11  1  8]
 [ 0  3  9 10 11 12  5  8  2  1  4  7  6]
 [ 5  6 12  2  9  8 11  1  0  7 10  3  4]
 [ 3  2  5  8  7  1  4 10 11 12  0  6  9]
 [ 1  8 11  4  5  6  7  0  3 10  9 12  2]
 [12  0  1  7 10  4  3  6  9  8  2  5 11]
 [ 4 11 10  0  3  2  9 12  5  6  7  8  1]
 [10  9  3  6 12  0  1  2  8 11  5  4  7]
 [ 6  7  8  9  2  5 12 11  1  4  3 10  0]
 [ 9 12  6  5  8 11 10  4  7  0  1  2  3]
 [ 2  5  4 11  1  7  8  9 10  3  6  0 12]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 8  1  2  3  4 10  0  7  6  9 12 11  5]
 [ 0  3  9 10 11 12  5  8  2  1  4  7  6]
 [ 1  8 11  4  5  6  7  0  3 10  9 12  2]
 [10  9  3  6 12  0  1  2  8 11  5  4  7]
 [ 2  5  4 11  1  7  8  9 10  3  6  0 12]
 [ 7 10  0 12  6  9  2  3  4  5 11  1  8]
 [ 3  2  5  8  7  1  4 10 11 12  0  6  9]
 [ 4 11 10  0  3  2  9 12  5  6  7  8  1]
 [ 9 12  6  5  8 11 10  4  7  0  1  2  3]
 [11  4  7  1  0  3  6  5 12  2  8  9 10]
 [ 5  6 12  2  9  8 11  1  0  7 10  3  4]
 [12  0  1  7 10  4  3  6  9  8  2  5 11]
 [ 6  7  8  9  2  5 12 11  1  4  3 10  0]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 8  1  2  3  4 10  0  7  6  9 12 11  5]
 [ 6  7  8  9  2  5 12 11  1  4  3 10  0]
 [12  0  1  7 10  4  3  6  9  8  2  5 11]
 [ 5  6 12  2  9  8 11  1  0  7 10  3  4]
 [11  4  7  1  0  3  6  5 12  2  8  9 10]
 [ 9 12  6  5  8 11 10  4  7  0  1  2  3]
 [ 4 11 10  0  3  2  9 12  5  6  7  8  1]
 [ 3  2  5  8  7  1  4 10 11 12  0  6  9]
 [ 7 10  0 12  6  9  2  3  4  5 11  1  8]
 [ 2  5  4 11  1  7  8  9 10  3  6  0 12]
 [10  9  3  6 12  0  1  2  8 11  5  4  7]
 [ 1  8 11  4  5  6  7  0  3 10  9 12  2]
 [ 0  3  9 10 11 12  5  8  2  1  4  7  6]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 8  1  2  3  4 10  0  7  6  9 12 11  5]
 [ 9 12  5  6  7  8  1  4 11 10  0  3  2]
 [ 6  0  3  9 10 11 12  5  8  2  1  4  7]
 [11 10  4  7  0  1  2  3  9 12  6  5  8]
 [12  2  1  8 11  4  5  6  7  0  3 10  9]
 [ 0  3  6  5 12  2  8  9 10 11  4  7  1]
 [ 5  4  7 10  9  3  6 12  0  1  2  8 11]
 [ 2  9  8 11  1  0  7 10  3  4  5  6 12]
 [ 3  6  0 12  2  5  4 11  1  7  8  9 10]
 [ 1  7 10  4  3  6  9  8  2  5 11 12  0]
 [ 4  5 11  1  8  7 10  0 12  6  9  2  3]
 [ 7  8  9  2  5 12 11  1  4  3 10  0  6]
 [10 11 12  0  6  9  3  2  5  8  7  1  4]]

********************************************
	The pandiagonal Latin square
********************************************

[[ 8  1  2  3  4 10  0  7  6  9 12 11  5]
 [10 11 12  0  6  9  3  2  5  8  7  1  4]
 [ 7  8  9  2  5 12 11  1  4  3 10  0  6]
 [ 4  5 11  1  8  7 10  0 12  6  9  2  3]
 [ 1  7 10  4  3  6  9  8  2  5 11 12  0]
 [ 3  6  0 12  2  5  4 11  1  7  8  9 10]
 [ 2  9  8 11  1  0  7 10  3  4  5  6 12]
 [ 5  4  7 10  9  3  6 12  0  1  2  8 11]
 [ 0  3  6  5 12  2  8  9 10 11  4  7  1]
 [12  2  1  8 11  4  5  6  7  0  3 10  9]
 [11 10  4  7  0  1  2  3  9 12  6  5  8]
 [ 6  0  3  9 10 11 12  5  8  2  1  4  7]
 [ 9 12  5  6  7  8  1  4 11 10  0  3  2]]

********************************************
	The pandiagonal Latin square
********************************************

[[11  7  2  3  4  5  0  9  8  1 10  6 12]
 [ 3 12  8  1  0  9  4  5  6  7  2 11 10]
 [ 9  4  0 12  5  1 10  3  2 11  6  7  8]
 [ 0  8  9 10 11  6  2  1  7  3 12  5  4]
 [ 5  1  7  6  2 10 11 12  0  8  4  3  9]
 [10  6  5 11  7  3  9  8  4 12  0  1  2]
 [ 1  2  3  4 12  8  7  0  9  5 11 10  6]
 [ 7  0 12  8  3  4  5  6  1 10  9  2 11]
 [12 11  4  0  9  2  1 10  5  6  7  8  3]
 [ 8  9 10  5  1  0  6  2 11  4  3 12  7]
 [ 6  5  1  9 10 11 12  7  3  2  8  4  0]
 [ 4 10  6  2  8  7  3 11 12  0  1  9  5]
 [ 2  3 11  7  6 12  8  4 10  9  5  0  1]]

********************************************
	The pandiagonal Latin square
********************************************

[[11  7  2  3  4  5  0  9  8  1 10  6 12]
 [ 2  3 11  7  6 12  8  4 10  9  5  0  1]
 [ 4 10  6  2  8  7  3 11 12  0  1  9  5]
 [ 6  5  1  9 10 11 12  7  3  2  8  4  0]
 [ 8  9 10  5  1  0  6  2 11  4  3 12  7]
 [12 11  4  0  9  2  1 10  5  6  7  8  3]
 [ 7  0 12  8  3  4  5  6  1 10  9  2 11]
 [ 1  2  3  4 12  8  7  0  9  5 11 10  6]
 [10  6  5 11  7  3  9  8  4 12  0  1  2]
 [ 5  1  7  6  2 10 11 12  0  8  4  3  9]
 [ 0  8  9 10 11  6  2  1  7  3 12  5  4]
 [ 9  4  0 12  5  1 10  3  2 11  6  7  8]
 [ 3 12  8  1  0  9  4  5  6  7  2 11 10]]

********************************************
	The pandiagonal Latin square
********************************************

[[11  7  2  3  4  5  0  9  8  1 10  6 12]
 [ 6  5  1  9 10 11 12  7  3  2  8  4  0]
 [ 7  0 12  8  3  4  5  6  1 10  9  2 11]
 [ 5  1  7  6  2 10 11 12  0  8  4  3  9]
 [ 3 12  8  1  0  9  4  5  6  7  2 11 10]
 [ 4 10  6  2  8  7  3 11 12  0  1  9  5]
 [12 11  4  0  9  2  1 10  5  6  7  8  3]
 [10  6  5 11  7  3  9  8  4 12  0  1  2]
 [ 9  4  0 12  5  1 10  3  2 11  6  7  8]
 [ 2  3 11  7  6 12  8  4 10  9  5  0  1]
 [ 8  9 10  5  1  0  6  2 11  4  3 12  7]
 [ 1  2  3  4 12  8  7  0  9  5 11 10  6]
 [ 0  8  9 10 11  6  2  1  7  3 12  5  4]]

********************************************
	The pandiagonal Latin square
********************************************

[[11  7  2  3  4  5  0  9  8  1 10  6 12]
 [ 0  8  9 10 11  6  2  1  7  3 12  5  4]
 [ 1  2  3  4 12  8  7  0  9  5 11 10  6]
 [ 8  9 10  5  1  0  6  2 11  4  3 12  7]
 [ 2  3 11  7  6 12  8  4 10  9  5  0  1]
 [ 9  4  0 12  5  1 10  3  2 11  6  7  8]
 [10  6  5 11  7  3  9  8  4 12  0  1  2]
 [12 11  4  0  9  2  1 10  5  6  7  8  3]
 [ 4 10  6  2  8  7  3 11 12  0  1  9  5]
 [ 3 12  8  1  0  9  4  5  6  7  2 11 10]
 [ 5  1  7  6  2 10 11 12  0  8  4  3  9]
 [ 7  0 12  8  3  4  5  6  1 10  9  2 11]
 [ 6  5  1  9 10 11 12  7  3  2  8  4  0]]

********************************************
	The pandiagonal Latin square
********************************************

[[11  7  2  3  4  5  0  9  8  1 10  6 12]
 [ 9  8  4 12  0  1  2 10  6  5 11  7  3]
 [ 0  6  5  1  9 10 11 12  7  3  2  8  4]
 [ 1 10  3  2 11  6  7  8  9  4  0 12  5]
 [ 2 11  7  0 12  8  3  4  5  6  1 10  9]
 [ 6 12  8  4 10  9  5  0  1  2  3 11  7]
 [ 4  3  9  5  1  7  6  2 10 11 12  0  8]
 [ 5  1  0  6  2 11  4  3 12  7  8  9 10]
 [ 7  2 11 10  3 12  8  1  0  9  4  5  6]
 [ 3  4 12  8  7  0  9  5 11 10  6  1  2]
 [12  0  1  9  5  4 10  6  2  8  7  3 11]
 [ 8  9 10 11  6  2  1  7  3 12  5  4  0]
 [10  5  6  7  8  3 12 11  4  0  9  2  1]]

********************************************
	The pandiagonal Latin square
********************************************

[[11  7  2  3  4  5  0  9  8  1 10  6 12]
 [10  5  6  7  8  3 12 11  4  0  9  2  1]
 [ 8  9 10 11  6  2  1  7  3 12  5  4  0]
 [12  0  1  9  5  4 10  6  2  8  7  3 11]
 [ 3  4 12  8  7  0  9  5 11 10  6  1  2]
 [ 7  2 11 10  3 12  8  1  0  9  4  5  6]
 [ 5  1  0  6  2 11  4  3 12  7  8  9 10]
 [ 4  3  9  5  1  7  6  2 10 11 12  0  8]
 [ 6 12  8  4 10  9  5  0  1  2  3 11  7]
 [ 2 11  7  0 12  8  3  4  5  6  1 10  9]
 [ 1 10  3  2 11  6  7  8  9  4  0 12  5]
 [ 0  6  5  1  9 10 11 12  7  3  2  8  4]
 [ 9  8  4 12  0  1  2 10  6  5 11  7  3]]

********************************************
	The pandiagonal Latin square
********************************************

[[10  1  2  3  7  5  6  8  4  0  9 11 12]
 [ 2 11  0  1 12  3  4  5  9  7  8 10  6]
 [ 9 10 12  8  4  0  2  3  1  5  6  7 11]
 [ 7  8  9  0 11 12  1 10  6  2  4  5  3]
 [ 4  6  7  5  9 10 11  2  0  1  3 12  8]
 [ 3  5  1 10  6  8  9  7 11 12  0  4  2]
 [ 1  2  6  4  5  7  3 12  8 10 11  9  0]
 [12  0 11  2  3  4  8  6  7  9  5  1 10]
 [11  7  3 12  1  2  0  4  5  6 10  8  9]
 [ 8 12 10 11  0  9  5  1  3  4  2  6  7]
 [ 6  4  8  9 10  1 12  0  2 11  7  3  5]
 [ 0  9  5  7  8  6 10 11 12  3  1  2  4]
 [ 5  3  4  6  2 11  7  9 10  8 12  0  1]]

********************************************
	The pandiagonal Latin square
********************************************

[[10  1  2  3  7  5  6  8  4  0  9 11 12]
 [ 5  3  4  6  2 11  7  9 10  8 12  0  1]
 [ 0  9  5  7  8  6 10 11 12  3  1  2  4]
 [ 6  4  8  9 10  1 12  0  2 11  7  3  5]
 [ 8 12 10 11  0  9  5  1  3  4  2  6  7]
 [11  7  3 12  1  2  0  4  5  6 10  8  9]
 [12  0 11  2  3  4  8  6  7  9  5  1 10]
 [ 1  2  6  4  5  7  3 12  8 10 11  9  0]
 [ 3  5  1 10  6  8  9  7 11 12  0  4  2]
 [ 4  6  7  5  9 10 11  2  0  1  3 12  8]
 [ 7  8  9  0 11 12  1 10  6  2  4  5  3]
 [ 9 10 12  8  4  0  2  3  1  5  6  7 11]
 [ 2 11  0  1 12  3  4  5  9  7  8 10  6]]

********************************************
	The pandiagonal Latin square
********************************************

[[10  1  2  3  7  5  6  8  4  0  9 11 12]
 [ 6  4  8  9 10  1 12  0  2 11  7  3  5]
 [12  0 11  2  3  4  8  6  7  9  5  1 10]
 [ 4  6  7  5  9 10 11  2  0  1  3 12  8]
 [ 2 11  0  1 12  3  4  5  9  7  8 10  6]
 [ 0  9  5  7  8  6 10 11 12  3  1  2  4]
 [11  7  3 12  1  2  0  4  5  6 10  8  9]
 [ 3  5  1 10  6  8  9  7 11 12  0  4  2]
 [ 9 10 12  8  4  0  2  3  1  5  6  7 11]
 [ 5  3  4  6  2 11  7  9 10  8 12  0  1]
 [ 8 12 10 11  0  9  5  1  3  4  2  6  7]
 [ 1  2  6  4  5  7  3 12  8 10 11  9  0]
 [ 7  8  9  0 11 12  1 10  6  2  4  5  3]]

********************************************
	The pandiagonal Latin square
********************************************

[[10  1  2  3  7  5  6  8  4  0  9 11 12]
 [ 7  8  9  0 11 12  1 10  6  2  4  5  3]
 [ 1  2  6  4  5  7  3 12  8 10 11  9  0]
 [ 8 12 10 11  0  9  5  1  3  4  2  6  7]
 [ 5  3  4  6  2 11  7  9 10  8 12  0  1]
 [ 9 10 12  8  4  0  2  3  1  5  6  7 11]
 [ 3  5  1 10  6  8  9  7 11 12  0  4  2]
 [11  7  3 12  1  2  0  4  5  6 10  8  9]
 [ 0  9  5  7  8  6 10 11 12  3  1  2  4]
 [ 2 11  0  1 12  3  4  5  9  7  8 10  6]
 [ 4  6  7  5  9 10 11  2  0  1  3 12  8]
 [12  0 11  2  3  4  8  6  7  9  5  1 10]
 [ 6  4  8  9 10  1 12  0  2 11  7  3  5]]

********************************************
	The pandiagonal Latin square
********************************************

[[10  1  2  3  7  5  6  8  4  0  9 11 12]
 [ 9  7 11 12  0  4  2  3  5  1 10  6  8]
 [ 5  6  4  8  9 10  1 12  0  2 11  7  3]
 [ 0  2  3  1  5  6  7 11  9 10 12  8  4]
 [ 1 10 12  0 11  2  3  4  8  6  7  9  5]
 [ 2 11  7  9 10  8 12  0  1  5  3  4  6]
 [ 3 12  8  4  6  7  5  9 10 11  2  0  1]
 [11  0  9  5  1  3  4  2  6  7  8 12 10]
 [ 7  8 10  6  2 11  0  1 12  3  4  5  9]
 [ 6  4  5  7  3 12  8 10 11  9  0  1  2]
 [12  3  1  2  4  0  9  5  7  8  6 10 11]
 [ 8  9  0 11 12  1 10  6  2  4  5  3  7]
 [ 4  5  6 10  8  9 11  7  3 12  1  2  0]]

********************************************
	The pandiagonal Latin square
********************************************

[[10  1  2  3  7  5  6  8  4  0  9 11 12]
 [ 4  5  6 10  8  9 11  7  3 12  1  2  0]
 [ 8  9  0 11 12  1 10  6  2  4  5  3  7]
 [12  3  1  2  4  0  9  5  7  8  6 10 11]
 [ 6  4  5  7  3 12  8 10 11  9  0  1  2]
 [ 7  8 10  6  2 11  0  1 12  3  4  5  9]
 [11  0  9  5  1  3  4  2  6  7  8 12 10]
 [ 3 12  8  4  6  7  5  9 10 11  2  0  1]
 [ 2 11  7  9 10  8 12  0  1  5  3  4  6]
 [ 1 10 12  0 11  2  3  4  8  6  7  9  5]
 [ 0  2  3  1  5  6  7 11  9 10 12  8  4]
 [ 5  6  4  8  9 10  1 12  0  2 11  7  3]
 [ 9  7 11 12  0  4  2  3  5  1 10  6  8]]

********************************************
	The pandiagonal Latin square
********************************************

[[12  2  5  3  4  1  6  7  8  0 10 11  9]
 [ 6  3  4  2  5  8 11  9 10  7 12  0  1]
 [ 0  5  6  7 12  9 10  8 11  1  4  2  3]
 [ 7 10  8  9  6 11 12  0  5  2  3  1  4]
 [ 8  9  7 10  0  3  1  2 12  4  5  6 11]
 [10 11 12  4  1  2  0  3  6  9  7  8  5]
 [ 2  0  1 11  3  4  5 10  7  8  6  9 12]
 [ 1 12  2  5  8  6  7  4  9 10 11  3  0]
 [ 3  4  9  6  7  5  8 11  1 12  0 10  2]
 [ 5  6  3  8  9 10  2 12  0 11  1  4  7]
 [ 4  7 10  0 11 12  9  1  2  3  8  5  6]
 [ 9  1 11 12 10  0  3  6  4  5  2  7  8]
 [11  8  0  1  2  7  4  5  3  6  9 12 10]]

********************************************
	The pandiagonal Latin square
********************************************

[[12  2  5  3  4  1  6  7  8  0 10 11  9]
 [11  8  0  1  2  7  4  5  3  6  9 12 10]
 [ 9  1 11 12 10  0  3  6  4  5  2  7  8]
 [ 4  7 10  0 11 12  9  1  2  3  8  5  6]
 [ 5  6  3  8  9 10  2 12  0 11  1  4  7]
 [ 3  4  9  6  7  5  8 11  1 12  0 10  2]
 [ 1 12  2  5  8  6  7  4  9 10 11  3  0]
 [ 2  0  1 11  3  4  5 10  7  8  6  9 12]
 [10 11 12  4  1  2  0  3  6  9  7  8  5]
 [ 8  9  7 10  0  3  1  2 12  4  5  6 11]
 [ 7 10  8  9  6 11 12  0  5  2  3  1  4]
 [ 0  5  6  7 12  9 10  8 11  1  4  2  3]
 [ 6  3  4  2  5  8 11  9 10  7 12  0  1]]

********************************************
	The pandiagonal Latin square
********************************************

[[12  2  5  3  4  1  6  7  8  0 10 11  9]
 [ 4  7 10  0 11 12  9  1  2  3  8  5  6]
 [ 1 12  2  5  8  6  7  4  9 10 11  3  0]
 [ 8  9  7 10  0  3  1  2 12  4  5  6 11]
 [ 6  3  4  2  5  8 11  9 10  7 12  0  1]
 [ 9  1 11 12 10  0  3  6  4  5  2  7  8]
 [ 3  4  9  6  7  5  8 11  1 12  0 10  2]
 [10 11 12  4  1  2  0  3  6  9  7  8  5]
 [ 0  5  6  7 12  9 10  8 11  1  4  2  3]
 [11  8  0  1  2  7  4  5  3  6  9 12 10]
 [ 5  6  3  8  9 10  2 12  0 11  1  4  7]
 [ 2  0  1 11  3  4  5 10  7  8  6  9 12]
 [ 7 10  8  9  6 11 12  0  5  2  3  1  4]]

********************************************
	The pandiagonal Latin square
********************************************

[[12  2  5  3  4  1  6  7  8  0 10 11  9]
 [ 7 10  8  9  6 11 12  0  5  2  3  1  4]
 [ 2  0  1 11  3  4  5 10  7  8  6  9 12]
 [ 5  6  3  8  9 10  2 12  0 11  1  4  7]
 [11  8  0  1  2  7  4  5  3  6  9 12 10]
 [ 0  5  6  7 12  9 10  8 11  1  4  2  3]
 [10 11 12  4  1  2  0  3  6  9  7  8  5]
 [ 3  4  9  6  7  5  8 11  1 12  0 10  2]
 [ 9  1 11 12 10  0  3  6  4  5  2  7  8]
 [ 6  3  4  2  5  8 11  9 10  7 12  0  1]
 [ 8  9  7 10  0  3  1  2 12  4  5  6 11]
 [ 1 12  2  5  8  6  7  4  9 10 11  3  0]
 [ 4  7 10  0 11 12  9  1  2  3  8  5  6]]

********************************************
	The pandiagonal Latin square
********************************************

[[12  2  5  3  4  1  6  7  8  0 10 11  9]
 [ 0  3  6  9  7  8  5 10 11 12  4  1  2]
 [ 6  4  7 10  0 11 12  9  1  2  3  8  5]
 [ 9 10  8 11  1  4  2  3  0  5  6  7 12]
 [ 3  0  1 12  2  5  8  6  7  4  9 10 11]
 [ 2  7  4  5  3  6  9 12 10 11  8  0  1]
 [ 5  6 11  8  9  7 10  0  3  1  2 12  4]
 [ 8  9 10  2 12  0 11  1  4  7  5  6  3]
 [ 7 12  0  1  6  3  4  2  5  8 11  9 10]
 [ 1 11  3  4  5 10  7  8  6  9 12  2  0]
 [ 4  5  2  7  8  9  1 11 12 10  0  3  6]
 [10  8  9  6 11 12  0  5  2  3  1  4  7]
 [11  1 12  0 10  2  3  4  9  6  7  5  8]]

********************************************
	The pandiagonal Latin square
********************************************

[[12  2  5  3  4  1  6  7  8  0 10 11  9]
 [11  1 12  0 10  2  3  4  9  6  7  5  8]
 [10  8  9  6 11 12  0  5  2  3  1  4  7]
 [ 4  5  2  7  8  9  1 11 12 10  0  3  6]
 [ 1 11  3  4  5 10  7  8  6  9 12  2  0]
 [ 7 12  0  1  6  3  4  2  5  8 11  9 10]
 [ 8  9 10  2 12  0 11  1  4  7  5  6  3]
 [ 5  6 11  8  9  7 10  0  3  1  2 12  4]
 [ 2  7  4  5  3  6  9 12 10 11  8  0  1]
 [ 3  0  1 12  2  5  8  6  7  4  9 10 11]
 [ 9 10  8 11  1  4  2  3  0  5  6  7 12]
 [ 6  4  7 10  0 11 12  9  1  2  3  8  5]
 [ 0  3  6  9  7  8  5 10 11 12  4  1  2]]

© 2021 ipgmvq

GPL-3.0 License