Leonhard Euler created the following magic square.

This magic square has three properties:

- Each row and each column sums to 260.
- Each half-row and each half-column sums to 130.
- The sequence of squares containing 1, 2, 3, …, 64 form a knight’s tour.

The following Python code verifies that the magic square has the advertised properties.

# Euler's knight's tour magic square a = [[ 1, 48, 31, 50, 33, 16, 63, 18], [30, 51, 46, 3, 62, 19, 14, 35], [47, 2, 49, 32, 15, 34, 17, 64], [52, 29, 4, 45, 20, 61, 36, 13], [ 5, 44, 25, 56, 9, 40, 21, 60], [28, 53, 8, 41, 24, 57, 12, 37], [43, 6, 55, 26, 39, 10, 59, 22], [54, 27, 42, 7, 58, 23, 38, 11]] # Divide the chess board into four 4x4 blocks. # Verify that in each block the rows and colums sum to 130. # It follows that each entire row and entire column sums to 260. for hblock in [0, 1]: for vblock in [0, 1]: for i in range(0,4): row_sum = col_sum = 0 for j in range(0,4): row_sum += a[hblock*4 + i][vblock*4 + j] col_sum += a[hblock*4 + j][vblock*4 + i] assert(row_sum == 130) assert(col_sum == 130) # Report whether it is legal for a knight to move from a to b. def knight_move(a, b): return ((abs(a[0] - b[0]) == 2 and abs(a[1] - b[1]) == 1) or (abs(a[0] - b[0]) == 1 and abs(a[1] - b[1]) == 2)) # Map each square to its coordinates. coordinate = {} for row in range(0, 8): for col in range(0, 8): coordinate[ a[row][col] ] = (row, col) # Verify that the sequence of numbers are legal knight moves. for i in range(1, 64): assert knight_move( coordinate[i], coordinate[i+1] ) # If the script gets this far, no assertion failed. print "All tests pass."