Die Lösung lautet 13, berechnet mit folgendem Python Programm:

for A in range(16):
  for B in range(16):
    C = 7;
    D = 3;
    for E in range(16):
      F = 1;
      for G in range(16):
        H = 6
        for I in range(16):
        J = 2
        if A+B+C == C+D+E and C+D+E == E+F+G and E+F+G== G+H+I and G+H+I == I+J+A:
          print (A)