If your "&" means "+", then A = 2500-k B = k-1400 C = 3100-k D = k-2000 E = 5300-k F = k You can choose any value for k and all the equations check: A+B=1100, B+C=1700, C+D=1100, D+E=3300, E+F=5300, F+A=2500 For example choose k = 2200 A = 2500-2200 = 300 B = 2200-1400 = 800 C = 3100-2200 = 900 D = 2200-2000 = 200 E = 5300-2200 = 3100 F = 2200 Checking: A+B=1100, B+C=1700, C+D=1100, D+E=3300, E+F=5300, F+A=2500 Or choose k = 2350 A = 2500-2350 = 150 B = 2350-1400 = 950 C = 3100-2350 = 750 D = 2350-2000 = 350 E = 5300-2350 = 2950 F = 2350 Checking: A+B=1100, B+C=1700, C+D=1100, D+E=3300, E+F=5300, F+A=2500 So there are many solutions if "&" is taken to mean "+" Edwin