Another service from Omega

The System of Equations

The information given in the problem can be written as four linear equations in four unknowns:
  • N is the three digit number "xyz"
    > E1 := 100*x + 10*y + z = N:
  • N equals 15 times the sum of its digits
    > E2 := 15*(x + y + z) = N:
  • Reversing the digits increases N by 396
    > E3 := x + 10*y + 100*z = N + 396:
  • One's digits is one larger than the sum of the other two
    > E4 := z = x + y + 1: 
    • > solve({E1, E2, E3, E4}, {x,y,z,N});

                         {y = 3, z = 5, N = 135, x = 1}