Neptune

Four words add up to a fifth word numerically:

     mars
    venus
   uranus
   saturn
  -------- +
  neptune

Each of the ten letters (m, a, r, s, v, e, n, u, t, and p) represents a digit in the range 0 up to 9 (equal letters represent equal digits and different letters represent different digits). Furthermore, the digits 1 and 6 are being used most frequently.

 

Answer:

The easiest way to solve this problem is by writing a computer program that systematically tries all possible mappings from the digits onto the letters. This will give you only one solution which meets the condition that the digits 1 and 6 are most frequently used:

     mars         m = 4
    venus         a = 5
   uranus         r = 9
   saturn         s = 3
 -------- +       v = 2            4593
  neptune         e = 0           20163
                  n = 1          695163
                  u = 6          358691
                  t = 8        -------- +
                  p = 7         1078610