Distinct positive integers have been assigned to the letters of the alphabet. Adding up the values of the letters in their names results in the following totals:

SUN = 18
MERCURY = 33
VENUS = 39
MOON = 36
EARTH = 31
MARS = 32
JUPITER = 50
SATURN = 33
URANUS = 36
NEPTUNE = 29
PLUTO = 40

What is the total value of PLANETS?

S+U+N = 18 & V+E+N+U+S = 39, therefore E+V = 21
S+U+N = 18 & S+A+T+U+R+N = 33, therefore A+R+T = 15
S+U+N = 18 & U+R+A+N+U+S = 36, therefore A+R+U = 18
E+A+R+T+H = 31 & A+T+R = 15, therefore E+H = 16
A+R+U = 18 & A+R+T = 15, therefore U = T+3
(M+O+O+N)+(M+A+R+S)+(U+R+A+N+U+S) =
   2*(M+O+A+R+S+U+N) = 36+32+36 = 104;
   [2*(M+O+R+A+S+U+N) - 2*(S+U+N)]/2 = [104 - 2*(18)]/2;
   therefore M+O+R+A = 34
M+A+R+S = 32 and M+A+R+O = 34, therefore O = S+2

Using the above information and a spreadsheet, I was able to deduce the following:

A = 12
C = 6 (if Y = 7) or 7 (if Y = 6)
E = 3
H = 13
I = 15 (if J = 16) or 16 (if J = 15)
J = 16 (if I = 15) or 15 (if I = 16)
L = 14
M = 10
N = 4
O = 11
P = 8
R = 1
S = 9
T = 2
U = 5
V = 18
Y = 7 (if C = 6) or 6 (if C = 7)

The value of PLANETS, therefore, is 52.

Observation: If V had the value of 17, the values of the letters would run the gamut from 1 to 17, but, as it is, V=18 and 17 is skipped. [If V=17, VENUS=38].

The values of the two 'forgotten' dwarf planets:
CERES = 22 or 23 (depending on the value of C), and
ERIS = 28 or 29 (depending on the value of I)

Posted by Dej Mar on 2007-11-13 22:47:54