Different letters represent different numbers and none of them is equal to zero.

  NOSIER
+ ASTRAL
  725613

What word does the final result represent ?

NOSIER + ASTRAL = 725613
T=1 N=2 S=3 A=4 L=5 E=6 I=7 R=8 O=9
293768 + 431845 = 725613

725613=INLETS

Explanation:

L+R results in 3. Nonzero distinct possibilities for (L,R) are (1,2), (2,1), (4,9), (9,4), (5,8), (8,5), (7,6), (6,7).

Suppose (L,R)=(5,8)
100000(A+N) + 10000(O+S) + 1000(S+T) + 100(I+8) + 10(A+E) + 13 = 725613
A+E=10
The possibilities for (A,E) are:
(1,9),(3,7),(4,6),(6,4)

Case 1: (A,E)=(1,9). Then I=7.
100000(1+N) + 10000(O+S) + 1000(S+T) + 1613 = 725613
S+T=14 This does not allow any values of (S,T) different than 1,5,8,9
So Case 1 is ruled out.

Case 2: (A,E)=(3,7)
100000(3+N) + 10000(O+S) + 1000(S+T) + 100(I+8) + 113 = 725613
then I=7, which is wrong since E=7
So Case 2 is wrong.

Case 3: (AE)=(4,6) (Then again I=7)
100000(4+N) + 10000(O+S) + 1000(S+T) + 1613 = 725613
Then (S,T)=(1,3),(3,1)

Case 3a: (S,T)=(1,3)
100000(4+N) + 10000(O+1) + 5613 = 725613
O=1, which is disallowed since S=1
So Case 3a is ruled out.

Case 3b: (S,T)=(3,1) (Then O=9)
100000(4+N) + 125613 = 725613
N=2
This case works.
Edited on December 28, 2003, 3:25 pm

Posted by Penny on 2003-12-28 15:23:53