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A classic game (Posted on 2005-06-22) Difficulty: 3 of 5
Substitute digits for letters (different letters, different digits; same letters, same digits) so ALPHABET + LETTERS = SCRABBLE. No number begins with zero.

Can you manage without a computer program?

See The Solution Submitted by e.g.    
Rating: 3.0000 (2 votes)

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Solution Since I donīt have a computer... | Comment 5 of 10 |
A L P H A B E T
   L E T T E R S  
------------------
SC R A B B L E
 
Since B + E = B, E could only be zero.
 
A L P H A B 0 T
   L 0 T T 0 R S
------------------
SC R A B B L 0
 
S = A + 1, and T + S = 10, so T + A = 9. Since A + T = B, B = 9.
 
A L P H A 9 0 T
   L 0 T T 0 R S
------------------
SC R A 9 9 L 0
 
R + 1 = L and P + 1 = R, so P + 1 + 1 = L ---> L = P + 2.
 
Since L + L = C (carrying 1), L could only be 6 or 7 or 8.
 
1) For L = 6, P = 4, R = 5 (and C will be 2):
 
A 6 4 H A 9 0 T
   6 0 T T 0 5 S
------------------
S 2 5 A 9 9 6 0
 
S = A + 1. So S could only 7. If S = 7, A would be 2 (C is already 2). Thus, (1) is false.
 
2) For L = 7, P = 5, R = 6 and C = 4. 
 
A 7 5 H A 9 0 T
   7 0 T T 0 6 S
------------------
S 4 5 A 9 9 7 0
 
S + T = 10 ===> (S,T) = (2,8) or (8,2)
 
2.1) (S,T) = (2,8)====> A = 1, H = 3
 
1 7 5 3 1 9 0 8
   7 0 8 8 0 6 2
-----------------  
2 4 5 1 9 9 7 0===========>SOLUTION !!!
 
2.2) (S,T) = (8,2) =====> A = 2 =====>impossible.
 
3) L = 8, P = 6, but C = 6 (carrying 1)====> impossible.
 
 
Unique solution !

  Posted by pcbouhid on 2005-06-22 20:45:15
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