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?
A L P H A B E T
L E T T E R S
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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
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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
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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
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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
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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
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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 !
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Posted by pcbouhid
on 2005-06-22 20:45:15 |
Since I donīt have a computer...
