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| Substitute seen, get result (Posted on 2007-05-10) |
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Substitute the letters S, E and N by valid digits to satisfy the following alphametic equation.
(SEEN)Base 8 - (SEEN)Base 5
= (SEEN)Base 7
NOTE: S is NOT zero.
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Submitted by K Sengupta
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Rating: 3.0000 (1 votes)
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Solution:
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Transforming the given relationship to the decimal system, we have:
S(8^3 - 5^3 - 7^3) + E(8^2+8-5^2 -5-7^2-7)
+ N(1-1-1) = 0
Or, 44S = 14E + N
Since, E and N are digits in base 5; it follows that E, N< =4. This gives:
44S< = 14*4 + 4 = 60 < 88, so that S< 2, giving S=1
Accordingly, 14E + N = 44.
Since 0<=N< =4, it follows that:
40< = 14E< =44, so that E=3, giving:
E= 44- 14*3 = 2
Consequently, (S, E, N) = (1, 3, 2) is the only solution to the given problem.
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