[rookie1ja]

No. 18 - Back to the Cryptograms and Algebra Puzzles
Replace the same characters by the same numerals so that the mathematical operations are correct.
A^L = LEBKA

Spoiler for Solution:

No. 18 - solution
5⁷ = 78125

[guderman]

two possible answers here.

we realize that the number has to be at least 5 digits long, so we need to look for a power that has five digits...

3^9 = 19683,

which is too small.

the next one in the neighborhood is 4^8, which is also too small, and without even bothing to do the next multiplication, one can see that 4^9 would have too many digits.

that brings us to...

5^7 = 78125,

which is a correct answer. But is it the only one? 6^6 is slightly too small (and besides, one can make the reasonable assumption that different letters mean unique numbers). 7^5 is too small while 7^6 is too big. 8^5 is too small, and the next higher power will have too many digits. That brings us to the last possibility, which is 9^5 = 59049, which is a possibility, but only if you allow different letters to mean the same digit. I am assuming that such is not allowed, which would negate this option, so that means that 5^7 is the correct answer.

[BoilingOil]

Quote

.....

5^7 = 78125,

.....

I see no way to improve on your mathematic skills here, guderman. And I'm known to do such things sometimes
Very well done.


BoilingOil

[cpotting]

9 and 5 also work, if you allow multiple letters to represent the same digit [a reasonable assumption since a) the problem did not specify otherwise, and B) there are 26 letters and only 10 digits].

L = 5
E = 9
B = 4
K = 0
A = 9

[BoilingOil]

Quote

9 and 5 also work, if you allow multiple letters to represent the same digit [a reasonable assumption since a) the problem did not specify otherwise, and B) there are 26 letters and only 10 digits].

L = 5
E = 9
B = 4
K = 0
A = 9

Well, actually, several people try to pose this assumption because it wasn't explicitly excluded beforehand. Usually, this kind of problem would only be a real puzzle, if we assume that each DIFFERENT letter actually signifies a DIFFERENT digit. Otherwise, what would be the point?

And even if your assumption was allowable, your answer would still be wrong, because you switched the 0 and the 4

BoilingOil

[bob]

l2 is the equation 9 divided by 3.5678324 and then multiplied by 28. divid this by l and then plug in a as a variable. once you solve for a then just simplifly and divided your decimal or fraction by 9 again.

[cpotting]

Quote

And even if your assumption was allowable, your answer would still be wrong, because you switched the 0 and the 4

BoilingOil

oops