rookie1ja 13 Report post Posted March 31, 2007 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 This old topic is locked since solution is already provided in the Spoiler below. Pls visit New Puzzles section to see always fresh brain teasers. No. 18 - solution 5^{7} = 78125 Share this post Link to post Share on other sites

Guest Report post Posted September 26, 2007 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. Share this post Link to post Share on other sites

Guest Report post Posted September 26, 2007 ..... 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 Share this post Link to post Share on other sites

Guest Report post Posted September 27, 2007 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 Share this post Link to post Share on other sites

Guest Report post Posted September 27, 2007 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 Share this post Link to post Share on other sites

Guest Report post Posted October 7, 2007 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. Share this post Link to post Share on other sites

Guest Report post Posted October 9, 2007 And even if your assumption was allowable, your answer would still be wrong, because you switched the 0 and the 4 BoilingOil oops Share this post Link to post Share on other sites