rookie1ja Posted March 31, 2007 Report Share Posted March 31, 2007 No. 19 - Back to the Cryptograms and Algebra Puzzles Replace the same characters by the same numerals so that the mathematical operations are correct. KOV x KOV = DEDKOV 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. 19 - solution 376 x 376 = 141376 Link to comment Share on other sites More sharing options...

Guest Posted April 13, 2009 Report Share Posted April 13, 2009 (edited) Given : KOV x KOV = DEDKOV let x = KOV => x is 3 digit number x^2 = 1000 * DED +x x(x-1) = 1000*DED Now, x and x-1 are prime to each other and since 1000 (=2^3 * 5^3) is four digit number => Out of x and x-1 one should be of the form 8p and other 125q so that |8p - 125q| = 1 So, 3 digit multiples of 125 : 125,250,375,500,625,750,875 Now numbers 125q+1 and 125q-1 which are divisible by 8 are 376 and 624 So, 376*375 = 1000 * 141 and, 625*624 = 1000 * 390 Hence Ans : DEDKOV = 141376 Edited April 13, 2009 by guru_bhai Link to comment Share on other sites More sharing options...

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