[rookie1ja]

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

Spoiler for Solution

No. 19 - solution
376 x 376 = 141376

[guru_bhai]

Spoiler for Solution

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

This post has been edited by guru_bhai: 13 April 2009 - 04:50 PM