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# No. 19

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Replace the same characters by the same numerals so that the mathematical operations are correct.

KOV x KOV = DEDKOV

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No. 19 - solution

376 x 376 = 141376

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• 2 years later...

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 by guru_bhai
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