What is the smallest number which leaves a remainder:
9 when divided by 10;
8 when divided by 9;
7 when divided by 8;
6 when divided by 7;
5 when divided by 6;
4 when divided by 5;
3 when divided by 4;
2 when divided by 3;
1 when divided by 2 ?

[ In other words: Find the Least number which when divided by 'N' leaves a remainder '(N-1)', for N = 1,2,3,4,........,9,10].

Answer: 2519

Explanation:
Let's assume that the required number is N.

Then the number (N+1) is given by:
8x9x35 = 72x35 = 2520.

Here '8' takes care of divisibility by 2, 4 & 8;
and '9' takes care of divisibility by 3 & 9;
and '35' takes care of divisibility by 5 & 7;
and the combined product takes care of divisibility by 6 & 10;

Posted by Jayaram S on 2003-05-29 02:42:04