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;