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].

If it gives a remainder of 9 when divided by 10, then it has to be 1 less than a multiple of 10. Therefore, it is 1 less than a multiple of every number from 1 to 10. It has to be 1 less than the smallest number that is divisible by every number from 1 to 10, so it is 2519.

Posted by Math Man on 2011-01-01 16:04:23