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 we add 1 to the number, divided by 2...10 it will leave no remainder, so the number is one less than the LCM of 2...10, which is 2520.

Actually, the problem should read "the smallest POSITIVE number"; otherwise, -1 could also be considered to qualify, and so would -2521, -5041, and so on.

Posted by Federico Kereki on 2003-10-17 13:02:58