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 The Strange Number (Posted on 2003-05-29)
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].

 See The Solution Submitted by Ravi Raja Rating: 2.6667 (9 votes)

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 Puzzle Solution | Comment 7 of 9 |

By the problem, the remainder when N is separately divided by i for 1< = i<= 10, the remainder is (i-1).

In other words,
N( Mod i) = -1, for 1< = i<= 10

Consequently,
Minimum (N) = LCM(1,2,3,4,5,6,7,8,9,10) - 1
= 2520 - 1 = 2519

 Posted by K Sengupta on 2007-11-29 04:50:01

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