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## What is the number?

Posted by Rajesh Lal on April 17, 2010 – 10:56 pm

If you divide the number by 2 there will remainder of 1.
If you divide the number by 3 there will remainder of 1.
If you divide the number by 4 there will remainder of 1.
If you divide the number by 5 there will remainder of 1.
If you divide the number by 6 there will remainder of 1.
If you divide the number by 7 there will remainder of 1.
If you divide the number by 8 there will remainder of 1.
If you divide the number by 9 there will remainder of 1.
If you divide the number by 10 there will remainder of 1.
If you divide the Number by 11 there will remainder of 0.

This post is under “Tom” and has 3 respond so far.

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huh?

2. 2. Quaid Said：

The answer for the puzzle is

If you divide the number by 2 there will remainder of 1. ==> 3
If you divide the number by 3 there will remainder of 1. ==> 4
If you divide the number by 4 there will remainder of 1. ==> 5
If you divide the number by 5 there will remainder of 1. ==> 6
If you divide the number by 6 there will remainder of 1. ==> 7
If you divide the number by 7 there will remainder of 1. ==> 8
If you divide the number by 8 there will remainder of 1. ==> 9
If you divide the number by 9 there will remainder of 1. ==> 10
If you divide the number by 10 there will remainder of 1. ==> 11
If you divide the Number by 11 there will remainder of 0. ==> 11

3. 3. Chris Said：

I’m sure I did this before.
The lowest common multiple of 2,3,4,5,6,7,8,9,10 is 2520
i.e. 2520 (mod 2,3,…,10) = 0 and 2520 is the smallest number with that property.
Note that 2520*n + 1 = 1 (mod 2,3,…,10) any integer n
We need 2520*n + 1 = 0 (mod 11)
But 2520 (mod 11) = 1
=> 2520*n + 1 = n + 1 = 0 (mod 11)
=> n = 10
So the required number is 25201

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