# Here is the Solution

# Can you find it!

I just found a number with an interesting property: When I divide it by 2, the remainder is 1. When I divide it by 3, the remainder is 2. When I divide it by 4, the remainder is 3. When I divide it by 5, the remainder is 4. When I divide it by 6, the remainder is 5. When I divide it by 7, the remainder is 6. When I divide it by 8, the remainder is 7. When I divide it by 9, the remainder is 8. When I divide it by 10, the remainder is 9. It is not a small number, but it is not really big, either. When I looked for a smaller number with this property I could not find one. Can you find it?

**SOLUTION : **If a number n on being divided by x leaves remainder x-1, then if n+1 is divided by x, the remainder should be zero.

The converse of this property is also true. If a number m on being divided by x leaves remainder 0, then m-1 will give remainder x-1 when divided by x.

The smallest number that gives 0 as remainder when divided by any number from 2-10 will be LCM of 2 to 10, i.e. 2520 (you can find it). So, 2519 will follow the remainder properties mentioned in the problem. Answer is 2519.