Originally Posted by

**Vicky1997** Let Si be the set of all intergers n such that 100i < or = n < 100 (i + 1).

For example, S4 is the set {400, 401,402,........499}. How many of the sets S0, S1, S2, S3,................ S999 do not contain a perfect square?

I tried to make a pattern

1 2 3 4 5 6 7 8 ............ 50

1 4 9 16 25 36 49 64 ............ 2500

3 5 7 9 11 13 15

and I see the difference between two squares have a pattern of 2n-1

therefore, when 2n-1 >100 there will be some sets that don't have a square. n <50 there will be squares in each set.

Up to S25 there should be at least one square in each set.

I am stuck from here because it will be impossible for me to try out all the sets...

Thanks.

Vicky.