Please help!Tom bought a notebook with 100 sheets and numbered it pages consectutively from 1 to 200. Jerry pulled out 43 sheets and added up all...

There is notebook with pages numbered 1 through 200. 43
random sheets are removed (therefore 86 page numbers). Therefore, the question
is:

Is it possible for 86 random numbers between 1 and 200
to add up to 2011?

The answer is no, it is not
possible. Suppose the first 43 sheets were removed (thus giving us page numbers 1 - 86).
This would give us a lower bound, since these are the lowest possbile numbers.
But

1 + 2+ 3+ ... + 86
= 3741.

Therefore, the sum must be greater than or equal
to 3741. 2011 is less than this, so the sum cannot equal
2011.