SOLUTION: tom brought a notebook with 100 sheets and numbered its pages consecutively from 1 to 200. Jerry pulled out 43 sheets and added up all 86 page numbers written on both sides of each

Every sheet has an odd number on the front and the next even number on the back.  

Let every front page have odd number  i=1,...,43
and every back page have the next even number , i=1,...,43
Thus the 43 sums of the numbers on the 43 pages, front and
back, are , i=1,...43

We are investigating whether the sum of those 43 sums can be 2011.

Suppose 



 

 



Divide both sides by 2



Thus we have reached a contradiction since we have
an even number equalling to an odd number.

So we have shown that the sum cannot be 2011.

Edwin