There is exactly one solution. The notebook had 64 pages and the sheet with the page numbers 29 and 30 is ripped out.
Let b>0 be the number of sheets. The number of pages will be 2b. We are looking for a number 2b such that
1+2+⋯+(2b−1)+2b=2(2b)⋅(2b+1)>2021.
Since 2602=1800 has the right order of magnitude, we check the integers beginning with b=30 and find:
262⋅63=1953<2021<264⋅65=2080.
Therefore, the smallest possible number of pages is 64.
The torn out sheet h contains the page numbers 2h−1 and 2h (first odd, then even).
This gives the equation
2h−1+2h=2080−2021=59
which implies h=15.
So, one solution is that the book originally had 32 sheets and the 15th sheet with page numbers 29 and 30 has been torn out.
It remains to explain why this is the only solution. If the book has 64 sheets, this is the only possibility because h could be computed uniquely. Now, assume that the number b of sheets is larger than 32 and the number of pages at least 66.
The sheet that has been torn out can have at most page numbers 2b−1 and 2b, so the remaining sum is at least 1+2+⋯+63+64=2080>2021. So there cannot be a solution with more than 32 sheets.