{∅, {∅}, {∅, {∅}}} : Rage Against the Meat Grinder

Some questions are very badly written. But I am trying to sort out these things. Keep well.

Yes, that can be very frustrating, and it takes a great deal of confidence to determine just when there is such a mistake.

Now, "All the page numbers from a book are added,beginning at page 1 .However, one page number was mistakenly added twice.The sum obtained was 1000."

I would not know where to begin except brute force.

The sum of the numbers 1 to 44 is 990.

(1 + 44)/2 * 44 = 990

Page 10 may have been counted twice, which would result in 1000.