1. [8] Amelia wrote down a sequence of consecutive positive integers, erased one integer, and scrambled the rest, leaving the sequence below. What integer did she erase?
$$
6,12,1,3,11,10,8,15,13,9,7,4,14,5,2
$$
Answer:
16
Solution: The sequence of positive integers exactly contains every integer between 1 and 15 , inclusive. 16 is the only positive integer that could be added to this sequence such that the resulting sequence could be reordered to make a sequence of consecutive positive integers. Therefore, Amelia must have erased the integer 16 .