Before you get too excited, this is a probabilistic algorithm, not a deterministic one. Feels weird to call it an "extension" when you lose an absolute guarantee, but still cool nonetheless.
It's a solution to the problem: given a list of n-1 unique integers 1 through n, find the missing integer.
The trick is that when you xor all of the numbers in the list together and then xor that with the xor of 1 through n, the result is the missing number.
The trick is that when you xor all of the numbers in the list together and then xor that with the xor of 1 through n, the result is the missing number.