How to find values ​​in a huge array?

Question

Programming

This is the question I was asked at the interview, but unfortunately I was not ready for it:
1) There is a large array of values ​​presented in binary form
2) In this array, each value has a pair, the same value, and only one value does not have a pair
3) Values ​​enter the buffer, but the buffer is much smaller than the array (let's say only one value can be placed)
4) Find the value without a pair
I was given hints:
- use binary operations
- matrix trace Tell me
where to at least dig. Thank you.

Answer 1

XOR through the entire array - the output will be a lone element

Answer 2

XOR is a trivial problem!!!
Let me ask you another one:
Write a recursive factorial function that will iteratively calculate the result.