There's a more general formulation, which is that every value but one must appear even numbers of times, and the one must appear some odd number of times.
How about every value appears 0 mod n times except one which appears 1 mod n times? :)
Solution: xor is just addition mod 2. Write the numbers in base n and do digit-wise addition mod n (ie without carry). Very intuitive way to see the xor trick.
Solution: xor is just addition mod 2. Write the numbers in base n and do digit-wise addition mod n (ie without carry). Very intuitive way to see the xor trick.