Single Number - XOR Properties

XOR has two key properties: $1.$ $a \oplus a = 0$ (self-inverse).

$2.$ $a \oplus 0 = a$ (identity).

XOR all elements. Pairs cancel out ($a \oplus a = 0$), leaving only the unique element.

Example: $4 \oplus 1 \oplus 2 \oplus 1 \oplus 2 = 4 \oplus (1 \oplus 1) \oplus (2 \oplus 2) = 4 \oplus 0 \oplus 0 = 4$.