Pair things up. If everything has a partner, the number is even. If one's left out alone, it's odd. That's the whole rule.
Quick checks
- Ends in 0, 2, 4, 6, 8 → even
- Ends in 1, 3, 5, 7, 9 → odd
- Even + even = even · odd + odd = even · even + odd = odd
- Odd × odd = odd, every other product is even
Half of all whole numbers are even, half are odd. Forever. The pattern never breaks.