Sometimes a seemingly minor rule is enough to make impossible what seems only difficult. The key is to find what remains invariant.

The impossible row of cards

Reasoner
Pure logic

Riddle statement

You start with the row of cards

4, 2, 6, 1, 5, 3.

The only operation allowed is to exchange two adjacent cards whose sum is odd.
Can

1, 2, 3, 4, 5, 6 be reached in this way?