An odd number of positions is impossible because if your first position has an even number of 1's then your last position must have an odd number of 1's. All e

An odd number of positions is impossible because if your first position has an even number of 1's then your last position must have an odd number of 1's. All even numbers should be possible though. For example, here is 6 positions: 000, 001, 011, 111, 110, 100 - and this strategy can generalize to any even number.