I am not taking any constraint as such but orderings are (00, 01, 11, 10), (01, 11, 10, 00), (11, 10, 00, 01) and (10, 00, 01, 11) are not exactly different in the sense that they are just rotating the numbers by 1 place.
On the other hand, as I said earlier (00, 01, 11, 10) and (00, 10, 11, 01) are distinct orderings.
Also, for 3-bit numbers, I kind tried to find the no. of possible orders by brute-force method. I came up with the following orderings till now-
- (000, 001, 011, 010, 110, 111, 101, 100),
- (000, 001, 011, 010, 110, 100, 101, 111),
- (000, 001, 011, 111, 101, 100, 110, 010),
- (000, 001, 101, 100, 110, 111, 011, 010),
- (000, 001, 101, 100, 110, 010, 011, 111),
- (000, 001, 101, 111, 011, 010, 110, 100),
- (000, 010, 110, 100, 101, 111, 011, 001),
- (000, 010, 011, 001, 101, 111, 110, 100),
- (000, 100, 110, 010, 011, 111, 101, 001),
- ...
If I am not mistaken, I already have 9 orderings for 3-bit numbers.