That seemed surprisingly high a number to me.915,103,765 - the number of ways to combine six two-by-four Lego bricks of the same color
Assume the following:
- the bricks are indistinguishable (all the same color).
- the bricks must be connected (i.e. 6 bricks side-by-side is not allowed).
- the bricks are all lug-side up.
- rotationally symmetric arrangements are the same.
What if we relax the rotational symmetry constraint?
What if the bricks were different colors? - I assume this will give us 6! times as many
Do any of these rules come in around the 915 million mark?