You have a supply of two different sizes of blocks: some weigh 1kg, others are heavier than 1kg but not as much as 2kg (you get to decide the exact weight of these heavier blocks but they must all weigh the same).

If none of the five positions is allowed to be left empty, and each of the five piles is different, what is the minimum number of blocks you can arrange at the five points of a regular penta-star so that the entire arrangement is balanced around the centre?

Bonus: would it make a difference if one of the positions can be left empty (but only one as otherwise two ‘piles’ would be the same)?