Is it possible to order a complete set of chess pieces of the same color (8 Pawns, 2 Knights, 2 Bishops, 2 Rook, Queen and King) in such a way that none of them attack each other? If so, how?
I give you the following:
This solution can arise in a regular chess game, where the black king is superfluous. The conditions would still be met if the black king were removed. White needs to make 25 moves (Queenside castle, thanks to h34 in comments) to get into this position, but due to the need of capturing all opposing pieces, a game leading to this position would probably take more turns.
Here is a solution that also maximizes the number of pawns on the board. It also takes into account pawn promotion and the no-pawns-on-first-row rule.
The area of influence by the rooks is constant wherever they are (2 rows and 2 columns). I placed the bishops and the knights to the side to minimize their area of influence and the rooks on the next columns so the 2 required by the rooks overlap with most of the squares controlled by the knights and bishops.
There are 5 columns remaining at this point and pawns placed in a column render the columns next to them useless. This means the best way to place them is to put them on columns 1, 3 and 5. This leaves the Queen on column 2 or 5.