Single Comment

Given the number of actual Queens and potential Queens (Pawns) at the start
of the game, 18. It would be less only if it were impossible for all the
Pawns to reach the 8th rank. It might seem impossible given the following
considerations:

For any Pawn to reach its 8th rank, it must get by the opposing Pawn. So
either that Pawn must be captured, or the Pawn must capture another piece
to get around it. Not including the King, which can't be captured, the
Queen, which is already a Queen, and the Pawns, which are potential
Queens, there are six pieces left to each side that could be captured. So
six Pawns on each side could get to the 8th rank without capturing
opposing Pawns. Then it might seem that only half of the remaining Pawns
can get to the 8th rank, for a total potential of 16 Queens.

But wait. This chain of thinking is deceptive. When a Pawn captures an
enemy piece to get by an enemy Pawn, it also makes way for that enemy
Pawn. Therefore, there need be only eight Pawn captures between both
sides. If each side captures four pieces with its Pawns, it would let four
of its own Pawns get by and make way for four enemy Pawns. One possible way
to do this is for White to move its a, c, e, and g Pawns to the b, d, f,
and h files, while Black does the reverse. Thus, all the Pawns could get
through, for a full total of 18 Queens on the board.

One possible impediment is the danger of premature checkmate. This can be
prevented by surrounding one's King with one's own Queens as Pawns
promote to them. So, given cooperation between both players, a game of
Chess can have up to 18 Queens on the board.