Tokarev S.i.

On the first horizontal line of the chessboard, there are 8 black queens, and on the last - 8 white queens. In what minimum number of moves can the white queens exchange places with the black ones? White and black move alternately, one queen per move.
The queen on the squares b1 and b8, which moved earlier, could not move to the opposite rank with that move, meaning these two queens together made at least three moves. Similarly, the pairs of queens on the files c, ..., g each made at least three moves. The first of the four corner queens to move did not land on a corner square with that move, so they made at least five moves in total. Therefore, a total of at least $6 \cdot 3 + 5 = 23$ moves are required.

An example of 23 moves is shown in the figure (the black queen moves first):
![](https://cdn.mathpix.com/cropped/2024_05_06_123645a38d760684829ag-15.jpg?height=854&width=1294&top_left_y=-2&top_left_x=386)

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