Swapping 6 queens in a 4x4 grid

Question

What is the least number of moves required to swap black and white queens? Queens move using standard chess rules – any number of empty cells vertically, horizontally or diagonally in a straight line. You do not need to alternate players.

Here is a similar question for rooks: Swapping 3 rooks in a 3×3 grid

chess combinatorics

Here is a similar question for rooks: Swapping 3 rooks in a 3x3 grid

Dr Xorile · Accepted Answer

It can actually be done in 17 moves.

Alaiko · Answer

Using the notation, (x = black queen, o = white queen, - = empty space), I came up with the following series of steps:
Starting Position:
x x x - 
x x - o 
x - o o 
- o o o 
1:

2:

3:

4:

5:

6:

7:

8:

9:

10:

11:

12:

13:

14:

15:

16:

17:

18:

This is also the solution with the least number of steps.

EDIT: As noted by @Bass below, the above explanation does not always hold true. So, there could theoretically be a lower limit than the one I explained.

Albert.Lang · Answer

Here is another optimal one.

Not correcting for symmetries there are

A brute force program finds all of them in less than a minute.

Swapping 6 queens in a 4x4 grid

3 Answers

Add your own answers!

Ask a Question