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Is it possible to interchange the positions of the the two black knights and two black rooks with those of the two white knights and two white rooks? Movements allowed are those of the corresponding pieces in the game of chess within the portion of the board available. White and black moves need not alternate.

If so, what is the least number of movements necessary?

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It an be done in 22 moves.

Let the central square be e5.
1. Nf3-e5-g6
3. Nd4-f3-e5-c4
6. Nd7-e5-f3
8. Nf6-d7
9. Re6-f6
10. Rd5-d4
11. Re4-e6
12. Rf5-d5
13. Rd4-e4
14. Rf6-f5
15. Nf3-d4
16. Nd7-e5-f3
18. Ng6-e5-d7-f6
21. Nc4-e5-d7

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