# Solution

(related to Problem: A New Bishop's Puzzle)

Play as follows, using the notation indicated by the numbered squares in Diagram A:—

Move White Black
1. 18—15 3—6
2. 17—8 4—13
3. 19—14 2—7
4. 15—5 6—16
5. 8—3 13—18
6. 14—9 7—12
7. 5—10 16—11
8. 9—19 12—2
9. 10—4 11—17
10. 20—10 1—11
11. 3—9 18—12
12. 10—13 11—8
13. 19—16 2—5
14. 16—1 5—20
15. 9—6 12—15
16. 13—7 8—14
17. 6—3 15—18
18. 7—2 14—19

Diagram B shows the position after the ninth move. Bishops at $1$ and $20$ have not yet moved, but $2$ and $19$ have sallied forth and returned. In the end, $1$ and $19,$ $2$ and $20,$ $3$ and $17,$ and $4$ and $18$ will have exchanged places. Note the position after the thirteenth move.

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### References

#### Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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