# Solution

(related to Problem: The Motor-garage Puzzle)

The exchange of cars can be made in forty-three moves, as follows: $6-G,$ $2-B,$ $1-E,$ $3-H,$ $4-I,$ $3-L,$ $6-K,$ $4-G,$ $1-I,$ $2-J,$ $5-H,$ $4-A,$ $7-F,$ $8-E,$ $4-D,$ $8-C,$ $7-A,$ $8-G,$ $5-C,$ $2-B,$ $1-E,$ $8-I,$ $1-G,$ $2-J,$ $7-H,$ $1-A,$ $7-G,$ $2-B,$ $6-E,$ $3-H,$ $8-L,$ $3-I,$ $7-K,$ $3-G,$ $6-I,$ $2-J,$ $5-H,$ $3-C,$ $5-G,$ $2-B,$ $6-E,$ $5-I,$ $6-J.$ Of course, "$6-G$" means that the car numbered "$6$" moves to the point "$G.$" There are other ways in forty-three moves.

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### References

#### Project Gutenberg

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

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