(related to Problem: The Kennel Puzzle)
The first point is to make a choice of the most promising knight's string and then consider the question of reaching the arrangement in the fewest moves. I am strongly of opinion that the best string is the one represented in the following diagram, in which it will be seen that each successive number is a knight's move from the preceding one and that five of the dogs $(1, 5, 10, 15,$ and $20)$ never leave their original kennels.
This position may be arrived at in as few as forty-six moves, as follows: $16—21,$ $16—22,$ $16—23,$ $17—16,$ $12—17,$ $12—22,$ $12—21,$ $7—12,$ $7—17,$ $7—22,$ $11—12,$ $11—17,$ $2—7,$ $2—12,$ $6—11,$ $8—7,$ $8—6,$ $13—8,$ $18—13,$ $11—18,$ $2—17,$ $18—12,$ $18—7,$ $18—2,$ $13—7,$ $3—8,$ $3—13,$ $4—3,$ $4—8,$ $9—4,$ $9—3,$ $14—9,$ $14—4,$ $19—14,$ $19—9,$ $3—14,$ $3—19,$ $6—12,$ $6—13,$ $6—14,$ $17—11,$ $12—16,$ $2—12,$ $7—17,$ $11—13,$ $16—18 = 46$ moves. I am, of course, not able to say positively that a solution cannot be discovered in fewer moves, but I believe it will be found a very hard task to reduce the number.
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