# Solution

(related to Problem: Visiting The Towns)

Note that there are six towns, from which only two roads issue. Thus $1$ must lie between $9$ and $12$ in the circular route. Mark these two roads as settled. Similarly mark $9,$ $5,$ $14,$ and $4,$ $8,$ $14,$ and $10,$ $6,$ $15,$ and $10,$ $2,$ $13,$ and $3,$ $7,$ $13.$ All these roads must be taken. Then you will find that he must go from $4$ to $15,$ as $13$ is closed, and that he is compelled to take $3,$ $11,$ $16,$ and also $16,$ $12.$ Thus, there is only one route, as follows: $1,$ $9,$ $5,$ $14,$ $8,$ $4,$ $15,$ $6,$ $10,$ $2,$ $13,$ $7,$ $3,$ $11,$ $16,$ $12,$ $1,$ or its reverse — reading the line the other way. Seven roads are not used.

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### References

#### Project Gutenberg

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

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