THE FIFTEEN TURNINGS.
(
Unicursal and Route Problems)
Here is another queer travelling puzzle, the solution of which calls for
ingenuity. In this case the traveller starts from the black town and
wishes to go as far as possible while making only fifteen turnings and
never going along the same road twice. The towns are supposed to be a
mile apart. Supposing, for example, that he went straight to A, then
straight to B, then to C, D, E, and F, you will then find that he has
travelled thirty-seven miles in five turnings. Now, how far can he go in
fifteen turnings?
Answer:
It will be seen from the illustration (where the roads not used are
omitted) that the traveller can go as far as seventy miles in fifteen
turnings. The turnings are all numbered in the order in which they are
taken. It will be seen that he never visits nineteen of the towns. He
might visit them all in fifteen turnings, never entering any town twice,
and end at the black town from which he starts (see "The Rook's Tour,"
No. 320), but such a tour would only take him sixty-four miles.
