Answers 369
- RAILWAY ROUTES
There are 2,501 ways of going from B to D, as follows:I-line journey I route 2 variations 2
2-line journey I route 9 variations 9
3-line journey 2 routes 12 variations 24
4-line journey 5 routes 18 variations 90
5-line journey 4 routes 72 variations 288
6-line journey 14 routes 36 variations 504
8-line journey 22 routes 72 variations 1,584
2,501We have only to consider the routes from B to D. The I-line route is direct
to D. The 2-line route is CD. The two 3-line routes are CBD and DCD. The
five 4-line routes are DB CD, DCBD, CBCD, CDCD, and CDBD. Each
of these routes is subject to a number of variations in the actual lines used, and
for a journey of a given number of lines there is always the same number of
variations, whatever the actual route. A 7-line journey is not possible.
- A CAR TOUR
The number of different routes is 264. It is quite a difficult puzzle, and con-
sideration of space does not admit of my showing the best method of making
the count.- MRS. SIMPER'S HOLIDAY TOUR
There are sixty different routes by which Mrs. Simper, starting from H,
might visit every one of the towns once, and once only, by the roads shown,
and return to H, counting reversals of routes as different. But if the lady is to
avoid going through the tunnels between Nand 0, and Sand R, it will be
found that she is restricted to eight different routes.
If the reader is sufficiently interested he may wish to discover these eight
routes for himself. If he does so, he will find that the route that complies with
the conditions, avoids the two tunnels, and delays her visit to D as long as
possible, is as follows: HISTLKBCMNUQRGFPODEAH. This is, therefore,
undoubtedly her best route.