[103].—The Tube Railway.
There are 640 different routes. A general formula for puzzles of this kind is not practicable. We have obviously only to consider the variations of route between B and E. Here there are nine sections or "lines," but it is impossible for a train, under the conditions, to traverse more than seven of these lines in any route. In the following table by "directions" is meant the order of stations irrespective of "routes." Thus, the "direction" BCDE gives nine "routes," because there are three ways of getting from B to C, and three ways of getting from D to E. But the "direction" BDCE admits of no variation; therefore yields only one route.
| 2 | two-line | directions | of | 3 | routes | — | 6 |
| 1 | three-line | " | " | 1 | " | — | 1 |
| 1 | " | " | " | 9 | " | — | 9 |
| 2 | four-line | " | " | 6 | " | — | 12 |
| 2 | " | " | " | 18 | " | — | 36 |
| 6 | five-line | " | " | 6 | " | — | 36 |
| 2 | " | " | " | 18 | " | — | 36 |
| 2 | six-line | " | " | 36 | " | — | 72 |
| 12 | seven-line | " | " | 36 | " | — | 432 |
| —— | |||||||
| Total | 640 | ||||||
We thus see that there are just 640 different routes in all, which is the correct answer to the puzzle.
[104].—The Skipper and the Sea-Serpent.
Each of the three pieces was clearly three cables long. But Simon persisted in assuming that the cuts were made transversely, or across, and that therefore the complete length was nine cables. The skipper, however, explained (and the point is quite as veracious as the rest of his yarn) that his cuts were made longitudinally—straight from the tip of the nose to the tip of the tail! The complete length was therefore only three cables, the same as each piece. Simon was not asked the exact length of the serpent, but how long it must have been. It must have been at least three cables long, though it might have been (the skipper's statement apart) anything from that up to nine cables, according to the direction of the cuts.