148. A locomotive is on the main line of railway; the trucks marked
1 and 2 are on sidings which meet at the points, where there is room
for one truck only and not for the locomotive. It is desired to
reverse the position of the trucks--that is, put 1 where 2 is, and
2 where 1 is, and yet leave the locomotive free on the main line.
This must be done by means of the locomotive only, either pulling
or pushing the trucks--it may be between them, thus pulling one and
pushing the other--but no truck must move without the locomotive.
[Illustration]
In working this puzzle out, it would be best to draw the diagram
on an enlarged scale, and have articles to represent the trucks and
locomotive.
149. In a public square there is a fountain containing a quantity
of water; around it stand a group of people with pitchers and
buckets. They draw water at the following rate: The first draws
100 quarts and one-thirteenth of the remainder, the second 200 quarts
and one-thirteenth of the remainder, the third 300 quarts and
one-thirteenth, and so on, until the fountain was emptied. How many
quarts were there in the fountain?