Mathematical_Recreations-Kraitchik-2e

Mathematical Recreations
is taken out, Hilary climbs in and descends, bringing up 80sthenes.
Both men get out and the box is sent down a second
time. Hilary gets in at the bottom, and Babylas descends,
bringing up both Hilary and the box. Hilary and Babylas
get out and the box is sent down a third time. This time
Sosthenes goes down as the box comes up. The box is lowered
a fourth time and Hilary goes down bringing Sosthenes
up. Sosthenes goes down bringing the box up, and the box
is lowered for the fifth and last time.
To get across the river, Sosthenes crosses first with his bag.
He leaves it and returns to bring Hilary's bag. On his return
from this trip Sosthenes is taken across by Hilary, who returns
with his own bag. Hilary then takes Babylas over, and
makes two more round trips to get the two bags.
Perhaps it is easier to be honest.
Here is another variation of the fundamental problem.
Three citizens and three robbers are to get across a river in a
boat holding only two persons. How shall it be done so that
there are never more robbers than citizens together at any
time?
This problem differs from that of the jealous husbands only
in that no citizen shows any preference for any robber. For
we showed in the former case that it was necessary that the
women should not outnumber the men whenever they were
together. Hence any solution of the corresponding problem
of the jealous husbands yields a solution of this problem;
and all solutions of this problem can be obtained by permuting
the various robbers in the solutions obtained from the
first problem.
2. SHUNTING PROBLEMS
1. A railroad track and two spurs form a triangle as in
Figure 101. The portion of the track at C is just long enough
to accommodate one caboose, but it will not take a locomotive.