Mathematical_Recreations-Kraitchik-2e

Mathematical Recreations
fering interpretations of what constitutes a trip. The solution
above assumes that a trip is a crossing between the
island and either bank of the river. If a crossing from on€bank
to the other is a single trip, the number of trips is
reduced, though the distance traveled is the same.
Tarry has complicated the problem still further by supposing
the wives unable to manage the boat. In the solution
of this problem we assume that a trip includes a crossing
from bank to bank. Our first endeavor is to free two men
from their wives. This may be accomplished as follows:
Trip Bank Island Bank Trip Bank Island Bank
----- ---
- AaBb· .. - - 6 ACeDd Bb a
1 BbCc·· . - Aa 7 ADd··· BbCe a
2 ABbCc·· . - a 8 ABCDd··· be a
3 ACcDe·· . Bb a 9 CDd··· be AaB
4 ABCeDd·· . b a 10 BCDd··· be Aa
5 CeDd··· ABb a
Now Band C are free to row the other couples across. This
they can do in four trips for each couple. First B takes C to
the other bank and returns; then the couple rows over and
C brings back the boat. At the end of 10 + 4(n - 4) trips
just one couple are on the first bank with Band C and the
boat, band c are on the island, and the others are on the
second bank. The crossing can now be completed in the following
11 trips:
Trip Bank Island Bank
------
Trip Bank Island
----
Bank
I Dd be AaBCEe·· . 7 d e AaBbCDEe·· .
2 CDd be AaBEe·· . 8 d Ce AaBbDEe·· .
3 d be AaBCDEe·· . 9 d - AaBbCeDEe·· .
4 d BbCe AaDEe·· . 10 Dd - AaBbCcEe·· .
5 d Ce AaBbDEe·· . 11 - - Aa···
6 d CeD AaBbEe·· .