# Math Help - River Crosser

1. ## River Crosser

We got 6 couples: Aa Bb Cc Dd Ee Ff (Capitals = husbands).
They're all on one side of a river, and want to cross over.

The guys are terribly jealous and insist on always having
their wives by their sides; so a wife is always with her
husband, on either side of the river or in the boat, if
there is another guy around.

EXCEPTION to above:
F hates his wife and doesn't care which guy(s) she's with;
they really can't stand each other and don't want to be
in boat at same time, or on river banks while boat crosses.
F : I hate your guts, f !
f : I shudda listened to mudder and never marry ya, ya jerk !!
(You may wish to know that during my research for this
puzzle, I found out that F doubled the life insurance on f).

They have one boat; it's capacity is up to 3 persons.

A special boating license to drive boat is required;
only one of the husbands has one; sorry, forgot which husband.

Of the wives, only f has one: she just finished the boating
course and has been issued a temporary license:
good for 4 one-way crossings ONLY.

So, when boat is crossing, f and/or that licenced husband
must be in the boat.

What is the minimum number of one-way trips required to get
everybody across ?

2. The mystery upper case licence holder turned out to be E. The order could be easily rearanged were it some other letter.

Presumably there are no rules about who can be with who on the first shore as many would be violated from the start.

Trips:

fAa
f
fBb
f
EC
E
Ec
E
ED
E
Ed
E
Ee
E
EF
E
Ef

It's probbably quite long at 17 trips but it's a start.

There 12 letters and a 3 letter boat, somone has to drive the boat back each time so possibly there should be no solutions in less than 11 trips.

3. Quite a few illegals in your 17 trips; here's 2:
fAa
f
fBb
f
EC : no, wives e and c are left with D and F
E
Ec : no, C won't allow his wife alone with E
E
ED
E
Ed
E
Ee
E
EF
E
Ef

4. Oh yeah. Sorry about that.

5. Well, here's solution (before I lose it!):
Code:
     START SIDE     BOAT       OTHER SIDE
0) AaBbCcDdEeFf
1)   BbCcDdEeF      Aaf       Aa         f
2) A BbCcDdEeF      A          a         f
3)     CcDdEeF      ABb       AaBb       f
4)     CcDdEeFf     f         AaBb
5)       DdEeF      fCc       AaBbCc     f
6)       DdEeFf     f         AaBbCc
7)         EeF      fDd       AaBbCcDd   f
8) Aa      EeFf     Aaf         BbCcDd
9)  a       e f     AEF       A BbCcDdE F
10) Aa      Ee f     AE          BbCcDd  F
11)  a         f     AEe       A BbCcDdEeF
12) Aa         f     A           BbCcDdEeF
13)                  Aaf       AaBbCcDdEeFf