# Crossing The River (Humans And Monsters Puzzle With A Twist)

3 couples on one side of a river. Aa Bb Cc (caps representing husbands, lowercase representing wives)

One boat in which 2 people can travel at a time.

At least one person must row the boat wherever it needs to be taken. The boat cannot travel to any side by water current.

People can travel with someone of the other gender only if they are their spouse. No man or woman can travel with someone they are not married with. (This is what makes this puzzle different from $n$ couples crossing a river)

No woman can be left on a side with another man unless her husband is also present there.

What is the method for all of them crossing the river?

• You say "No woman can be left on a side with another man". What if there's a brief stopover? Like what if a is on the far side alone, B and b row over, then B comes right back. Is that prohibited? – Duncan Mar 4 '16 at 22:52
• Yes. It is prohibited. – Youstay Igo Mar 4 '16 at 22:54
• I'm not seeing how it's different from the linked question. Can you give an example of something prohibited in this problem that is allowed in the other one? – f'' Mar 4 '16 at 23:05
• Not allowing the travelling part. And not allowing any person to move to the other bank with opposite gender person(s) even for a touchdown. – Youstay Igo Mar 4 '16 at 23:16
• Wife not travelling with anyone of the other gender but your spouse is part of the original - this is basically the same puzzle except that asked for the formula (but many answers show the pattern as well). Unless you can point to some part that people are miss-understanding. – LinkBerest Mar 5 '16 at 0:10

Here goes:

Aa cross over. A crosses back.
Departure side: A, Bb, Cc
Destination side: a

Next, bc row over, c rows back alone.
Departure side: A, B, Cc
Destination side: ab

AB row over together, Bb row back.
Departure side: Bb, Cc
Destination side: Aa

Now the two men head over. BC to destination. Send a back.
Departure side: abc
Destination side: ABC

Now it's simple. ab over, a back, then ac over and done!

I'll solve it.

DESTINATION SOURCE
$[-,-,-,-,-,-]$ $\leftarrow (a,b)$ $[A,a,B,b,C,c]$

$[a,b,-,-,-,-]$ $\rightarrow (b)$ $[A,B,C,c,-,-]$

$[a,-,-,-,-,-]$ $\leftarrow (b,c)$ $[A,a,B,b,C,-]$

$[a,b,c,-,-,-]$ $\rightarrow (c)$ $[A,B,C,-,-,-]$

$[a,b,-,-,-,-]$ $\leftarrow (A,B)$ $[A,B,C,c,-,-]$

$[a,A,b,B]$ $\rightarrow (a,A)$ $[C,c,-,-,-,-]$

$[b,B,-,-,-,-]$ $\leftarrow (A,C)$ $[C,c,A,a,-,-]$

$[A,C,B,b]$ $\rightarrow (b)$ $[a,c,-,-,-,-]$

$[A,B,C,-,-,-]$ $\leftarrow (b,c)$ $[a,b,c,-,-,-]$

$[A,B,b,C,c,-,-]$ $\rightarrow (b)$ $[a,-,-,-,-,-]$

$[A,B,C,c,-,-]$ $\leftarrow (b,a)$ $[a,b,-,-,-,-]$

$[A,a,B,b,C,c]$ $[-,-,-,-,-,-]$

$11$ Trips total.
$6$ forwards.
$5$ backwards.