Tuesday, December 9, 2014

Drama Galore!

It was a beautiful day, perfect for a stroll. After leaving the cars at the edge of the woods, four couples moved towards the river, reaching its bank after a two-mile walk. The restaurant where they intended to dine was on the other side, partially hidden by trees.

But even on a perfectly planned day, evil could come and spoil it. During the stroll, Albert quietly told Amanda that she shouldn't have dressed quite so promiscuously, whilst she replied that he could have done a better job in refraining from making his oh-so-kind compliments to the other three girls. Bernard whispered menacing words at Barbara The Easy Flirt (as he called her then), and Barbara told him that his relationship with the other girls was of dubious morality. Simillar sorts of exchanges happened between Charles and Corinna, and between Douglas and, err, Diana. Reaching the river and seeing the flowing water did little to tame the souls. On the contrary, when the eight friends noticed that instead of the large boat that would carry them all over to the opposite bank, there was only a little boat that would carry no more than two persons at once, the irritation grew to the point that everybody started arguing with everybody else.

The river was about one hundred yards wide, with a small island in the middle. None of the four men were keen on leaving his girlfriend alone with one or more of his other male friends. On the other hand, the women found out that they could only agree on one point: none of their boyfriends should be alone on the boat when one of the girls, excluding his girlfriend, was all alone on any of the two banks or on the island.

Once the tempers calmed, Bernard and Douglas forumlated a plan involving many trips.

How many trips would it take to ferry everyone across whilst still adhering to the wishes of all the people?

 

Notes:
  • In case you haven't guessed, the couples are, Albert and Amanda, Bernard and Barbara, Charles and Corinna, and Douglas and Diana.
  • No woman should stay on one of the banks, on the island, or on the boat, in the company of one or more other men and without her boyfriend
  • No man should be alone on the boat when one of the girls, except his girlfriend, was all alone on one of the two banks or on the island

Drama Galore Puzzle Solution

They needed seventeen trips, frenquently using the island in the middle of the river as temporary destination. If we denote the names of the men with their initial in upper case, and the names of the women with their initial in lower case (by complete chance, the initials of the men are the same as the initials of their girlfriends), we would get the following table:
Trip # Departure bank Direction Island Direction Arrival bank
1 ABCDcd -
=>
ab
2 ABCDbcd
<=
- a
3 ABCDd
=>
bc a
4 ABCDcd
<=
b a
5 CDcd b
=>
ABa
6 BCDcd
<=
b Aa
7 BCD
=>
bcd Aa
8 BCDd
<=
bc Aa
9 Dd bc
=>
ABCa
10 Dd abc
<=
ABC
11 Dd b
=>
ABCac
12 BDd
<=
b ACac
13 d b
=>
ABCDac
14 d bc
<=
ABCDa
15 d -
=>
ABCDabc
16 cd
<=
- ABCDab
17 - -
=>
ABCDabcd