There are 8 people that need to cross a river. The water is too deep and fast to walk or swim across, and the only transportation device available is a raft. The raft can only be operated by adults, cannot float across the river on its own, and can carry at most two people.
The 8 people are a juvenile delinquent, her jailer, and a dysfunctional family of six: mother, father, two sons, and two daughters. To be clear, the only adults are the jailer, the mother, and the father.
Unfortunately some people fight with each other:
The juvenile delinquent will fight with anybody if her jailer is not present.
The father fights with either daughter if the mother is not present to mediate.
The mother fights with either son if the father is not present to mediate.
How can these 8 people cross the river without any fights? How many trips on the raft did it take?
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In order to advance to the other side of the water, we have to transport the people in specific groups that "get along." These would be the jailer and delinquent, dad and 2 sons, and mom and 2 daughters. Since dad and mom cannot leave initially without the other fighting with the children, we have to start with:
1) Jailer and delinquent cross
With the raft on the other shore, we only have one viable choice to pilot the craft:
2) Jailer back (why the delinquent doesn't leave is beyond me, but I digress)
Now, back on shore, we can take any of the three adults again, but we still have conflict between a single parent and the children. But, the jailer can pilot one of the children across without problems, so we will choose one of the boys.
3) Jailer and boy cross
We again can only choose the jailer to pilot back, but we cannot leave the boy with the delinquent, so the delinquent must go back with the jailer.
4) Jailer and delinquent back
Now, with one of the sons on the opposite shore, the father and remaining son can cross without any conflicts.
5) Father and son cross
The father, as the only adult, must return.
6) Father back
Now, father cannot take the girls, the jailer could take the delinquent, but not be able to leave, and the mother would be walking into a fight alone with one of the girls. The only choice would be to take mom and dad at the same time.
7) Mother and father cross
We will leave the father with his sons and mother will return.
8) Mother back
When I originally did this, I was stuck as to who to move back to the other shore, since mom could take a daughter, but the children would start to fight with their respective parents. Looking at it, I noticed that by moving the jailer and the delinquent, I would create a mirror image of the two shores.
9) Jailer and delinquent cross
From here, I just reversed the steps using the mother and daughters
10) Father back
11) Mother and father cross
12) Mother back
13) Mother and daughter cross
14) Jailer and delinquent back
15) Jailer and daughter cross
16) Jailer back
17) Jailer and delinquent cross
So, the entire trip took 17 one-way trips for the eight people to cross. This isn't too bad, considering that if everyone got along with each other, it would still take 13 trips to transport 3 adults and 5 children across the river.
Solution
