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Video Reflection

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* to the child where in trip 16 the child will cross the river to pick up the other child. Trip 17 both of the children will cross the river again together, one of them staying and one going back for trip 18. The child will then hand the boat to the last standing adult who will take the boat across for trip 19, give the boat to the child for trip 20, and the child will pick up the last child for the final trip, 21 and the two will make it across the river. Those will be some pretty tired children!

1. What if there were 4 adults and 6 children?

Again, I would solve this problem like I solved the rest of them. The first trip would be two children going across together. Trip 2 would be one child coming back, giving the boat to an adult for trip 3. Trip 4 would be the child coming back and picking up another child and trip 5 would be one child staying, and one child going back, giving the boat to an adult who for trip 6, will take the boat across the river. Trip 7 would be the child on the far side of the river coming back, picking up another child and trip 8 would be those two going across the river together. Trip 9 would be one of those children coming back, giving the boat to an adult, and letting the adult take it over for trip 10. Trip 11 would be that adult giving the boat back to the child and letting him take it back where he will pick up his friend for trip 12. Trip 13 the two kids will ride across the river together and trip 14 would be one of the children coming back alone. Trip 15 would be where the child gives the boat to an adult and lets the adult go across, give the boat back to the child and let the child take it back for trip 16. At this point in time we have 4 adults on the far side, and 6 children on the starting side with the boat. For trip 17 two kids will go over together, and trip 18 would be one of them staying and one of them taking the boat back. Trip 19 would be the child that came back picking up another child and bringing that child across. Trip 20 would be one of those children staying and one coming back. Trip 21 would be the child that came back would grab another child and take that child across and drop the child off. Trip 22 would be one of those children coming back. Trip 23 would be two more children going across, one staying, one coming back for trip 24. And trip 25, the last trip, would be the final two children going across the river.

5. The problem can be generalized only if the number of children is greater than or equal to two. Generalized problem is t=4a +2(c-2) + 1. T= number of trips, C= number of children, A = number of adults.
You get 4a because it takes four trips to get one adult over to the other side, and the boat back to where it started. Two children must go together first so there is one child on each side in order to get the adult across the river, and the boat back to where it started.
2(c-2) is because each child takes two trips, minus the last two children. Two children go over and one brings the boat back to the original side.
+1 is because the final two children only have to take one trip because they can cross the river together and they are finished with the trip.

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