8 adults and 4 children need to cross a river in a small boat that can hold one adult or one or two children. How many one-way trips will it take for all of them to cross the river?
A) 37
B) 35
C) 12
D) 32
E) 16

Question

8 adults and 4 children need to cross a river in a small boat that can hold one adult or one or two children. How many one-way trips will it take for all of them to cross the river? ​
A) 37
B) 35
C) 12
D) 32
E) 16

Quizplus · Accepted Answer

For the adults, each requires a separate trip, so that's 8 trips. For the children, since the boat can hold two at a time, the 4 children can cross in 2 trips. However, after each trip with the children, the boat is on the opposite side of the river, so an adult (or a child, but using an adult is more efficient since they must cross anyway) must row back to bring the boat back, adding an additional trip for each crossing except the last one. Thus, for the children, it's 2 trips across and 1 trip back, totaling 3 trips for the children. Therefore, the total number of trips is 8 (for the adults) + 3 (for the children) = 11. However, this calculation misses the essential point that for every trip across the river, except the very last one, someone must return with the boat. This means every crossing effectively counts as two trips until the final crossing. So, the correct calculation should consider the return trips for the adults as well. Since there are 8 adults and they don't need to return, their trips are straightforward. But for the 2 trips to take the children across, there's an additional return trip after the first child crossing, making it 3 trips for the children. The mistake in the initial calculation is not accounting for the return trips correctly. The correct approach is to calculate the total number of crossings, including those necessary to bring the boat back. Given the error in the initial explanation and the options provided, none directly match the correct calculation methodology, suggesting a misunderstanding in the puzzle's constraints or a mistake in the calculation. The correct answer should account for all necessary crossings and returns, which isn't accurately reflected in the initial response.

8 Adults and 4 Children Need to Cross a River