Getting the family across on one raft

Question

A family must cross a river using a small raft. The raft carries a load of at most 100 kg per trip, and it needs at least one person aboard to paddle it (it can't drift back empty).

The two adults weigh 100 kg each, and the two children weigh 50 kg each. So an adult can only ride alone, while the two children can ride together (50 + 50 = 100), or a single child can ride alone.

What sequence of trips gets all four across, and how many one-way crossings does it take?

Accepted Answer

The bottleneck is that each adult must cross by themselves, which means a child has to keep ferrying the raft back. The trick is to use the two children as the "shuttle service." Here is a working schedule (N = near bank, F = far bank). It takes 9 one-way crossings: 1. Both children cross together → they're on F. 2. One child paddles back → one child on F, one on N. 3. An adult crosses alone → that adult on F. 4. The child waiting on F paddles back → both children on N, one adult on F. 5. Both children cross together → both children on F, one adult on F. 6. One child paddles back. 7. The seco…

Getting the family across on one raft

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