A frugal canal-crossing

Question

You've been sent out to round up some escaped animals. While you have some of them under control now, you've ended up trapped on the wrong side of a canal. Currently, you have 5 animals:

• A perivine, a large leafy snail that's harmless to other animals
• An aras, a small flute-horned antelope that eats leafy things like the perivine
• A water-leaper, a winged frog that loves to eat meat, especially bovids like the aras
• A gooseface, a human head with many goose heads attached. They like to attack aquatic animals like the water-leaper
• A serpard, a long-necked lion that eats human flesh. While tame enough, it will eat part-humans, such as goosefaces

While they're calm enough now, they won't be if you wander off and leave them alone. Hopefully they'll also be fine if you keep predators and prey away from each other.

While considering what to do, a trader floats up the canal, and offers to sell you a boat. She has 5 types:

• A small row-raft for £50, which can carry you and 1 passenger
• A larger row-raft for £150, which can carry you and 2 passengers
• A sail-raft for £200, which can carry you and 3 passengers
• A large canoe for £280, which can carry you and 4 passengers
• A powered boat for £500, which can carry you and 5 passengers

You could buy any one of them if she takes credit, but you don't want to overspend.

What is the cheapest boat that could get you and the animals across the river, without losing any of the animals?

Answer 1

The five-passenger boat is obviously possible, as you can simply bring every animal in one trip.

The four-passenger boat is

also possible. Take any four animals, leaving one behind. Then take three back, and return to pick up the final animal. This will only leave one animal alone, which will not result in any harm.

The three-passenger boat is

also possible. If you take the perivine, water-leaper, and serpard, you can take them over, leave them unattended, and return for the aras and gooseface, as none of them will attack the others.

The two-passenger boat is

also possible. Take the aras and gooseface over first; they can be left alone, as can the other three animals. Then, bring over the perivine and serpard, and return with the aras and gooseface. If you then bring over just the water-leaper, you can leave it alone with the perivine and serpard and return to pick up the aras and gooseface.

The one-passenger boat is

not possible, as the chain is too large to break up without removing at least two animals.

Thus, the least expensive option is

the £150 two-passenger boat. Unless you consider that time is money, but that's left as an exercise for the reader...