You are on an island, and must transport 3 moose across a strait to the mainland. While they can swim across the strait, they will likely end up running into the forest and leaving you behind. While you have a boat, it would be dangerous to try and transport multiple moose. The moose will be calm if they are all together, alone, or swimming, but will become violent if 2 are left together. A lone orca, seeing your plight, has come to help you by guiding a moose across the strait. However, the orca likely just wants to eat the moose, and so you don't want to let them be alone with the moose. So, what is the smallest number of crossings required to bring the moose to the mainland?
put one moose in my boat and have another swim across, guided by the orca. So each one is guided and will not get lost in the woods. They are 2 together now, but they are calm while swimming. And the orca is supervised.
leave the one guided by the orca on the opposite bank, maybe tie it to a tree so it doesn't run off, and take the one still in my boat with me back across the river.
have the still hungry orca hope for a second chance at a snack and let it guide the third moose over, while the first one rides for a third and final time in my boat, from where I can again keep a keen eye on the orca.
All three are on the other side, and it took us three trips across the river.
This is minimum because
you explicitly state that me and the orca can each guide only one at a time and an unguided moose will escape. So that means I can only get two across on the first trip. And I must return to get the third one, as if nothing else I must accompany it to protect it from the orca. No chance for any meeting half-way trickery, as the orca could very well be a lot faster than my boat if it doesn't have a moose to guide along.
Nitpicky as I am, I'd like to point out that just sticking to the question, I think the minimum number is actually
just one. The reason I don't get away with zero trips is that I have to guard the orca not to eat a moose while it's on its way. So I have the orca guide one moose over and I travel along to guard the orca. One moose can travel in my boat or swim, the third one swims. We all arrive at the same time, and I have brought all three moose over to the mainland as requested. - Afterwards, the third one might escape and the other two might attack each other. But by then, the request was already fulfilled.
This seemed far too easy. And since nobody else solved it, I probably missed something. However, I couldn't find where this solution contradicts the conditions.