There is a small island in the centre of a lake. The lake has two banana trees. The monkey wants to get all the bananas from the island and so he goes to the crocodile to ask for help. The crocodile says that for every one-way journey he needs one fish. But the monkey has only three fish and in order to get all the bananas out of the island he has to make two round trips. Will the monkey succeed in bringing all the bananas off the island? If yes, how?
Idea 1. Find a second crocodile willing to undercut the first croc's wage -- after all, 3 fish is better than no fish!
Idea 2. Trick the croc into signing a contract in which "one-way trip" is not specified by distance, but by traveling in a line of the croc's choosing from point A to point B. Tell the croc you want to go clean to the other side of the lake. The croc, hoping to minimize distance, goes through the middle of the lake (over the island), and you, the monkey, jump off the croc's back and grab a shipment of bananas, then hop back on the croc's back before it re-enters the water. This should be doable because you're a quick monkey. When you get to the far side, drop off a shipment of bananas and use your second one-way trip to go back to point A, grabbing the second shipment of bananas en route. Then walk back around to the far side of the lake on foot to reclaim your stashed bananas (you still have a fish left over this way)
Idea 3. Pay the croc to take you to the island. Get the bananas and pay the croc for a return trip. Drop them off and pay the croc to take you back once more. Get your bananas and then just don't pay the croc to take you back. Now the croc is stuck on this boring island and eventually it will leave of its own accord. Hop on its back when it does and get the free ride back to shore.
Idea 4. Convince the croc to loan you the labor, then once you have all the bananas, trade a few for the last fish.
Idea 5. Ditch the crocodile. Craft a raft and harnesses for the fish and let them drag you around the lake at random. When you're close enough to the shore, jump off and pull in the fish, grab the bananas, and keep doing that back and forth until you're done.
Idea 6. Promise the croc a 50% raise in exchange for it getting paid half upfront and half at the end. Give it your 3 fish upfront, collect all the bananas, and then climb a super tall tree where you say you have the rest of the croc's payment. Then tell the croc that you're not gonna throw it the 3 other fish. It gets super mad and starts climbing the tree. Right before it gets to you, swing on a vine back to the floor. The croc is now stuck in the tree, too high for it to drop down out of. While it tries to figure out how to get down, take the bananas and run.
We Need More Ideas:
Idea 7. When the croc gives you its demands, say "Eh, nevermind... but hey, you know what? I'm gonna loan you my favorite book!" Give the croc a philosophical, religious, or otherwise ethical text that promotes doing nice things for others without reward. The croc will see this as you doing a nice thing for it (loaning it your favorite book!) and its heart will be filled with warmth. It will now offer to give you the rides for free! (WARNING: do not read the book yourself, or you may end up deciding there are more important things in life than scamming for bananas.)
Idea 8. Convince the croc that your fish are each 4/3 the size of a regular fish, and that he's getting the same amount of fish by weight as if you gave him 4 regular fish.
Idea 9: Find some math trickery like Monty Hall and use it to gamble against the croc for free passage.
Idea 10: Tell the croc, "Well, I've only got three fish, but I caught them in like 5 seconds in a secret lake! After the first round trip I'll give you the longitude of the lake, and after the second I'll give you the latitude! And hey, I'll throw in these three fish for free!" Then make up some coordinates a few miles away.
Idea 11: Convince the croc that it's bad at counting and that you're actually holding four fish.
Idea 12: Try eating the fish, maybe you'll like them more than bananas.
Idea 13: Get 1 shipment of bananas back to shore by paying the croc 2 fish, then sacrifice one banana to get its seeds. Then go around to all your monkey friends with the seeds telling them they're magic seeds that will grow a magical banana orchard, and they only cost 1 fish apiece. Then whenever their orchards grow and they're not that magical, blame it on their irrigation or something. You only really need to get 1 monkey to fall for this, but if more do then you've got more bargaining power amongst the crocs.
Idea 14: When the croc proposes its deal, say "Whatever dude!" and hurl the first fish, as if in anger, to the island. The croc will frantically swim to the island to retrieve the fish, and you catch a ride (it won't mind since this is kind of what it asked for anyway). You do this three times, picking up a fish-shaped rock somewhere along the way. The final time, throw the rock back to shore. The croc won't examine it too closely because it's far away and it already expects a fish, so it will take you back. (WARNING: you might have some smooth-talking to do to make the croc not mad at you.)
Idea 15: Challenge the croc to a thumb-wrestling match for free passage vs. free fish.
Idea 16: Tell the croc you're a casting director and your movie needs a croc who's good at ferrying monkeys carrying bananas. Perform an impromptu audition, and then tell the croc that it'll hear from you soon.
Definitely Gonna Need a Few More
Idea 17: "Alright, here's fish #1-- oh wait, this is a PoisonHead fish, let me cut off the poisonous part for you. Here's fish #2, a PoisonMiddle fish, let me just take care of that... Here's fish #3, a PoisonTail fish (chop)... and WHAT'S THAT BEHIND YOU?! (krazy glue time) Oh nevermind, anyway, here's fish #4!"
Idea 18: Hide your 3 fish on the mainland, and put pieces of paper next to all of them. 2 scraps say "For your next clue, go to the banana island" and the last one says "Now, to find the great fish hoard, solve this puzzle:" and just write random letters. Write two more "clues" with the location of the second and third fish on them, and keep them in your hand. Tell the croc you found the start of what looks like a treasure hunt and take it to the first fish. It will see the note and take you to the banana island. While you're there, grab the bananas and drop the clue to the 2nd fish on the ground. Repeat the process. When you get to the third clue, you can be like "Well, it's been fun, but I gotta go" and leave the croc to puzzle over the impossible riddle!
Idea 19: Just a simple fish on a stick ploy.
Idea 20: Instead of giving the croc the fish to eat, release them in the pond and tell the croc "They will interbreed and this time next year the pond will be teeming with thousands of fish! So basically I gave you thousands of fish! Surely that's worth a few trips across the ol' lake!"
Idea 21: Introduce the croc to the concept of exercise.
Idea 22: Dare the croc. "Bet you can't carry me across FOUR times, twice laden with bananas!"
Idea 23: (WARNING: SOMEWHAT DANGEROUS & SLOW) Wait till the croc is sleeping. stand with one leg on either side of its torso and incredibly slowly ease yourself down onto it, so that you don't wake it up. When it wakes up, it will have no idea that it's carrying you, and will go about its day. Let the croc carry you around the pond and grab the bananas when the croc randomly passes by/climbs the banana tree.
Idea 24: Wait till you randomly find a crocodile tooth, and put it on a pendant around your neck. "This is all that's left of the last crocodile who tried to cross me!"
Idea 25: Pay for a ride to the island. Get all the bananas off the trees and put them in the water. They'll float (do bananas float? Probably) to shore, and you can splash them there to hasten this process. Then pay for a ride back.
Idea 26: If a banana floats then surely a heap of bananas + a monkey still floats. Just hold em all and paddle back to shore!
An obvious solution is...
The monkey needs to make trips that run tangential to the island. Since the island is in the centre of the lake, this is achievable. As the boat continues in the same direction, it is still a one-way journey, and the monkey can get all of the bananas with only two trips.
Alternatively, the monkey could just get more fish from the lake, but that's not really in the spirit of the question.
The question doesn't really clarify, but I'll assume that there is a bunch of bananas (meaning connected, not meaning many) on each tree. Or a single banana, but I'll go with bunches, because a monkey could easily handle two bananas, even on a crocodile's back.
The monkey spends one fish to get to the island (two remaining), and removes the bunch from each tree. Being a monkey and knowing that bananas float (due to his monkey recipes), the monkey throws one bunch into the water, away from the island. The crocodile is evidence that anything living in the lake will want to eat fish, so the bunch should be fine floating where it is.
The monkey spends another fish returning to the lake shore (one left) with his first bunch of bananas.
He then spends his last fish (none remaining), and instructs the crocodile to swim past the bobbing bananas straight to the opposite shore. Using monkey hands, feet, tooth, and tail, the monkey should be able to collect his second bunch on the trip across the lake.
Once on the shore again, the monkey circles the lake to his other bunch and happily leaves, while the crocodile begins to wish it were in a river instead.
This was based slightly on Glenn O.'s answer, but doesn't rely on the integrity of the crocodile to count one trip tangent to the island -with a break in the middle- as simply one trip. Since the third trip in my answer wouldn't require a stop, I think it would qualify as a valid single trip, payable by a single fish.
Here's an idea:
Crocodiles aren't limited to the water, so make the trip one that goes directly through the island to the other side of the lake. While the crocodile is crossing the island, collect the bananas from one tree. Get on the crocodile before it's finished crossing the island, then let it swim to the other side to complete the first trip. Repeat this going the other way. Voila, you've spent two fish to get the bananas from both trees!
What if crocodile is already on island while monkey being at edge of lake asking to crocodile? This way crocodile has to make only 3 meaningful journeys in respect to monkey.
1- Island to edge(1 banana, 1 fish)
2- Edge to island(1 fish)
3- island to edge(1 banana, 1 fish)
Here is my solution:
monkey is not on the Island, but the trees arent on the island, there are in the lake, as can read in the description. So the monkey is on one of those trees, but not in island. first monkey had to travel from tree to lakeside, which costvhim 1 fish. after he will do next trip to second tree from lakeside to tree and back, which cost him 2 fish, which is totally 3 fish.
Here is the answer:
! Monkey spends and fish and reaches the island, he collects all the bananas and comes back to crocodile!
SURPRISE!!! Crocodile met his old friend there and was talking to him.
Monkey convinces the second crocodile to travel along with him for a fish and carries 2 bundles back with the help of 2 crocodiles.
It's rather simple:
Go across on the crocodile, collect bananas, come back. Two fish and you're done.
But wait, how would that work?
It's in the wording of the question.
'But the monkey has only three fish and in order to get all the bananas out of the island he has to make two round trips.'
Clearly, the monkey could only carry half the bananas in one trip. But, with the help of the crocodile, he can haul all of them in one trip.