Three Stars Across the River

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An interesting riddle over there at Popular Mechanics, a new reading on wolf, goat and cabbage classic.

Three movie stars, Chloe, Lexa, and Jon, are filming a movie in the Amazon. They’re very famous and very high-maintenance, so their agents are always with them. One day, after filming a scene deep in the rainforest, the three actors and their agents decide to head back to home base by foot. Suddenly, they come to a large river.

Three-stars-accross-the-river

On the riverbank, they find a small rowboat, but it’s only big enough to hold two of them at one time. The catch? None of the agents are comfortable leaving their movie star with any other agents if they’re not there as well. They don’t trust that the other agents won’t try to poach their star.

For example, Chloe’s agent is okay if Chloe and Lexa are alone in the boat or on one of the riverbanks, but definitely not okay if Lexa’s agent is also with them.

So, how can they all get across the river, in as few crossings as possible?

As you can guess, there is not a single solution to this problem; actually, it doesn't matter in which order stars or their agent arrive at the destination bank. Solution where Chloe and Jon arrive last to the destination bank is basically the same as solution where Chloe and Lexa arrive last, provided that the respective agents are on the proper bank - what matters are not actual names, but rules: at no point in time, one star can be anywhere beside agent of other two stars if her own agent is not there.

This leads to potentially disputable point; one proposed solution includes Chloe and her agent first crossing towards the far bank; Chloe then leaves her agent there, and rows back to the near bank of the river; in the third crossing, two remaining agents on the near side go to the distant bank. After that, things seem nice: we have all three stars on the near bank, and all three agents on the distant bank. The transfer proceeds with 6 more crossings untill everyone is safe on the other side, with total of 9 crossings.

But what I don't like here is switch between second and third crossing: Chloe jumps out of the boat and technically she is on the same bank with two agents of other stars, while her own agent is on the other side of the river... so, she violated basic presumption of the task!

I solved the riddle with 11 crossings without running into this issue. Can you solve it in less attempts? If you wish, comment below or reach me via contact form.

Ready to see the solution? Scroll further (please note, it is image; if you don't see it, check your AdBlock or browser settings; alternatively, you can access the image file here):

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Three-stars-accross-the-river

This solution actually incorporates a bit of thinking outside the box; attempting to minimize number of crossings, I initially always drove two persons, full boat, from the near bank to the destination, and always one person from distant bank to the near bank, it sounds logical - why would I ship two persons from one bank to another, and then again two persons back... but key is those two persons are different ones, hence it is required to maintain puzzle requirements.

In that regard, puzzle resembles me of another variation to that same problem:

In the middle of the night, four explorers carrying one single lamp are trying to escape the dragon they accidentally woke up in his den. Dragon is sleepy and cannot run fast, so they managed to make some advantage. But then, they arrive at the wooden bridge over the abyss that can sustain only two people at the time, and they need the lamp to cross it.

One of explorers is math professor, and he know very well his fellow explorers, so he knows they need 1 minute, 2 minutes and 5 minutes each to cross the bridge; professor himself is the slowest one, and it takes him 10 minutes to the other side of the abyss. Professor looks behind at the progress dragon is making, and to his horror, quickly calculates that dragon will reach them in 17 minutes.

Can they all pass the bridge on time, before the dragon gets there, so they can burn the bridge from the other side and get rid of their unwanted follower?

Hope you liked the movie stars puzzle; let me repeat the source, so you can check more interesting puzzles of different difficulty level: Popular Mechanics, and riddle author, @LauraFeiveson.

Check for more brainteasers!

Infinite Chocolate Bar

You have a chocolate bar, 6x4 squares in this example, you extract one square from the chocolate, you cut and rearrange remaining 23 chocolate squares, and, voila!, you magically again have all 24 squares at your disposal!

Click here to check if it is really possible

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