Sunday Puzzle 07/12

[GREENcar]

A hint for anyone still working on this: What would your approach be if the people took, say, 1,2 99 and 100 minutes?
What I’m interested in is if anyone can find a general rule for the best way to get across (you can win glory, honour, fame and all that stuff)

[GREENcar]

I’m not going to post the solution here, but a clue to everyone: the answer seems counter-intuitive. (As a hint – think about what you would do if Person 1 took 1 minute, Person 2 took 2 minutes, Person 3 took 99 minutes and Person 4 took 100 minutes).
What I actually wanted to ask is whether anyone can come up with a general rule for the best strategy with four people (or more!) crossing the bridge.
Best one gains fame, honour, glory and all that.

[Crackerjack_404]

@GREENcar

Assuming everyone walks at the pace of the slowest person, you’d want the two fastest to act as shuttlers and the two slowest to only cross once, together. The huge time gap between the 1,2 min pair and the 99,100 pair does make the optimal strategy more intuitive here, and probably more pronounced with even larger group

Here are some of my other proposals: assume the fastest person can just carry everyone else on their back and then they can sprint across the bridge. Or assume Schrödinger’s principle applies and if we don’t observe them crossing, they’re both on and not on the other side, so the problem becomes trivial… Or if you’re in Middle Earth and everything else fails, just summon the eagles.

Before I come up with more silly ways, I think the general way to solve this is done quite well by modelling it as a graph and then applying a shortest path algorithm.

[Author]

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