On Wed, Feb 17, 2016 at 11:29 AM, Seb Perez-D <sbprzd+mathfun@gmail.com> wrote:
I like the (somewhat well known) task of minimizing the time to cross a bridge in the dark, knowing that the bridge can only carry two persons, that there is only one flashlight needed, and that these 4 persons can cross the bridge in 1, 2, 5 and 10 minutes respectively. Hint: you can do better than 19 minutes.
This is an example of a phenomenon I find interesting, where are intuitions can lead us to slightly inferior solutions, but they won't lead us to extremely inferior solutions. I'll bet that many people, in trying to solve the above problem, came up with a 19 minute solution, and maybe had some difficulty finding the 17 minute solution. But try giving someone who hasn't solved the problem before a similar problem, where the crossing times are 1, 2, 1,000,000, and 1,000,003 minutes. Now people find it much easier to find the solution that takes 1 million-and-change minutes, rather than the one that takes 2 million-and-change. A similar thing happens with the Monty Hall problem. You can model the problem with 3 cards. One of which, the Ace of spades, represents the prize. We shuffle the 3 cards, you choose 1, but don't turn it up yet, and I take the other two, look at them, and turn one of them (never the Ace of Spaces) face up. Now I ask if you want to switch to the other face-down card, and many people see no reason to switch; they erroneously reason "2 cards, I don't know anything about either, so the chances are 1/2 that each is the Ace of Spades". But give people the 52-door version of the same problem and see what happens. They choose a card, and leave it face down. I look at the other 51 cards, pull out the 37th card, and turn up the other 50, none of which are the ace of spades, face up. Now pretty much everyone wants to switch to the 37th card. Most explanations I've seen as to why people get the Monty Hall problem wrong would predict that people would have just as much trouble getting the 52-card problem right as the 3 card problem, but in fact, lots of people get the 3-card problem wrong, and pretty much everyone gets the 52 card problem right. Andy Latto andy.latto@pobox.com