The 21st century solution to this problem is to contact the other person on your cell phone. -- Gene On Friday, May 19, 2017, 2:10:43 PM PDT, Allan Wechsler <acwacw@gmail.com> wrote:At this point, regarding the Mosteller problem, Dan's hint is something that I thought of for about ten seconds, and dismissed it because I was thinking of it as a math problem. Two people sitting separately, trying to decide what is the most salient point in NYC, didn't seem very mathematical to me. Isn't this Brent's "psychology problem"? I'm going to be very skeptical if it turns out that the answer is "Go to Times Square and wait.". Especially since finding somebody in Times Square isn't trivial! How many "most salient points" are there in NYC? All this does is reduce N, maybe by a lot, but not enough. I'm going to be *somewhere* at the moment specified; the chance that we have both picked the same somewhere is 1/N. On Fri, May 19, 2017 at 5:01 PM, Dan Asimov <asimov@msri.org> wrote:
I'd like to think about and even discuss this ultra-fascinating question — *without* knowing the answer (or hints) — with others in the same boat.
So, would it be OK if anyone posting a spoiler about this adds the word
SPOILER
to the subject line? If that wouldn't screw up threading or anything too badly.
—Dan
On May 19, 2017, at 1:36 PM, Cris Moore <moore@santafe.edu> wrote:
There is a variant where you have agreed to meet a friend in Vienna, at the Cafe Mozart. You arrive in the city, and find to your horror that there are N cafes called Cafe Mozart. Each day, you and your friend each go to one of these cafes at noon, hoping to see each other. How can you minimize the expected number of days before you meet?
This problem is fairly easy if you and your friend agree on your roles in advance. For instance, one of you can go to the same cafe every day, while the other goes through all N in random order, then the expected time is N/2.
It gets more interesting if you don’t have such a prior agreement, so that you and your friend have to follow the same randomized strategy. In that symmetric case, can you achieve an average less than N?
[Spoiler]
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