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] here is a recent paper on this topic: https://arxiv.org/abs/1609.01582 - Cris
On May 19, 2017, at 12:29 PM, Dan Asimov <asimov@msri.org> wrote:
This reminds me of the very first rendezvous problem I heard, in a little book on probability by Frederick Mosteller (et al.?) from the 1960s:
----- You have agreed to a rare meeting in New York City with an old friend at a date and time both of you will have no trouble remembering. When the arrangement was made, however, the location of the was to be determined, and now that the date and time are upon you, you realize that a) no place was ever set for the meeting and b) you have no way of communicating with your friend now that you are both somewhere in New York City unbeknownst to the other.
Problem: What do you do to maximize the chance of meeting the other person at the appointed time? -----
—Dan ———— Note: Wording of problem is my own, as I don't know which book I saw it in.
On May 17, 2017, at 10:58 PM, Dave Dyer <ddyer@real-me.net> wrote:
My ultimate rendezvous problem:
You and your partner are located at separate locations somewhere in the milky way galaxy. You have a ship capable of acceleration to light speed in negligible subjective time, and a beacon that can be detected over any distance its light reaches.
Rendezvous for a victory drink before either of you dies of old age.
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