Two geography math puzzles

Given: I’m in an East Coast (USA) state and you’re in a West Coast state. What are the odds that our clocks (correctly) show the same time? (You can assume randomness based on population or geographic area as you wish, either answer is OK).

Given: We are parachuted into random (dry land) locations on the Earth. What are the odds that to get from my country to your country I must cross at least four borders?

I’d like to post more but I think I am outpacing my commenters; the more you comment, the more new posts you’ll get. I hope they’ll be varied enough that everyone finds something they like, a polymath ought to be able to do that.

Added 11/8: Answers now in the comment section.

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2 Responses to Two geography math puzzles

  1. Answer to first puzzle:

    The only part of any East Coast state in the Central time zone is the westernmost 10 counties in the Florida panhandle, which have an area of 7548 square miles. The 14 East coast states have an area of 394,608 square miles so my chance of being in the Central Time Zone is 1.9128%.

    The only part of any West Coast state in the Mountain time zone is Malheur County in Oregon, which has an area of 9930 square miles. The 3 West coast states have an area of 333,377 square miles so your chance of being in the Mountain Time Zone is 2.9786%.

    These multiply to 0.05697% or about 1/1755, which, a couple of hours after I write this, will be the probability that our clocks are synchronized because the Central Time Zone will have gone off Daylight Savings time while the Mountain Time Zone will not have yet. But considering all times as equally likely, we have to divide by the number of hours in a year (8766 on average) to get the overall probablity of 0.000006499%, or about 1/15,400,000 .

    Answer to second puzzle: Naah, I’ll wait until someone posts a comment about it.

  2. Still no responses? OK. The only two “doubly landlocked” countries (countries which do not touch the sea or any countries which touch the sea) are Liechtenstein and Uzbekistan. These are 62 square miles and 172,700 square miles respectively, and the total land area of the world is 57.3 million square miles, so the probability I landed in Liechtenstein and you landed in Uzbekistan is (62*172,700)/(57,300,000*57,300,000) = 0.00000000326. Double this since you could have been the one who landed in Liechtenstein, and we get 0.00000000652 or a chance of about 1 in 153 million.

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