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[doep] Daily (Intermittent) Open-Ended Puzzle: Dig a hole…

The following is an Order of Magnitude puzzle: Guess within an order of magnitude of the answer and you win! You win nothing!

If you were to start any spot on land on Earth and dig a hole through the center of the Earth, what percent of the time would you come out on another spot on land, as opposed to having water spray out, comically spinning the Earth out of orbit to its death? (To be precise, the question isn’t about water spraying or not spraying out of the hole. It’s about the percentage of times you’d hit land.)

(All of this came from a mailing list I’m not supposed to acknowledge. Answers authenticated by the good folks at Wikipedia.)

2 Responses to “[doep] Daily (Intermittent) Open-Ended Puzzle: Dig a hole…”

1. Well 2/3 of the earth’s surface is water. But this puzzle asks what percentage of land is directly opposite to other pieces of land. So if all land was directly opposite all other land, then 1/6 of the land would be opposite 1/6 of the land and you would tunnel through to land 100% of the time. It also could be that all 1/3 of land is always opposed by water. Both of these exact symmetries are possible but not likely. Since land is distributed upon the surface of the Earth unevenly, there is a higher likelihood that you would tunnel through to water. Yet I believe there is more land mass in the Northern Hemisphere and less in the Southern Hemisphere. So if you dug from the Southern Hemisphere you would have more of a chance of hitting land and less chance if you started from the Northern Hemisphere. My guess would be that you would come out on land 11% of the time.

2. The Wikipedia article on Antipodes has a clever map that makes it clear how poorly arranged the continents are for those who want land-to-land tunnels. http://en.wikipedia.org/wiki/Antipodes

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