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You are given a 2 dimensional world map of all the countries (it can not be on a sphere), dated in the 21st century (no dinosaur map allowed!), large enough so that a human can distinguish France and Switzerland.

You must draw segments such that all countries have exactly one segment on it. How many segments do you need at minimum?

A trivial non optimal answer is one segment per country!

But for sure, you can use one segment to touch France, Switzerland, Italy and more.

Here is an example of allowed map:

world map from Wikipedia

EDIT, improvement thanks to @Tim Seifert, the type of map you are using must exist and be defined in Wikipedia to avoid that you use a custom map where all countries are aligned :)

EDIT2, improvement thanks to @Ben A. and @bobble, whenever you have a doubt about some part of the map to be a country or not (for instance you could have a doubt about Taiwan but for France, I don't think there is any doubts), you can choose to discard it and avoid putting a segment on it. Or you can consider it to be a country, that is up to you and the former will result in a smaller number of segments. A possible suggestion is to use the list of the 193 member states of the United Nations.

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    $\begingroup$ What is a "segment"? An arc of a great circle? Or should that depend on the map projection we're using? $\endgroup$ Commented Jun 18 at 15:11
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    $\begingroup$ " EDIT, improvement thanks to @Tim Seifert, the type of map you are using must exist and be defined in Wikipedia to avoid that you use a custom map where all countries are aligned :)" I did not think of that possibility, thanks for helping me improve the puzzle! $\endgroup$ Commented Jun 18 at 15:23
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    $\begingroup$ What is a country? $\endgroup$ Commented Jun 18 at 18:49
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    $\begingroup$ @BenA.'s question is very important. Defining a "country" is not for the faint of heart (link leads to YouTube), and will very quickly run into geopolitical messes. For example: Taiwan. $\endgroup$ Commented Jun 18 at 19:14
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    $\begingroup$ In order to make the puzzle clear and concise, you should provide a specific map to use and identify every region considered to be a country for the purpose of this puzzle. $\endgroup$ Commented Jun 19 at 19:38

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You just need one really wide line segment. There didn't seem to be any restrictions on that! enter image description here It touches all exactly once.

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    $\begingroup$ A line segment has no width. $\endgroup$ Commented Jun 18 at 18:38
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    $\begingroup$ Worth a shot given how much is left unrestricted, but I agree $\endgroup$ Commented Jun 18 at 18:40
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    $\begingroup$ Nice try and agree with Daniel Mathias' comment :) $\endgroup$ Commented Jun 19 at 5:35
  • $\begingroup$ There is a restriction. "Countries have exactly one segment on it." DV for ignoring that restriction. $\endgroup$ Commented Jun 19 at 18:51
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    $\begingroup$ A joke answer to a poorly defined question isn't an answer, at best a comment to illustrate it. Quite plainly, your thick line touches Antarctica twice. $\endgroup$ Commented Jun 19 at 19:24

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