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This puzzle is an attempt of improvement to my previous closed and poorly described puzzle.

You are given the following map of Europe:

enter image description here

And the following list of 50 Europe countries:

  1. Albania
  2. Andorra
  3. Armenia
  4. Austria
  5. Azerbaijan
  6. Belarus
  7. Belgium
  8. Bosnia and Herzegovina
  9. Bulgaria
  10. Croatia
  11. Cyprus
  12. Czechia
  13. Denmark
  14. Estonia
  15. Finland
  16. France
  17. Georgia
  18. Germany
  19. Greece
  20. Hungary
  21. Iceland
  22. Ireland
  23. Italy
  24. Kazakhstan
  25. Latvia
  26. Liechtenstein
  27. Lithuania
  28. Luxembourg
  29. Malta
  30. Moldova
  31. Monaco
  32. Montenegro
  33. Netherlands
  34. North Macedonia
  35. Norway
  36. Poland
  37. Portugal
  38. Romania
  39. Russia
  40. San Marino
  41. Serbia
  42. Slovakia
  43. Slovenia
  44. Spain
  45. Sweden
  46. Switzerland
  47. Turkey
  48. Ukraine
  49. United Kingdom
  50. Vatican City

Using the above map, you must place line segments such that all 50 countries have exactly one segment on it. It is fine if the same line segment leaves and reenters the same country.

How many segments do you need at minimum? A trivial non-optimized answer is 50 segments, one per country! However, you can use one segment to touch France, Switzerland, Italy and more.

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    $\begingroup$ Perhaps explicitly clarify that a line segment has no width, to avoid a repeat joke answer? $\endgroup$ Commented Jun 20, 2025 at 1:45
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    $\begingroup$ Can I just say - well done for taking on board the user feedback on your previous attempt, putting it into action, and producing a much-improved puzzle as a result. This is an excellent reaction to receiving criticism (constructive or otherwise). An attitude of creative persistence like this is great to see :) $\endgroup$ Commented Jun 20, 2025 at 14:29
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    $\begingroup$ What is a line segment on a round Earth? A great circular arc? Can you go the long way around with a majot arc? $\endgroup$ Commented Jun 20, 2025 at 15:25
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    $\begingroup$ @Cheshire_the_Maomao Common sense says it's Asian, but some parts of western Kazakhstan are geographically in Europe (as opposed to Armenia and Cyprus, completely in Asia geographically) and it tries to align itself with Europe to some degree (at least some Kazakh sports teams compete in Europe, for example). $\endgroup$ Commented Jun 25, 2025 at 6:25
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    $\begingroup$ @Stiv, you made me smile :D $\endgroup$ Commented Jul 1, 2025 at 2:16

3 Answers 3

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10
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I believe I have a solution with 9: enter image description here Projection dependent and may be cheating slightly on the microstates around Italy. Kosovo is included despite technically not being required by the question.

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    $\begingroup$ Nice remark about projections skewing the result. Though it is not relevant in this puzzle since the map is provided. $\endgroup$ Commented Jun 20, 2025 at 14:46
10
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10 is possible:enter image description here

Now I'm not so sure if $\le 9$ is possible.

Old post for storage purposes: 15 is certainly possible (note Kaliningrad is part of Russia) -- enter image description here 14 lines are drawn above. I forgot Cyprus, hence the 15.

However, I believe that it is possible to get $\le 9$.

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  • $\begingroup$ I believe not San Marino, Vatican and Malta can form a straight line. The square box is much larger than its real land. $\endgroup$ Commented Jun 25, 2025 at 6:12
6
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EDIT: This answer is incorrect - I have missed Liechtenstein.

I believe I have a solution with

8 line segments. Please verify that I included all the requires locations. Include Malta on the Italy, Vatican, San Marino line as other solutions have done.

Please ignore the red lines, I wrote a little utility to help with drawing lines and their intersections before realizing that countries couldn't be hit more than once (optimal number allowing overlap is 6) Original map colored in with the line segments on top

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  • $\begingroup$ You missed Malta, but that can be fixed by adjusting one line to match that used in the other solutions (though I don't think that line really works). $\endgroup$ Commented Jun 20, 2025 at 18:11
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    $\begingroup$ +1 for the solution. You can fix the Malta issue by adjusting the line through Portugal and Spain to cross it $\endgroup$ Commented Jun 20, 2025 at 20:04
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    $\begingroup$ @WilhelmLaibach not without sacrificing Andorra. $\endgroup$ Commented Jun 20, 2025 at 21:02
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    $\begingroup$ I'm missing Liechtenstein? $\endgroup$ Commented Jun 20, 2025 at 23:36
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    $\begingroup$ I've reviewed the comments and updated my answer to reflect that it is not correct. I will post a new answer if I'm able to find a valid solution with either eight lines or with nine lines but no fudging on San Marino, Vatican, and Malta. $\endgroup$ Commented Jun 23, 2025 at 16:50

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