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You are given the next list of 48 flags.

enter image description here

  • For each pair of flags that are side by side, you score 1 point per color they share as a frontier. For instance France and Finland score 1 point thanks to the blue.

enter image description hereenter image description here

  • We don't require the exact same blues, or same colors here. Common sense will be requested for you to tell this is approximately the same color. I won't accept white of France is same color as yellow of Vatican :)

  • Some other examples are Croatia and Denmark score 2 points, while Spain and Norway score 1.

  • Greece and Austria don't score points because they are not neighbors.

Your aim is to find an optimal 6x8 arrangement of those flags to maximize the score. The current score of the above image is 46+28=74 as shown below.

Please look at edit at the end of the puzzle :)

enter image description here

  • You must provide a representation of the arrangement like in the puzzle so we can see your solutions. Only solutions with a visual image should be ticked :)

  • You can use other images of the flags if you prefer as long as it's the same 48 flags. For instance, this Wikipedia page seems perfect.

  • When you are doubting whether two colors are the same, this means they are close enough and you can use them as the same. If you have no doubt, example red and blue totally different, then they are different!

EDIT thanks to a comment now deleted: The flag of North Macedonia is wrong in the picture so it should be a score of two and this is the flag you should use:

enter image description here

EDIT thanks to @oAlt, another good example is Greece and Hungary score 2 points because there are two different segments where white is shared.

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  • $\begingroup$ Is there a standard version of the flags (say, accurate up to pixel level)? Some combinations seem to be really tricky to tell the score (with bare eyes). Also it might be useful to give a list of "standard colors", such as yellow, red, blue, green, white, etc., so that one knows which colors should be considered identical. $\endgroup$ – WhatsUp Nov 5 '20 at 21:25
  • $\begingroup$ For example, is purple considered as a separate color? Some of the purple (e.g. in Croatia) looks closer to black, while some others look closer to blue, and many seem to be in-between. $\endgroup$ – WhatsUp Nov 5 '20 at 21:33
  • $\begingroup$ @WhatsUp, many thanks for your comments, I have added this wikipedia link in my puzzle en.wikipedia.org/wiki/Flags_of_Europe and I also wrote that if you doubt between two colors, don't doubt anymore and use them to greater your score! If you don't doubt, two very different colors, then it is all set :) $\endgroup$ – JKHA Nov 5 '20 at 21:37
  • $\begingroup$ Hello, just want to clarify something: so basically, the only colors that matter here are those nearest to the borders of a flag? $\endgroup$ – oAlt Nov 6 '20 at 1:08
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    $\begingroup$ @oAlt, Greece and Hungary score 2 points because there are two different segments where white is shared :) I think it's good we keep these comments for next readers :) $\endgroup$ – JKHA Nov 6 '20 at 11:08
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I suspect this question can only be definitively answered with some clever programming, but here's a slight improvement using just manual placement of flags:


enter image description here

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  • $\begingroup$ That's great! I also believe that because the combinatorics are very big and I also think it's unlikely to find an optimal solution by hand! $\endgroup$ – JKHA Nov 11 '20 at 17:40
  • $\begingroup$ See update about North Macedonia. $\endgroup$ – RobPratt Nov 15 '20 at 14:50
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...would you mind if I gave a score of...

125? enter image description here The numbers indicate sums (rows, columns, or neighboring cells.) Colors on the right side of the screen are accepted colors for this puzzle. This is attempt #1 by the way.

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  • $\begingroup$ BTW, there are a few "barely" parts, like F5-G5 as 4 instead of 3. $\endgroup$ – Player1456 Nov 10 '20 at 10:36
  • $\begingroup$ That's great! I think your Andorra is 7 instead of 8? $\endgroup$ – JKHA Nov 10 '20 at 13:12
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    $\begingroup$ There's another pixel-perfect part. (Andorra-Czechia, bottom-left pixel) $\endgroup$ – Player1456 Nov 11 '20 at 0:00

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