31

We are looking for 4 categories.

32 different flags

Other (independently solvable) puzzles of this type: 2, 3, 4, 5, 6, 7, 8, 9, 10.

sarsaparilla
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    Some of those definitely aren't real flags :-D – Rand al'Thor Feb 05 '20 at 09:32
  • Is the space after the first column of flags intended? – Edivad Feb 05 '20 at 09:41
  • The premise is a bit vague >.> are we supposed to identify different vexillological characteristics? – Adib Feb 05 '20 at 10:09
  • @Evidad Yes it is. – sarsaparilla Feb 05 '20 at 10:23
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    @Adib I guess part of the puzzle is finding out exactly what to do to solve it (although I have included a hint). – sarsaparilla Feb 05 '20 at 10:26
  • I'm pretty sure I know how to solve this puzzle (at least the first step of it), but I don't have any proper to do that for now... – athin Feb 05 '20 at 13:02
  • @athin Any proper? – Rand al'Thor Feb 05 '20 at 13:06
  • @Randal'Thor rot13(V'z fher jr unir gb KBE gur svefg synt jvgu gur frpbaq "synt". Gur erfhyg vf n arj synt, naq guvf fubhyq or gura or KBE-rq jvgu gur arkg "synt", naq fb ba hagvy gur raq. V qba'g xabj ubj gb rnfvyl KBE gjb vzntrf jvgubhg pbqvat n cebtenz.. Lrg guvf znl or cbffvoyr gb or fbyirq znahnyyl ohg V'z abg tbbq jvgu pbhagel synt. Srry serr gb hfr guvf vqrn!) – athin Feb 05 '20 at 14:02
  • @athin I wasn't asking to get your idea, just pointing out the typo (wrong word?) in your comment :-P – Rand al'Thor Feb 05 '20 at 14:06
  • @Randal'Thor ah right, rip my english, "proper way" I mean >< – athin Feb 05 '20 at 14:15
  • @athin I have tried that, and while it may depend on something like that I don't think it is that simple. – Weather Vane Feb 05 '20 at 14:16
  • Is it important that the colours of the flags like UK and Belgium are not their actual colours? – LeppyR64 Feb 05 '20 at 15:57
  • @Randal'Thor Most decent image manipulation programs can do that - if you don't have e.g. Photoshop available, Paint.NET can do it, and that's free. Probably GIMP too, also free, though the UI has a bit more of a learning curve. – Darrel Hoffman Feb 05 '20 at 20:01

3 Answers3

21

The four groups of flags (and their connections) are as follows...

NB This was solved independently of @Adib's answer, but their working was very useful for corroborating with my own afterwards, as - before a couple of corrections thanks to @Jens in comments - we initially agreed on 86% of the flags (yes, I worked out the percentage!).

Note that in each case:

The OP has provided us with a starting flag in its usual colours. The 7 flag designs that follow it are then a sequence of pairwise mergings of 8 flags, the first of which is the given starting flag, and all of whose countries satisfy a certain theme. I don't profess to understand anything technical behind the merges but I assume like others suggest that there is some algebra going on with the RGB codes. (My key approach to solving was to note that where one merged flag contains white, the other flag's colour shows in the merged image; where both merged flags are white, the merged image shows black.)

Group 1:

Belgium, France, Russia, Croatia, England, Sweden, Uruguay, Brazil.

These are the quarter finalists at the men's football World Cup in 2018.

Group 2:

Mali, Ukraine, Poland, Hungary, Sudan, Iran, Niger, Algeria.

All of these countries border exactly 7 other nations. I shall not list them here, for brevity's sake, but note that Algeria's total includes the disputed territory of Western Sahara as one of the seven.

Group 3:

UK, India, Russia, France, Pakistan, North Korea, China, USA.

These are all countries known to have nuclear weapons.

Group 4:

Uzbekistan, Estonia, Honduras, Taiwan, Georgia, Faroe Islands, Tunisia, Japan.

Each of these nations have a capital city beginning with 'T'. These are (respectively): Tashkent, Tallinn, Tegucigalpa, Taipei, Tblisi, Tórshavn, Tunis and Tokyo.

Stiv
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  • France! Excellent observation! – Adib Feb 06 '20 at 08:27
  • @Adib That was a surprisingly tricky one! In my case I spotted the connection between the others first and that helped me pinpoint it as the missing one... – Stiv Feb 06 '20 at 08:34
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    If my understanding of the blending process is correct, the flag next to Mali is that of rot13(Hxenvar). – Jens Feb 06 '20 at 18:15
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    Also, it is not Palestine, but rot13(Fhqna). – Jens Feb 06 '20 at 18:49
  • @Jens I'd been toying with that Palestine alternative all afternoon with no success! However, that suggestion you make in your other comment is one I hadn't even considered! I'll have a play... :) – Stiv Feb 06 '20 at 19:04
  • @Stiv You're very close to the complete answer :-) – sarsaparilla Feb 08 '20 at 12:43
  • Well done! The checkmark is yours. – sarsaparilla Feb 10 '20 at 15:02
  • Thanks @sarsaparilla - the final category just clicked today at lunchtime while looking at them all on a map! – Stiv Feb 10 '20 at 15:05
  • @Stiv That's great :) Well this was the first puzzle I posted on this site, and I had no idea if it would be far too easy, or near impossible to solve. By the way I am working on part two of Fun with Flags, which will be up tomorrow. – sarsaparilla Feb 10 '20 at 15:09
4

Partial attempt:

Each flag is paired except at the right hand side of the chart where it appears once.
Otherwise each flag appears in adjacent images so that two flags are superimposed.
I have several possibilities for the flags left blank (e.g. outlined cross, three stripes).
So far, the arrangement I have is like this:

enter image description here

I can't figure out how the colour blending works. It looks as if the r-g-b colour components are exclusive-ORed between two flags sharing the same image. But if you look at the first two images on the bottom row, that would mean a flag has two horizontal bands in height ratio of 1:2 and I can't find a flag like that. It looks as if there might be a different rule in various situations.

Weather Vane
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    You've misused Japan where you meant Tunisia. – Ian MacDonald Feb 05 '20 at 15:00
  • @IanMacDonald thanks, I have corrected that - I had them the wrong way round. – Weather Vane Feb 05 '20 at 15:05
  • rot13(Vf vg Fjrqra orgjrra Ratynaq naq Hehthnl?) – Alain Remillard Feb 05 '20 at 15:37
  • @AlainRemillard Rot13(Creuncf, V unir rvgure Qraznex be Fjrqra.) – Weather Vane Feb 05 '20 at 15:58
  • Georgia is incorrect - that looks like a Scandinavian flag – Adib Feb 05 '20 at 21:27
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    @Adib the fragment of motif near the top left corner seems to be part of a Maltese cross and I can not find any other flag it might be a part of. If you look at a full size download of the image posted, you can detect the outline of the three other crosses of the Georgia flag overlaid on the flag of Rot13(Gnvjna) and on the next flag which I could not identify. – Weather Vane Feb 05 '20 at 21:42
  • @WeatherVane Oh my goodness, I was on my phone and didn't notice the faint colors! On my laptop, after zooming in, I can see it. Sorry about that! – Adib Feb 05 '20 at 23:13
  • @WeatherVane the unknown flag is rot13(Snrebr Vfynaq) – Adib Feb 05 '20 at 23:17
  • @Adib IMO there are six, or maybe more, possible flags it might be, depending on how the colours work out. Rot13(Obhirg Vfynaq, Snebr Vfynaqf, Vprynaq, Wna Znlra, Abejnl, Finyoneq). – Weather Vane Feb 05 '20 at 23:23
  • I see, but I think it's highly probable it's what I shared because I inverted the colors on Photoshop, and I noticed that doing so shows the correct colors for surrounding flags: ROT13(Ubaqhenf Trbetvn Abegu Xbern). – Adib Feb 05 '20 at 23:27
  • @Adib perhps you have found the colour scheme - keep working on it and post an answer! – Weather Vane Feb 05 '20 at 23:29
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    @Adib perhaps the "four categories" are Rot13(naq be abg kbe). – Weather Vane Feb 05 '20 at 23:35
  • With alpha, it's a bit tricky, no? Rot13(Ubj jbhyq "abg" jbex jvgu na nycun punaary?) – Adib Feb 05 '20 at 23:44
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    The blending seems to work like this: 1. Take the RGB values of the flag you know. 2. Subtract the RGB values of the blended flag to its right. 3. If the subtraction gives a negative value, add 256. 4. The resulting RGB values give the colors of the flag that was blended with the known flag. As an example, the flag blended with Uzbekistan is the Estonian flag. – Jens Feb 06 '20 at 06:03
4

Partial Attempt:

My flag map:

Row 1: Belgium,Romania,(UNKNOWN),Russia,Croatia,England,Sweden,Uruguay,Brazil
Row 2: Mali,(UNKNOWN),Poland,Hungary,Kuwait/Palestine,Iran,Niger,Algeria
Row 3: UK,India,(UNKNOWN MONO/TRI-COLOR),Pakistan,N.Korea,China,US
Row 4: Uzbekistan,(UNKNOWN TRI-COLOR),Honduras,Taiwan,Georgia,Faroe Island,Tunisia,Japan

I think the first category is..

Color inversion. After inverting the colors, I noticed certain flag colors pop up. For example, Honduras, Hungary, Faroe Island, Georgia, Pakistan, Brazil - they all have their correct color. Inverted

The methods I've tried so far is using OpenCV2 to experiment on different color conversions, and one of the flags that was 'hidden' stood out very well when using color conversion from RGB to HSV (cv2.cvtColor(image, cv2.COLOR_BGR2YUV)).

Here's what I mean...

enter image description here

Adib
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