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Here is the flag of Norway. You can cut out rectangular non-overlapping regions from this flag to form flags of other countries. What is the most number of different country flags you can make?

Flag-of-Norway

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  • $\begingroup$ Idea from a Facebook post I've seen. $\endgroup$ Dec 17, 2022 at 23:11

2 Answers 2

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We can make

up to 9 flags!

enter image description here

We have 6 starting flags: Indonesia, France, Poland, Finland, Netherlands and Thailand.

Ignoring differences in shading, Monaco and Luxembourg can be added, and ignoring symbols then Malta can also be added for a total of 9!

It's known as the Mother of all Flags for a reason!

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  • $\begingroup$ Very nice! Let's see if anyone can improve on this. $\endgroup$ Dec 17, 2022 at 23:50
  • $\begingroup$ @DmitryKamenetsky going through the wikipedia page of flags by colour combinations - would you accept singapore? Or is the symbol too important to the flag $\endgroup$ Dec 18, 2022 at 0:07
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    $\begingroup$ I don't think the proportions are right for the Finnish flag. And why should we be allowed to ignore charges? $\endgroup$
    – msh210
    Dec 18, 2022 at 1:31
  • $\begingroup$ @msh210 the proportions for finland are off, but I think its fine as its still very recognisable as the flag. I think differences in shading is fine as most of these colours are off anyway (I know the france blue is definitely brighter) but the red blue white patterns are still very recognisable. Malta is the only one I'd really question whether its acceptable here - I've only included it as its the only flag which goes white-red vertically, but the missing symbol is key. Thats why I've said up to 9 flags in my answer, IMO theres defintely the 6 given, and the rest depends on the rules :) $\endgroup$ Dec 18, 2022 at 1:56
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    $\begingroup$ @DmitryKamenetsky in that case (unless I've missed something obvious) I believe this is all the countries possible, all others have large distinguishing symbols. Included Malta as the symbol is not distinguishing and the pattern is unique, the other 8 are all the colour only ones there are $\endgroup$ Dec 18, 2022 at 2:15
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The question says "cut out rectangular non-overlapping regions from this flag to form flags". Read literally, it suggests we are allowed to form flags from rectangular regions, not necessarily that the rectangular regions that are cut out must themselves be flags. If one permits reconstruction of flags from rectangular pieces cut out of the flag, I can get:

17 flags:

Image

Directly stealing from BeastlyGerbil's answer, Malta, Monaco, Indonesia and Poland all require just one rectangle. I split France, Netherlands, Luxembourg and Thailand across several rectangles to address proportion issues, and Finland splits into four sections for the same reason. We also get to add:
Peru (2 sections, horizontally placed)
Austria (2 sections, vertically placed)
Russia (2 sections, vertically placed)
Costa Rica (4 sections, vertically placed; the blue splits in two parts)
Denmark (4 sections, on the corners)
Tonga, Switzerland and Iceland are a bit of a mess, but hopefully clear from the diagram.

There remains a legit question about shades of blue, as (say) the blue in the Russian flag is substantially lighter than that of Norway. But I have addressed all proportion issues: flags are constructed proportionally with the best information I could find with casual Internet searching (mostly Wikipedia).

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  • $\begingroup$ that's very clever :) $\endgroup$ Dec 19, 2022 at 11:46

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