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Given the following list of four corresponding series of numbers, what would the fifth line look like?


  • 1 : 1.4 / 3
  • 2 : 3 / 2 | 1 : 2 / 6
  • 2 : 3 / 2
  • 1 : 2 / 3

Hint 1: This puzzle was inspired by the prime number 119698.

Hint to Hint 1: The call is coming from inside the house, just nine doors down from this one.

Hint 2: The prime number might be flagged as both a bit 1337 and bit gangstah.

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    $\begingroup$ 119698 prime?! That's a new one on me... :) $\endgroup$
    – Stiv
    Feb 9, 2023 at 17:24
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    $\begingroup$ @Stiv Given how insanely good people here are at extracting really complex connections from nothing at all, I didn’t want to make the hint too easy. $\endgroup$ Feb 9, 2023 at 17:37
  • $\begingroup$ mysterious 119698 is even in every base $\endgroup$
    – Jasen
    Feb 18, 2023 at 11:11
  • $\begingroup$ @Jasen Oddly (!) enough, that doesn’t matter in the slightest. In fact, the hints aren’t mathematical at all. But the knowledge tag applies to both the actual puzzle and the hints. $\endgroup$ Feb 18, 2023 at 13:41
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    $\begingroup$ @Jasen I don’t even understand what that means… $\endgroup$ Feb 19, 2023 at 2:35

2 Answers 2

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Since it's been 3 weeks, a partial answer to explain the puzzle, without quite being able to spot the intended solution...

This puzzle has been inspired by another one on this site - namely, this one. The hints all point to this:

1. Check its URL - the puzzle can be found at node number 119698 on this very site (i.e. 'inside the house'). Since this puzzle clocks in at node number 119707, it can be found 'nine doors (i.e. nodes) down from this one'.

2. The creator of that puzzle is PSE user @Prim3numbah - a corruption of 'prime number', using a little 1337 (i.e. 'leetspeak' - here with the use of a '3' in place of an 'e') and 'a bit gangstah' in the use of the 'ah' ending in place of 'er'.

Now that puzzle revolved around...

...the aspect ratios of national flags (i.e. the standard proportions of their width and height). And that's again what is involved here. The first part of each row in the puzzle (before the slash) is one of these ratios.

There's another useful clue in the title too...

There are two capitalised letters in it - 'E' and 'U'. This means we are likely to need to think about European flags in particular.

And this is confirmed by an observation from the first line:

There are only two national flags whose standard aspect ratio is 1:1.4 (or 5:7) - Albania and Kosovo, both European.

So what might the numbers after the slashes represent? Something that immediately springs to mind...

...on looking at these flags is the number of colours used in the flag's design.

The number after the slash is a '3', and the flag of Kosovo uses 3 colours:
Flag of Kosovo

(Albania's has just 2 colours, so this would differentiate between them...)

So what does each row represent? I would suggest the following:

1 : 1.4 / 3: Kosovo:

Flag of Kosovo

2 : 3 / 2 | 1 : 2 / 6: Two nations (either side of the bar). The first (before the bar) could be Austria, Greece, Turkey or Ukraine:

Flag of Austria Flag of Greece Flag of Turkey Flag of Ukraine

The second (after the bar) is Croatia:

Flag of Croatia

2 : 3 / 2: Again, one of Austria, Greece, Turkey or Ukraine (presumably a different one):

Flag of Austria Flag of Greece Flag of Turkey Flag of Ukraine

1 : 2 / 3: Bosnia-Herzegovina, Hungary, Ireland, or the UK:

Flag of Bosnia-Herzegovina Flag of Hungary Flag of Ireland Flag of UK

However, since I have not yet managed to disambiguate these, it is impossible to know what the intention for a 'fifth line' would be. One thing that may come into play here is...

...differing statuses of EU membership, especially since (famously on all 3 counts) Kosovo is currently an applicant, Turkey's application is the subject of a high-profile freeze right now, and the UK is the only nation to have actually left the union. However, I'm not seeing it just yet...

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  • $\begingroup$ You are very, very close! Unfortunately, reading your answer, I just noticed a very lamentable typo in the question – a 2 should have been a 3 in the third line! I’ve fixed the question now. $\endgroup$ Mar 3, 2023 at 0:37
  • $\begingroup$ @JanusBahsJacquet Ah, ok - I'll alter my answer to reflect the intended wording... $\endgroup$
    – Stiv
    Mar 3, 2023 at 23:46
  • $\begingroup$ A hint to the disambiguation: An erroneous assumption has led you to look in a slightly wrong haystack, but you have nonetheless found the exact spot where the correct needle may be found. $\endgroup$ Mar 8, 2023 at 8:15
  • $\begingroup$ @JanusBahsJacquet Are you maybe suggesting that my interpretation of the number that follows the slash is incorrect...? $\endgroup$
    – Stiv
    Mar 8, 2023 at 8:36
  • $\begingroup$ Earlier than that, actually! $\endgroup$ Mar 8, 2023 at 10:05
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Since no other answers (or updates to Stiv’s answer) have appeared since March, I will fill in the blanks – with the note that Stiv came very close to the full solution.

Instead of posting the full logic from start to finish, I will refer to Stiv’s answer and only address the missed points:

Title clue

There's another useful clue in the title too...

There are two capitalised letters in it - 'E' and 'U'. This means we are likely to need to think about European flags in particular.

This is where things went slightly awry:

The capitalisation implies that we need to think about European Union flags, not European flags – this is important, because some of the flags are actually not traditionally considered European.

Defining logic

However, since I have not yet managed to disambiguate these, it is impossible to know what the intention for a 'fifth line' would be. One thing that may come into play here is...

...differing statuses of EU membership, especially since (famously on all 3 counts) Kosovo is currently an applicant, Turkey's application is the subject of a high-profile freeze right now, and the UK is the only nation to have actually left the union. However, I'm not seeing it just yet...

This actually – probably coincidentally – links to the exact Wikipedia article that holds the answer:

If you scroll down to the section Historical enlargements, there is a table of countries which have historically applied to become a member of the EU. Ordering that table by submission date, with newest submissions on top, provides the basis of the data.

Given that none of the newest applicants have been accepted into the EU yet, their defining commonality here is that they are not EU members (indeed, Georgia is arguably not in Europe), but hoping to be so.

Correct solution

The correct values for the rows in the question are thus:

1 : 1.4 / 3   :   Kosovo (submission date: 14 Dec 2022)

Kosovan flag

2 : 3 / 2 | 1 : 2 / 6   :   Georgia & Moldova (submission date: 3 March 2022)

Georgian flag Moldovan flag

2 : 3 / 2   :   Ukraine (submission date: 28 February 2022)

Ukrainian flag

1 : 2 / 3   :   Bosnia-Herzegovina (submission date: 15 February 2016)

Bosnian-Herzegovinian flag

And consequently, the next row would look like this:

2 : 3 / 5   :   Serbia (submission date: 22 Dec 2009, 5-coloured flag)

Serbian flag

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    $\begingroup$ Ah ok, yes I probably wasn't going to pick up on this without considering G.....a (and I guess I must have calculated the number of colours in M.....a wrongly, else I would have considered that). Sometimes it's hard to change your initial thinking when you've gone so far down a particular thought path already... $\endgroup$
    – Stiv
    Oct 7, 2023 at 7:18

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