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.

  • 2
    $\begingroup$ 119698 prime?! That's a new one on me... :) $\endgroup$
    – Stiv
    Feb 9 at 17:24
  • 2
    $\begingroup$ @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 at 17:37
  • $\begingroup$ mysterious 119698 is even in every base $\endgroup$
    – Jasen
    Feb 18 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 at 13:41
  • 2
    $\begingroup$ @Jasen I don’t even understand what that means… $\endgroup$ Feb 19 at 2:35

1 Answer 1


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...

  • $\begingroup$ 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 at 0:37
  • $\begingroup$ @JanusBahsJacquet Ah, ok - I'll alter my answer to reflect the intended wording... $\endgroup$
    – Stiv
    Mar 3 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 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 at 8:36
  • $\begingroup$ Earlier than that, actually! $\endgroup$ Mar 8 at 10:05

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