You woke up this morning locked in a room. The only apparent exit is a door with a terminal. On the screen you see the following:

> einn
Access granted. Door opened.
> três
Access granted. Door opened.
> dhá
Access granted. Door opened.
> seis
Access granted. Door opened.
> seven
Access granted. Door opened.
> cinq
Access granted. Door opened.
> vier
Access granted. Door opened.

The last line seems to be waiting for some input from you...

  • 3
    $\begingroup$ The next numerical value should perhaps be 12, as 1,3,2,6,7,5,4,12 occur in this order in the 4-bit Gray code. But I do not see a pattern in the languages. $\endgroup$ – Gamow Mar 7 '16 at 18:05
  • $\begingroup$ @Gamow It's also missing zero and could be a 3-bit gray code, although I'll grant that wouldn't really make sense given the current order. $\endgroup$ – Parthian Shot Mar 7 '16 at 18:30
  • 1
    $\begingroup$ This question has made me want to be on this stack much more often. $\endgroup$ – Qix Mar 7 '16 at 23:51
  • 9
    $\begingroup$ Just write anything. Clearly the door opens no matter what the input. $\endgroup$ – imallett Mar 8 '16 at 3:28

The answer is

twaalf, the Dutch word for the number twelve

The languages

go from West to East: Iceland $\rightarrow$ Portugal $\rightarrow$ Ireland $\rightarrow$ Spain $\rightarrow$ UK $\rightarrow$ France $\rightarrow$ Belgium.
Hence the next language should be Dutch.

The numerical values

follow the 4-bit Gray code (see here): 0000=0, 0001=1, 0011=3, 0010=2, 0110=6, 0111=7, 0101=5, 0100=4, 1100=12, 1101=13, 1111=15, 1110=14, 1010=10, 1011=11, 1001=9, 1000=8.
Hence the next number should be 12.

  • 2
    $\begingroup$ Had the same conclusion, but I couldn't make it to fit with 'vier' because I thought that was exclusive to german :-) $\endgroup$ – Carl Löndahl Mar 7 '16 at 18:12
  • $\begingroup$ @CarlLöndahl hahaha so did I! I had to check just to make sure. $\endgroup$ – question_asker Mar 7 '16 at 18:13
  • $\begingroup$ On the right track, but not quite $\endgroup$ – David Starkey Mar 7 '16 at 18:15
  • $\begingroup$ @DavidStarkey OK, updated $\endgroup$ – question_asker Mar 7 '16 at 18:19
  • 6
    $\begingroup$ Incredible. This site really does answer puzzles surprisingly quickly. $\endgroup$ – David Starkey Mar 7 '16 at 18:20

To provide step one (mostly) but to add a guess:

The inputs are numbers, following this pattern:

$$\begin{array}{l | c} \text{Language} & \text{Number} \\ \hline \text{Icelandic} & 1 \\ \text{Portuguese} & 3 \\ \text{Irish} & 2 \\ \text{Spanish} & 6 \\ \text{English} & 7 \\ \text{French} & 5 \\ \text{German} & 4 \\ \end{array}$$

So, the answer might be

osiem - Total guess as 8 hasn't been listed yet, and going eastward following the countries the languages are spoken in, so headed to Poland next.

  • $\begingroup$ please rollback the edit if it was not what you wanted :) $\endgroup$ – manshu Mar 7 '16 at 18:19
  • $\begingroup$ @manshu Exactly what I wanted. Thanks. Having serious issues today... $\endgroup$ – Aggie Kidd Mar 7 '16 at 18:20
  • $\begingroup$ Can you not put a mathjax table in a spoiler? $\endgroup$ – corsiKa Mar 7 '16 at 18:47
  • 1
    $\begingroup$ @corsiKa Yes you can. $\endgroup$ – Aggie Kidd Mar 7 '16 at 18:51
  • $\begingroup$ Ohhh that's smart! I tried to fiddle with it but got kerflustered and gave up... hahaha $\endgroup$ – corsiKa Mar 7 '16 at 19:00

The answer is



seven numbers are given: 1, 3, 2, 6, 7, 5, 4; and the (six) differences between them follow the following pattern: +2 -1 +4 +1 +2 -1; the next logical difference in that cycle (a repeating cycle of differences of +2, -1, +4, -1) is +4, so the next number is 4 + 4 = 8.

As for the languages

1. Icelandic, 2. Portuguese 3. Irish, 4. Spanish (also Portuguese, but since that's "taken up" already by the preceding "três", which cannot be confused with any other language, let's assume it's Spanish), 5. English, 6. French, 7. German or Dutch; I'm choosing Dutch because reasons following below.

Now the pattern in this set that

numbers [1,3] , [2,4], [5,7] are the sets of languages that are most related to each other within the sample of 7 languages given [Icelandic, Irish], [Portuguese, Spanish], [English, Dutch] . I'm specifically associating "English" with "United Kingdom" here, and not with any of the other dozen English-speaking languages in the world. Also note that this means 7. must be Dutch, because both Dutch is linguistically closer to English than German is, and the Netherlands are geographically closer to the U.K. than Germany is.

As for the language of the eight entry, [8]

it must be in the language most closely related to the sixth entry, [6], French, to follow the pattern. That's Italian, thus the answer is otto.

  • $\begingroup$ Meant to have a proper list for the numbered items but somehow couldn't make it work within Spoilered text even though adding two spaces at the end of each line. So sorry for the formatting. $\endgroup$ – LB7979 Jan 19 '17 at 11:12
  • $\begingroup$ Interesting, but the correct answer was already given and accepted as correct some 10 months ago. You should probably look at other answers before posting your own (to make sure you're not duplicating one), and concentrate on questions still missing an answer accepted as correct. In any event - Welcome to Puzzling SE! Take the tour, learn what we're all about, and see you around! $\endgroup$ – Rubio Jan 21 '17 at 1:23
  • $\begingroup$ @Rubio The original author of the question, David Starkey, only commented "not quite" to the first answer to the question, thus that answer wasn't right; and David Starkey didn't answer anything at all to the second answer given, so how could I know that was the right answer. $\endgroup$ – LB7979 Jan 22 '17 at 17:00
  • $\begingroup$ The big green check mark next to it indicates the asker has accepted that answer as the correct one. (Also if you read all the comments to the first question you'll see that the answer was edited following David Starkey's "not quite" comment, and that he commented that the update showed that "this site really does answer puzzles surprisingly quickly" - you may have to click "show X more comments" to see them all sometimes.) Hope that helps. $\endgroup$ – Rubio Jan 22 '17 at 17:08

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