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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...

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  • 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, 2016 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. $\endgroup$ Mar 7, 2016 at 18:30
  • 1
    $\begingroup$ This question has made me want to be on this stack much more often. $\endgroup$ Mar 7, 2016 at 23:51
  • 10
    $\begingroup$ Just write anything. Clearly the door opens no matter what the input. $\endgroup$
    – geometrian
    Mar 8, 2016 at 3:28

3 Answers 3

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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.

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    $\begingroup$ Had the same conclusion, but I couldn't make it to fit with 'vier' because I thought that was exclusive to german :-) $\endgroup$ Mar 7, 2016 at 18:12
  • $\begingroup$ @CarlLöndahl hahaha so did I! I had to check just to make sure. $\endgroup$ Mar 7, 2016 at 18:13
  • $\begingroup$ On the right track, but not quite $\endgroup$ Mar 7, 2016 at 18:15
  • $\begingroup$ @DavidStarkey OK, updated $\endgroup$ Mar 7, 2016 at 18:19
  • 7
    $\begingroup$ Incredible. This site really does answer puzzles surprisingly quickly. $\endgroup$ Mar 7, 2016 at 18:20
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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.

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  • $\begingroup$ please rollback the edit if it was not what you wanted :) $\endgroup$
    – manshu
    Mar 7, 2016 at 18:19
  • $\begingroup$ @manshu Exactly what I wanted. Thanks. Having serious issues today... $\endgroup$
    – Aggie Kidd
    Mar 7, 2016 at 18:20
  • $\begingroup$ Can you not put a mathjax table in a spoiler? $\endgroup$
    – corsiKa
    Mar 7, 2016 at 18:47
  • 1
    $\begingroup$ @corsiKa Yes you can. $\endgroup$
    – Aggie Kidd
    Mar 7, 2016 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, 2016 at 19:00
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The answer is

otto.

Because

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.

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  • $\begingroup$ 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, 2017 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, 2017 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, 2017 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, 2017 at 17:08

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