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There are three doors before you, of which only one is correct. Each door will take you one minute to open by default, but one of the incorrect doors contains a trap that will slow opening of any remaining doors by 50%. How long will it take you, on average, to escape this room?

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closed as unclear what you're asking by Rubio, Ankoganit, Rand al'Thor, IAmInPLS, Gamow Dec 13 '16 at 16:37

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    $\begingroup$ Your question is unclear. What do you mean by "Only the first door is the right way to go out." ? $\endgroup$ – Rubio Dec 13 '16 at 14:32
  • $\begingroup$ @Rubio, thanks for your reply. the first door is the right way to go out, when you choose first door, the game is over. $\endgroup$ – Donkey_JOHN Dec 13 '16 at 14:35
  • $\begingroup$ I tried to make the puzzle a bit clearer, could you please clarify whether the dangerous door makes a future door take 90 or 120 seconds? I think it's 120, but I'm not certain $\endgroup$ – Sconibulus Dec 13 '16 at 14:46
  • $\begingroup$ @Sconibulus Thanks for your amend. Can you show your logic behind it? many thanks. $\endgroup$ – Donkey_JOHN Dec 13 '16 at 14:49
  • $\begingroup$ "one of the incorrect doors contains a trap that will slow opening of any remaining doors by 50%" - Does this mean that if I open the trap door then next door will take two minutes, or one and one half minutes? $\endgroup$ – LeppyR64 Dec 13 '16 at 15:03
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Answer

the average is 2 min 20 seconds.

Reasoning:

You have 6 possible combinations of opening the doors.
Since we need to get the average, it is not important which door is the correct one and which one has the trap.
So let's consider door 1 as the correct door and 2 as the one with the trap.
Here are the sequences.

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1 2 3 - it takes you 1 minute because you go out on the first door opened.
1 3 2 - 1 min.
2 1 3 - 1 + 1.5 = 2.5 minutes (because you went through the trap on door 2)
2 3 1 - 1 + 1.5 + 1.5 = 4 min.
3 1 2 - 1 + 1 = 2 min.
3 2 1 - 1 + 1 + 1.5 = 3.5 min.

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So average is $\frac{1 + 1 + 2.5 + 4 + 2 + 3.5}{6} = \frac{14}{6} = 2.(3)$.

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  • $\begingroup$ This is exactly the same process/solution I came up with pretty much word for word. Good job. Too bad it got put on hold for being unclear... Although it should have been closed for being pure math and nothing to do with puzzles lol. $\endgroup$ – stack reader Dec 14 '16 at 1:38
  • $\begingroup$ @marius, if the man got the right door at first, why are you making it two possible combinations of 132 and 123 $\endgroup$ – Asterisk Feb 15 '18 at 13:36
  • $\begingroup$ @Asterisk. It took me a while to remember what I wrote a year + ago. :). I handle both cases because that's how averages work. There are 6 possible ways to arrange numbers 1, 2 and 3 and you need to go through all the combinations to get the average. $\endgroup$ – Marius Feb 15 '18 at 14:22
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I believe the math for the answer is

1/3*1min+1/6*2min+1/6*2min+penalty+1/6*(3min+penalty)+1/6*(3min+2penalty)

Which simplifies to

2 minutes + 2/3 penalty

Or, if my interpretation of the penalty is correct (doubling time it takes to go through the door)

2 minutes and forty seconds

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