The Temple of Doom

You and eight of your team members are trying to escape the Temple of Doom. You are running through a tunnel away from a deadly smoke and end up in a large hall. There are four paths ahead, and exactly one of them leads to the exit. It takes 20 minutes to explore any of the four paths one way, and your group has only 60 minutes until the deadly smoke suffocates you. The problem is that two of your friends are known to be delirious and it is possible that they do not tell the truth, but nobody knows which ones they are. How should you split the group and explore the tunnels, so that you have enough time to figure out which is the correct path and escape the temple?

You explore the first path. You send two of your teammates to explore the second path. You send the remaining six teammates in groups of three to explore each of the two remaining paths. If your path leads to the exit, then everything is good. Otherwise, you ask the two groups of three whether their paths lead to the exit. If in both groups everyone answers consistently, then nobody is lying, and you will escape. If in both groups there is a person whose answer is different from the others in the group, then the majority in both groups says the truth. Once again, you will know which path leads to the exit. Finally, if in exactly one of the groups everyone answers consistently, you ask the group of two. If the team members there answer consistently with each other, then they say the truth. You will have two groups which tell the truth and will know which path leads to the exit. If the answers of the teammates in the group of two differ, then in the inconsistent group of three the majority will be saying the truth. Again, you will be able to deduce which path leads to the exit.

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  1. Hi, I think I might have an easier and safer solution. There are 9 people right? Ok. We make three groups of three members each, each team has to explore the tunnel and return to report. This takes 20+20 minutes, and we have another 20 minutes left to exit safely. And there are two possibilities of making those three teams. Either those two delirious friends are both in the same team, either they are separate. So to make a scheme, it would look like this:
    1. TTI III III
    2. TII TII III, where “I” means healthy and “T” means delirious

    In case 1, there will be two teams who have explored the tunnels and all agree, and one team 2 vs 1. So if there is only one team 2vs1, we will take for good what the single 1 person says. So if any of the teams has discovered the exit, we will know. If not, then the fourth tunnel is the exit.

    In case 2, there will be one team that agrees on the state of the tunnel and two teams 2vs1. So if there are two teams 2vs1, we will take for good what the majority (the 2 who agree from each team) says. Again, if any of the teams has discovered the exit, we will know. Otherwise, the fourth tunnel is the exit.

    I assumed that you could also be one of the delirious team members. That’s why I believe that my method is the safest, as it doesn’t matter who is who. It’s only facts. What do you think?

    1. Hi Bianca. The delirious friends do not necessarily lie. So, it is possible to get 3-0 BLOCKED, 3-0 BLOCKED, and 2-1 BLOCKED, in which case you don’t know whether the EXIT is tunnel #3 or #4.

  2. No metter if those two are teling a true or lie, this combination – 3-3-2-1 is working.

  3. Simply I will wait in the hall and send a team of two to each tunnel, ordering them to escape incase you find an exit else come back.
    If they find the exit they will escape, incase you couldn’t find you come back. Now which ever team doesn’t come back will be the exit tunnel. 🙂

    1. If you do this, it is possible that the two delirious friends are sent to the escape tunnel and they come back. It is good if you check a tunnel yourself instead of waiting, since this will allow you to discard one of the options:)

  4. Seems that teams of 3 could be sent into 3 of the 4 tunnels. The 3 teams will come back with either a unanimous report or a 2 to 1 report. 1 team will definitely have a unanimous report. If the other two teams have a 2 to 1 report, then the majority report governs. If a second team gives a unanimous report, that means the two delirious teammates are in the same group and the minority report governs. Once the disposition of the 3 tunnels are known, you either know the way out based on the reports, or if none of the explored tunnels offers a way out, choose the 4th unexplored tunnel.

    1. Hi Stephen. If you make three groups of three people each, it is possible that the two delirious friends are in one group and they are sent to the escape tunnel. If their group votes 2-1 to choose another tunnel, then you will not know what to do.

      1. If they are in one group, then I will have 2 groups that are unanimous. If that is the case, then I know to believe the one person over the other two.

        1. I see where the confusion comes from. You do not know which friends are delirious and also delirious friends could either be telling the truth or lying.

    2. It’s not made clear that the 2 delirious friends could also be telling the truth, so I came to this conclusion as well.