Don't Be Surprised If You Can't Solve the Passcode Riddle

If you can’t, you’ll be fed to mutant salamanders!

In a world that is ruled by a totalitarian regime, you and two others have been captured by the government and trapped underground in the Roman Coliseum. Once trapped, you see multiple numbered hallways leading outside, each requiring its own passcode to get through.

You are told that one person can attempt escape, while the two others will be sent to the dungeon to be fed to mutant salamanders soon after. One person is chosen to escape, and this person is given an audio transmitter so that the other two can hear their instructions.

You and someone else are sent to the dungeon and the other person is led down one of the hallways and instructed that they are not allowed to speak. They are then told to enter a code consisting of 3 positive, whole numbers in ascending order. For example, if you have a code, x y z, then it must be true that x ≤ y ≤ z.

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This person is also told they are allowed to ask for 3 clues, but to enter the code as soon as they’ve deduced it, even if they haven’t been given all of the clues.

The person attempting escape ends up having to use all 3 clues, and you are able to hear these clues as well.

Here are the three clues, given in order:

1. The product of the three numbers is 36.
2. The sum of the numbers is the same as the number of the hallway being used to escape.
3. The largest number must be unique.

Keep in mind that the person attempting escape knows their hallway number, while you do not.

After the person manages to escape, you are allowed back into the room with the numbered hallways while you wait to be fed to the mutant salamanders. Can you find the passcode and hallway number and escape the Coliseum?

See if you can work out the answer and watch the video below for a full solution: