The three doors

Logic Level 2

The Manager to the exclusive program "Fly or Die!", looked for their lead actor, Lipstick Lil. There are 3 doors of which she might be in. However, in front of each door is a security guard who won't let him in.

"Where's lipstick Lil?" the manager asked.

"Room 1 or 3," said the first guard.

The manager went to room 2, "I'm looking for Lipstick Lil,"

"Room 2 or 3," said the guard at room 2.

The guard at room 3 gave a more helpful response. "She's in room 1 or 2," he said, "But exactly 2 of us guards are habitual liars."

If a habitual liar always lies, then in what room was Lipstick Lil in?

Insufficient Information Door 1 Door 2 Door 3

1 solution

Finn C
May 21, 2016

Lipstick Lil is in Room 3.

If Guard 1 lies, then Lipstick Lil is in room 2.

If Guard 2 lies, Lil's in Room 1.

Now let us consider Guard 3: If he's telling the truth Lil is in Room 1 and 2, which is not possible. So guard 3 must be lying.

This is our proof:

She has to be in room 3, so when the guard says she's in room 1 or 2 he is lying. When he say "2 of us Guards are habitual liars", he is lying, because there is only 1 liar - him.

Therefore, Lipstick Lil must be in Room 3.

Moderator note:

Great explanation. However, could it be possible that Guard 1 is telling the truth, Guard 2 is lying and Guard 3 is a joker (occasional liar)?

No, because I said "a habitual liar always lies"

Finn C - 5 years ago

Well, the problem doesn't rule out the possibility that there are occasional liars.

Also, you must consider the possibility that all three are lying.

Ivan Koswara - 5 years ago

I suppose just as possibility right ? If all three are lying then "Lipstick Lil" isn't in any because what says the first and the second already rule out 3 possible doors and he must be in one.

But it's nicer to check all cases. So , all of them can be liars , jokers or truth tellers.

Because the last guard says something which is auto-referential about them start with him since by what he says it must be considered that you obtain the most amount of information possible relating to the restrictions of the problem as it conditions who is what. If what the third says is true then there are 2 habitual liars and the third can't be because he is telling the truth. Also if he is a liar it can't be that there are 2 liars because then what he says is true and he can't be a liar. The first 2 can't be liars because then all the possible doors which are said by them are taken out and would mean that "LL" isn't in any. Because of that it means that the third lies or is a joker but not a truth teller. To say things in one statement this means that either the first either the second is not a liar and the third is a joker or liar. Then the right doors are either 1or3 or 2or3 or 1or2. Then for such a configuration is necessary that 2 statements are true and 1 is false because a door is right and is mentioned by 2 persons.

Therefore the statement which is false is mentioned by a joker/liar which let's the second statements of the third guard which says that there are two liars be false and would give for accepting the case of jokers in the problem more possible answers. So the values of the third for what he says and what he is varies and would make more sense to consider there are just lairs and truth tellers.

A A - 5 years ago

The three doors

1 solution

Moderator note:

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