[Guest]

Getting Into the Inner Sanctum

There are four doors X, Y, Z, W leading out of the Middle Sanctum. At least one of them leads to the Inner Sanctum. If you enter a wrong door, you will be devoured by a fierce dragon.

Well, there were eight priests A, B, C, D, E, F, G, H, each of whom is either a knight or a knave. They made the following statements to the philosopher:

A: X is a good door.

B: At least one of the doors Y, Z is good.

C: A and B are both knights.

D: X and Y are both good doors.

E: X and Z are both good doors.

F: Either D or E is a knight.

G: If C is a knight, so is F.

H: If G and I are both knights, so is A. (H is referring to himself when he says “I.”)

Which door should the philosopher choose?

[Guest]

I would say door X. There is no way I see to determine who is knight or knave, but the various scenarios all point to X being a safe door. Though I think it would be safer to just go home.

also, request for clarification.

G: If C is a knight, so is F

H: If G and I are both knights, so is A.

Do these mean "if and only if"

Edited May 27, 2011 by Nana7

[Smith]

My premise in taking my approach: OP states "at least one of them" (the doors) "leads to the Inner Sanctum". That could mean one, two, three, or all four doors lead to the IS. "IF you enter a wrong door" does not establish the certainty that there are any wrong doors. Based on these two considerations, it seems to my feeble mind that just about any or all of the eight priests could be knights. And, just for the record, where does it state that knights always tell the truth and knaves always lie? So, I'm choosing to approach this puzzle based on there being ONE correct door and THREE wrong doors. If I'm wrong about that assumption then I'll wait to see the better logic that others or ivcvolleyballer bring to light.

Given that there is ONE door leading to the Inner Sanctum (see above)...

And given that knights MUST always tell the truth...

1. C must not be a knight as both A and B cannot both be correct.

2. D and E cannot be knights because they claim that TWO doors are good.

3. F must not be a knight based on 2.

4. G does not make the statement that if C is NOT a knight then neither is F, only that if C IS then F IS. Nonetheless, based on 1, the point is moot as I have already disqualified F.

5. H therefore makes another moot statement. UNLESS - I am to infer that "If either G or I are not knights then NEITHER IS A". In that case I would have to disqualify A. But that only leaves me with B and a 50/50 chance.

6. H makes no other statements regarding doors, so I am left with A and B and they contradict one another. I choose door X. At least A has the guts to take a stand, not like sissy-man B with his "either-or" namby-pamby prattle.

Is it just me or were there truly some gaping holes in this puzzle? I only decided to answer it because there were no other replies when I started writing mine. We'll see how THAT worked out! hey, and if I'm way wrong about everything, it won't have been the first time (ever play Beginner Mafia with me?) and it probably won't be the last.

[Guest]

my friend gave me this puzzle and this is all there is. im still new to these logic puzzles so i thought maybe someone else could figure it out. but i also thought there was info missing and im glad im not the only one. thanks for the attempts

[Guest]

my friend gave me this puzzle and this is all there is. im still new to these logic puzzles so i thought maybe someone else could figure it out. but i also thought there was info missing and im glad im not the only one. thanks for the attempts

I suggest, we should post a puzzle only if we are ready to own it and have a definite answer. This will save the members' time.

[Guest]

Considering all are knaves.. W is the safest door.

[Peekay]

The statements are inconclusive and do not lead to a specific solution. However, if we assume that X is a good door, we do not land up with any obvious contradictions. So, that, at least, is a correct answer.

[Guest]

All of them r lying... And so the safe door is W...

[Guest]

There is some deduction that can be made, but much is left unknown.

In the table below K is a Knight, d is a door leading to the dragon, - represents a Knave or good door, and ? represents a 50% probability the choice is either Knight or Knave, or good or bad door (for the specific case given, not the overall or actual case).

ABCDEFGH WXYZ

======== ====

KKKKKKK? ?---

KKKK-KK? ?--d

K-----?? ?-dd

-K----K- ?d?-

-K-----? ?d?-

------K- -ddd

-------? -ddd

It seems, probability-wise, the most likely candidate of a good door is W.

[Guest]

im confuzed is there adifference betwwen inner sanctum the right door and the good door

[Guest]

I think that depends on how you read the term "If" in G and H. If you read it as "if and only if" then that does narrow down the possibilities and X will be a good door in all cases, I think. But if you read as as a simple conditional if that does not mean "if and only if" then you are right about all the possibilites that leaves open.

There is some deduction that can be made, but much is left unknown.

In the table below K is a Knight, d is a door leading to the dragon, - represents a Knave or good door, and ? represents a 50% probability the choice is either Knight or Knave, or good or bad door (for the specific case given, not the overall or actual case).

ABCDEFGH WXYZ

======== ====

KKKKKKK? ?---

KKKK-KK? ?--d

K-----?? ?-dd

-K----K- ?d?-

-K-----? ?d?-

------K- -ddd

-------? -ddd

It seems, probability-wise, the most likely candidate of a good door is W.

Googon, I think they all refer to the same thing, inner sanctum the right door and the good door. The door or doors you can use and not die.

[Guest]

The conditional IF p THEN q is TRUE if and only if

(1) p is FALSE

(2) q is TRUE, or

(3) both P and Q are TRUE.

Therefore there are three possibilies from

H: If G and I are both knights, so is A. (H is referring to himself when he says “I.”).

They are:

A_____ G_____ H_____

Knight Knight Knight

Knight Knave. Knight

Knave. Knave. Knight

Applying the statement

G: If C is a knight, so is F.

We have:

A_____ C_____ F_____ G_____ H_____

Knight Knight Knight Knight Knight

Knight Knave. Knight Knight Knight

Knight Knave. Knave. Knight Knight

Knight Knight Knave. Knave. Knight

Knave. Knight Knave. Knave. Knight

And, then from

C: A and B are both knights.

A_____ B_____ C_____ F_____ G_____ H_____

Knight Knight Knight Knight Knight Knight

Knight Knave. Knave. Knight Knight Knight

Knight Knave. Knave. Knave. Knight Knight

Knight Knight Knight Knave. Knave. Knight

Thus, from statements by H, G and C, it can be determined that both A and H are Knights.

From the statement 'A: X is a good door' and that the application of logic to the remaining statements do not contradict this possibility, we know that X is the door the philosopher should choose.