11 replies to this topic

[ivcvolleyballer]

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?

[Nana7]

Spoiler for my reply, gulp

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 by Nana7, 27 May 2011 - 01:41 AM.

[Smith]

Spoiler for Well... (That's a deep subject)...

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.

[ivcvolleyballer]

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

[Mukul Verma]

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.

[Silver Surfer]

Spoiler for Simplest solution that i can give is

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.

[Dr.Abhilash]

Spoiler for Simple

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

[Dej Mar]

Spoiler for observation

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]

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