Thursday, March 7, 2019

Darklands Puzzle #10

A door blocks the path. An inscription reads:
FACES ALWAYS LIE OR ALWAYS SPEAK TRUTH.
TOUCH ONE KNOB TO OPEN THE DOOR.
On the wall are six numbered faces, who speak:
One: "Gold opens the door."
Two: "Face One speaks truth. Copper cannot open the door."
Three: "Face Four is a liar."
Four: "Face Six is a liar. Face Six and myself are the only two liars."
Five: "Of the odd-numbered faces, exactly two tell the truth."
Six: "Lead cannot open the door."
Four metal keys hang nearby. You ponder, then use...
...the gold key.
...the silver key.
...the copper key.
...the lead key.
(Source: Darklands cluebook by MicroProse Software)

Four must be a liar because "knights" would never call themselves liars. Neither would knaves for that matter, at least not in an unqualified fashion. However the statement is a little more complex than that: "Face Six and myself are the only two liars" really means that there are other liars than Four. (Six is not a liar because Four said Six is a liar.)

If Five is a "knight" then Three and Five are the two "knights" of the odd-numbered faces and the choices are restricted to silver and copper. (One is a "knave" and Six, previously established as a "knight", has said that lead cannot open the door.) If, on the other hand, Five is a "knave", then only one of the odd-numbered faces can be a "knight": "exactly two" is ruled out and "all three" is contradicted by the assumption that Five is a "knave". In this case, Three is the only "knight" and lead and gold are still both ruled out. Whether Five is a "knight" or a "knave", the choices are still limited to silver and copper and One is a "knave".

Having established all of this, Two must also be a "knave", because Two claims that One speaks the truth, meaning that the copper key opens the door.

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