Wednesday, March 6, 2019

Darklands Puzzle #5

Here is a dark iron door. Carved in it are:
ONLY ONE KNOB OPENS THE DOOR.
ONLY ONE STATEMENT IS WHOLLY TRUE.
Four knobs are on the door, of gold, silver, copper and lead. Four statements are on the wall nearby:
  1. The gold knob opens the door.
  2. The lead knob opens the door.
  3. Neither the silver knob nor the gold knob open the door.
  4. The lead knob does not open the door.
Only one statement is true. But which? Only one knob opens the door. Which?
...gold.
...silver.
...copper.
...Iead.
(Source: Darklands cluebook by MicroProse Software)

The cluebook makes the very helpful suggestion of starting with focusing attention on statements #2 and #4. Only one of them can be true. If statement #2 is true then statement #3 is also, true, which contradicts the stipulations of the puzzle. This means that #4 is the only wholly true statement out of the lot. Because statement #3 is a logical conjunction, one of its operands is permitted to be true while the other is false, making it not wholly true. Statement #1 does not have this luxury and is therefore required to be false. This means that the silver knob opens the door.

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