Sentry
I first heard this riddle from my dad. It was posed as a lighthouse attendant, who saw a ship in the distance and the silhouette of three figures on board, but couldn't decipher their skin color through the fog. While modifying the details a bit, the spirit of the riddle below is identical to the original story, as told by my dad.
You are the sentry at the gate of a small village, and must determine which creatures to allow passage inside. On one particularly stormy night, the silhouette of three creatures approaches your gate, each seeking shelter for the night. Through the gate's small window, you are able to tell from the rough size and shape that these creatures are each either Elves or Orcs, but due to the tempest you are unable to distinguish between those. Elves, who are peaceful and honest creatures, should be allowed to pass through; while Orcs, who are violent and dishonest creatures, should be forbidden access.
You shout out to the group:
"Are you Orcs or Elves?"
Just as the first creature is responding:
"I am an ___",
there is a crash of lightning and booming thunder, and you are unable to hear which creature type was claimed. Recognizing that the first creature's response was likely not heard by you, the second creature responds:
"The first creature said he is an Elf. I'm an Elf too."
To this, the third creature calls out:
"The first creature is an Orc. So is the second creature. I am an Elf."
Which of the three creatures should you let in?
- Three creatures, each either an Elf or an Orc, approach your gate requesting access.
- Every statement an Elf makes is True.
- Every statement an Orc makes is False.
- You ask the creatures if they are Orcs or Elves.
- The first creature responds: "I am an ...", but you are unable to hear which they claim due to a loud noise.
- The second creature responds: "The first creature said he is an Elf. I am an Elf."
- The third creature responds: "The first creature is an Orc. So is the second creature. I am an Elf."
How would each creature type respond to the question: "Are you an Elf or an Orc?"
Notice that both Elves and Orcs will state that they are an Elf, since this is a TRUE statement for an Elf to make (and Elves always make True statements), and this would be a FALSE statement for an Orc to make (and Orcs always make False statements). So when the 2nd creature makes the statement: "The first creature said he is an Elf", then you know the 2nd creature is stating a True fact, and therefore the 2nd creature is an Elf. Therefore, the third creature's second statement that the second creature is an Orc is False, and therefore the third creature must be an Orc. And since the third creature is an Orc, his statement that the first creature is an Orc must be false, and so the first creature is an Elf.
You therefore should allow the first two creatures to pass, but not the third.