To recap, here’s the setup:

Through an entirely inexplicable series of events (alien abduction, too much fried chicken…just use your imagination), you find yourself on what you presume to be a deserted island.  However, as you wander the pristine beach which thinly skirts the edges of the island, you come across a sign that provides an incredibly convenient description of where you are and what you will be sure to experience:

Welcome, traveler, to the island!  While mostly uninhabited, this land is nonetheless shared by two civilizations: the Knights and the Knaves.  While their names most certainly begin with the same two letters, these cultures could not be more different.  In your travels, you will be well served to remember two simple rules: Knights always tell the truth, and Knaves always lie.  Please enjoy your stay!

Your curiosity piqued, you begin to explore the island and are promptly accosted by two men.  Seeming to have abandoned all mores of polite society, the two men do not introduce themselves to you whatsoever, but instead launch into a heated discussion amongst themselves, leaving you to stand in an awkward and somewhat cautious silence.  Finally, their voices fade into whispers and then stillness.  Abruptly the first man approaches you and curtly says:

My companion is a Knight.

Having exhausted his entire supply of conversation, the first man steps back while the second briskly steps forward and cryptically announces:

My companion and I are nothing alike!

And with that, as quickly as they appeared, the two men hurry off into the underbrush, leaving you to contemplate the uncomfortable exchange.

So then, of the Knight and Knave populations of this strange island, to which group did each man belong?

The Answer

The answer to this brain teaser is deceptively simple.  Based on the men’s statements, it’s obvious that both of them are knaves.  What is brilliant about this teaser is that, like all good teasers, it’s strength lies in misdirection.  Most people attempt to answer this by assigning one man to each population, simply because both populations were mentioned in the setup.  There is a subconscious expectation that one will belong to the Knights and one to the Knaves, even though this requirements is never laid out.  Awesome :)