It's time for the nefarious AIVD-puzzle.

The AIVD is the Dutch CIA. In 2012 they started publishing their puzzles. They became famous when the Dutch prime minister admitted defeat on the 2014 puzzle.

As you can imagine the puzzles are in Dutch, and since I had at least one person responding to one of the easier (though it took me hours) puzzles last year, here is, for your pleasure, the Tolkien-inspired puzzle:

#29: Raymond Merrill Smullyan (1919-2017)

Of the 13 dwarfs that accompany Bilbo on his jorurney, one or more have gotten under the influence of Sauron. Dwarfs under the influence of Sauron always lie, the others speak the truth (if they speak at all)

Which of the dwarfs tells the truth and which lie?

**Bifur, Bofur and Bombur**Gandalf called Bifur, Bofur and Bombur to him. One of the three stole a ring. Gandalf knows that the thief always lies, the other two will always tell the truth. He asks each of the three dwarfs: "Are you the thief?" Bombur is the only one to respond: "Either Bofur is the thief or it's me!"

**Dori and Nori**Gandalf called Dori and Nori to him, and asks if they know where Bilbo is. Dori replies he knows nothing. All Nori says is that both Dori and him are the same type (as in: that they either both lie or both tell the truth.)

**Oin, Gloin and Ori**Gandalf was looking for Bilbo and called Oin, Gloin and Ori to him, knowing that one of them knows where Bilbo is and that two of them are liars. Oin confessed that he knew where Bilbo was, and Gloin said he didn't know. When Ori answered whether or not Oin knows where Bilbo is, Gandalf knew who's lying and who's telling the truth.

*Gandalf couldn't hear Ori's answer.*

**Balin and Dwalin**Elrond had his suspicions on Balin and Dwalin. He asked them "Do you both tell the truth?" He couldn't tell anything from Balin's answer (which was yes or no).

Beorn asked "Are you both liars? He couldn't tell anything from

*Balin's*answer, which was yes or no.

Bard asked Balin: "Is it true that you tell the truth and Dwalin lies?" Bard couldn't learn anything from his answer.

Gandalf read this and knew of both Balin and Dwalin whether they lie or not.

**Thorin, Kili and Fili**The Arc Stone was stolen from Thorin's chambers. Bilbo, Kili and Fili were in these rooms and Thorin accuses them of theft.

Gandalf's research shows that if Bilbo was guilty, he would have had an accomplice.

He also finds that Kili and Fili are both either guilty or innocent. Gandalf knows that if there are two guilty dwarves, Bilbo is one of them. Fili and Kili both say Bilbo stole the Arc Stone.

**The Mordor Spy**Gandalf's problems aren't over yet. He now has to find out which of the dwarves spies for Mordor. With the knowledge who lies and who tells the truth, he can use clever questions to exclude dwarves from his research. The spy is one of the remaining dwarves of which Gandalf doesn't yet know whether they lie or not.

These dwarves are lined up next to each other in alphabetical order. The first dwarf says the last one in the row lies, but the second-to-last one tells the truth.

The second dwarf says he's innocent.

The second-to-last dwarf says the last dwarf lies. The last dwarf says he's guilty.