# Naughty Elves

Santa Claus was in a very bad mood when he discovered that some of his elves had stuck sandpaper on the skis of his sleigh. Of the 8 suspect elves, only two told the truth in the investigation that was carried out, which allowed the joker elf to be discovered:

Silly: It was Puk who did it.
Stump: No, it was me.
Pip: It wasn't Puk.
Puk: Pip lies.
Roly: The culprit could only be Stump or Jollly.
Poly: It was Stump.
Jolly: It wasn't neither Stump nor me.
Nick: Jolly tells the truth and neither was Puk.

Which of them spent so much joke on Santa Claus?

#### Solution

This is what the elves declared schematically:
Silly -> Puk
Stump -> Stump
Pip -> NO Puk
Puk -> Puk
Roly -> Stump O Jolly
Poly -> Stump
Jolly -> NO Stump AND NO Jolly
Nick -> NO Stump and NO Jolly and NO Puk

The last proposition is false, because from the information given by the elves it is clear that the culprit must be Stump, Jolly or Puk.

Nick lies and as he lies, what Jolly has said is not true, so Stump or Jolly is to blame.

Silly and Puk have also lied, because Puk can't be the culprit and we know that Pip and Roly are telling the truth (I can't be Puk and the culprit is between Stump or Jolly). As there are only two true elves Stump and Poly are lying, so Stump has not been guilty.

The culprit is Jolly.