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From the people behind the Alan Turing Cryptography Competition.

Puzzle 2.

Grobnog the Goblin King was sitting on his throne consulting with Torqmaga the Inquisitor. “Your Majesty, we've been infiltrated by a rogue group of Goblins,” said Torqmaga. “They call themselves Nilbogs. Physically they are identical to Goblins, but – unlike true Goblins – they always tell the truth.”

"Our whole society is founded on Goblins being evil and lying whenever they can!" said Grobnog. "We need to identify these interlopers!"

Torqmaga handed over a piece of paper. "I've tortured all of your subjects to find out who is a Goblin and who is a Nilbog. I can assure you that under my questioning, everybody was true to their real nature: every Nilbog told the truth and every Goblin lied."

Grobnog inspected the list. "What does 'or' mean here? Does it mean 'one or the other or both'?" he asked.

Torqmaga nodded. "Yes, your Majesty, it's the logical meaning of the word 'or'. It seems that torture turns Goblins and Nilbogs into very logical monsters. I'm sure you can work out from their statements below who is a Goblin and who is a Nilbog."

Agmiz “Fragdag would definitely say that I'm a Goblin.”
Bord “Exactly one of Iz and Molk is a Nilbog.”
Cherguff “Those good-for-nothing layabouts Dolk and Lold are the same type of monster as Molk.”
Dolk “Stop the torture! Bord and Yobblot are both Nilbogs or both Goblins!”
Erkaz “I may hate his guts, but Toxplok and I are the same type of monster.”
Fragdag “Quonk and Xinik are Nilbogs.”
Gneeg “Zisbut and I are different types of monster.”
Hrunk “Gneeg is most definitely a Goblin.”
Iz “Molk is a Nilbog and deserves everything Grobnog will do to him.”
Jop “Bord would say that Fragdag is a Nilbog.”
Klaatak “Lold is a traitorous Nilbog!”
Lold “Ronx is a loyal Goblin! Will you let me off the rack now?”
Molk “Erkaz never tells me the truth, she's a typical Goblin.”
Norbet “All I'll say is that Wizmok is a Goblin or Zisbut is a Nilbog.”
Oinq “Agmiz and Quonk are loyal to Grobnog! They're both Goblins!”
Plegkurk “Dolk and Hrunk are either both Nilbogs or both Goblins.”
Quonk “Oinq, if he ever stopped eating, would say that I'm a Nilbog.”
Ronx “Xinik and Bord are both evil Nilbogs.”
Squee “Lold is a typical Goblin - he owes me 200 silver pennies!”
Toxplok “That little toerag Cherguff would say I'm a Nilbog.”
Udonk “Iz would say that Ronx was a Goblin.”
Vuird “Ronx would say that Udonk is a Nilbog.”
Wizmok “What can I say? Iz is a Nilbog or Norbet is a Goblin. Will that do?”
Xinik “I know that if you ask Ronx then he'd say Squee is a Nilbog.”
Yobblot “Klaatak and Squee are both Goblins.”
Zisbut “Hrunk is a goblin — the most disgusting I've ever met.”

Your task is to work out which of the 26 monsters above are goblins and which are nilbogs.

Enter your answer as a sequence of 26 letters: G (for Goblin), N (for Nilbog) arranged in the order of the 26 goblins/nilbogs listed above. If you think that Agmiz is a Nilbog, Bord is a Nilbog, Cherguff is a Goblin, Dolk is a Nilbog, ..., Zisbut is a Goblin then you should enter your answer as NNGN...G.

Your answer:
No answers can currently be submitted as the competition is closed.
MathsBombe 2017 is organised by the The School of Mathematics at the University of Manchester.
Contact us via mathsbombe@manchester.ac.uk with any queries.