Prince Kevin the Questionable has been captured by the Goblins and has been imprisoned at the centre of the Goblins’ labyrinth. The Goblins decide to release him and permit him to find his own way out of the labyrinth---but there’s a twist. Hidden within the labyrinth are the silent, but deadly, Grues, who will kill any trespasser who comes their way. At each junction in the labyrinth, Prince Kevin meets a group of monsters comprising Goblins (who always lie) and Nilbogs (who always tell the truth), but who are otherwise identical and indistinguishable (apart from their name badges). At each junction the path through the maze splits left and right. Monsters always stay true to their type. Prince Kevin has to make the correct sequence of left/right turns, otherwise he will face certain death at the tentacles of a Grue.

Below is the information each group of monsters tell Prince Kevin at each junction. Your task is to work out the correct sequence of left and right turns that Prince Kevin should make.

Junction 1:

Stoik: You should go left if, and only if, I’m a Nilbog. \br\br

Junction 2:

Ves: At least one of us is a Goblin.

Threlkeld: You should go left

Junction 3:

Wizbit: Either I’m a Goblin or Inigo is a Nilbog

Inigo: You should go left

Junction 4:

Prees: If I’m a Nilbog then so is Zlapdud

Zlapdud: You should go left

Junction 5:

Boghat: I’m a Goblin but Fizzik isn't

Fizzik: You should go left

Junction 6:

Rolfish: All of us are Goblins

Bulfim: Exactly one of us is a Nilbog

Braag: You should go left

Junction 7:

Gonk: All of us are Goblins

Buramog: Exactly one of us is a Goblin

Splot: You should go left

Junction 8:

Pronk: Donk is a Goblin

Donk: Pronk and Ronk are of the same type: both Goblins or both Nilbogs

Ronk: You should go left

Junction 9:

Dadgad: At least one of us is a Goblin

Kog: That's true!

Bizkit: You should go left

Junction 10:

Onog: Lorzub is a Nilbog

Lorzub: If Onog is a Nilbog then so is Smersh

Smersh: You should go left

Junction 11:

Oomigag: Ommigeg is a Goblin and Ommigog is a Nilbog

Oomigeg: Ommigag would say that I’m a Goblin

Oomigog: Ommigeg and I are different types of monster

Oomigug: You should go left

Oomigug: (Also, both Oomigeg and Oomigog agree that you should go left.)

Junction 12:

Jax: Plord and Lumdum are both Nilbogs

Ezrin: Plord and I are different types of monster

Plord: Ezrin is a Goblin

Lumdum: Jax and Plord are the same type of monster

Nuzgut: Jax is a Nilbog

Lumdum: Jeff is a Nilbog.

Jeff: You should go left.

Enter your answer as a string of 12 characters comprising L and R. (For example, if you think that Prince Kevin should go left at Junction 1, right at Junction 2, right at Junction 3, etc, then you should enter LRR…)

Mathsbombe Competition 2020 is organised by the The Department of Mathematics at The University of Manchester.
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