Maths Olympiad Prep

Library / /104 of 175

, 2024

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

Jokers always lie. Clowns always tell the truth. A group of four, each of whom is a Joker or a Clown, make the following statements about each other: P says, "Q always lies"; Q says, "R always lies"; R says, "P always tells the truth"; S says, "Exactly two of P, Q and R are Jokers". How many of P, Q, R and S are Clowns?

(A) 00 (B) 11 (C) 22 (D) 33 (E) 44

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.