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Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

How many of the four statements below are true? 1. Exactly two of the statements are false. 2. This statement is true. 3. The previous statement is true. 4. The first three statements are false.

(A) $0$ (B) $1$ (C) $2$ (D) $3$ (E) $4$

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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.