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Number theory Difficulty 2.0 Junior Find the answer United Kingdom

How many sets of three consecutive integers are there in which the sum of the three integers equals their product?

(A) $0$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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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.