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Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

You can choose four positive integers $X$ , $Y$ , $Z$ and $W$ . What is the maximum number of odd numbers you can obtain from the six sums $X+Y$ , $X+Z$ , $X+W$ , $Y+Z$ , $Y+W$ and $Z+W$ ?

(A) $2$ (B) $3$ (C) $4$ (D) $5$ (E) $6$

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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.