Olympiad problems

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2014 JHMMC 7 Contest, 24

When submitting problems, Steven the troll likes to submit silly names rather than his own. On day $1$, he gives no name at all. Every day after that, he alternately adds $2$ words and $4$ words to his name. For example, on day $4$ he submits an $8\text{-word}$ name. On day $n$ he submits the $44\text{-word name}$ “Steven the AJ Dennis the DJ Menace the Prince of Tennis the Merchant of Venice the Hygienist the Evil Dentist the Major Premise the AJ Lettuce the Novel’s Preface the Core Essence the Young and the Reckless the Many Tenants the Deep, Dark Crevice”. Compute $n$.

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