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I saw an ad for a japanese radio station which had this in it. Here's the full facebook post for context. https://bit.ly/2vXWVHg
「一発解決お悩み相談」を始めました。
What I'm wondering here is how 一発 would translate. Explosive Solution? Homerun Solution? Perfect?
Also, why is there no particle between お悩み相談 and 一発解決?
発 is a counter for shots/launches (gun, rocket, arrow, fireworks, etc), and, by extension, trials/attempts. For example 一発で成功する means "to succeed on the first attempt", and 一発合格 means "pass on the first try". Likewise, 一発解決 describes how your trouble will be solved quickly without trying many options. So "instant" is close to this 一発, but there may be a better catchy word.
As for the "missing" particle between 一発解決 and お悩み相談, they are treating お悩み相談 as the "main" title and 一発解決 as its catchphrase or "subtitle". Just like title: subtitle is a common format in English (e.g, "Mad Max: Fury Road", "2001: A Space Odyssey"), in Japanese, attaching a subtitle/catchphrase-like word directly before a name is a common way to form an interesting title (e.g., 名探偵コナン, 燃えよドラゴン, ジャングルの王者ターちゃん, わくわく動物ランド).
One time resolution or quick resolution. They won't turn into your therapist for you to discuss all your troubles over several weeks. They answer one burning question you have and try to give their best advice. 一発 is an adverbial noun, it doesn't need a particle after it.
一発 is an adverbial noun, it doesn't need a particle after it. -- う～ん。。？ 「一発解決」って複合語になってて、「一発で解決する」って意味じゃないんですかね。。ad ですから…。こういう感じで。。→ japanese.stackexchange.com/a/19379/9831
why is there no particle between お悩み相談 and 一発解決?): japanese.stackexchange.com/a/19379/9831