nose out
nose out {v.}, {informal}
1. To learn by effort (something private or secret); uncover.
The principal nosed out the truth about the stolen examination.
2. To defeat by a nose length; come in a little ahead of in a race or contest.
The horse we liked nosed out the second horse in a very close finish.
The Democratic candidate nosed out his rival for Congress by a few hundred votes.
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Source: A Dictionary of American Idioms