I'm not sure if there are other words that fail, but my search for "Contains Words: do" with no other restrictions returns zero results, while Cmd-f "do" on the All Tasks page finds several.
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This is a MySQL issue, specifically you have to configure it to index words of 4 characters or less, and disable common stopwords (like an, the, etc).
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Yeah, see the MySQL docs on ft_min_word_len and ft_stopword_file. You or another administrator should have addressed or ignored some warnings about these settings already if you're near HEAD, but you'll need to set them more aggressively than we suggest to index words like "do", "the", etc. Indexing very short/common words may make the index huge and/or slow, although it'll probably be fine.
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Perhaps a warning when searching for words which are below the current known ft_min_word_len would demystify the behavior.