**Q&A** *When:* **Sep 1 **and Sep 4**, 6-7pm London time**, or **other times by request** (email/slack me to organize) *Where:* https://harvard.zoom.us/j/93864667215?pwd=azQxKzhtZUtlUkxJczNYOXVuSlhHUT09 **Abstract** Superlative-modified numerals (SMNs) exhibit many interesting patterns. Two notable sets of patterns are related to scalar implicatures and ignorance; for lack of space I will discuss them only cursorily here, though they will be kept in mind. Two further sets of patterns have to do with polarity sensitivity, and these are the focus of this talk: **(Polarity sensitivity 1, aka positive polarity)** SMNs are bad in downward-entailing (DE) environments, e.g., the scope of negation (*Jo didn't solve # at least 3 problems*) except for Strawson-DE environments, e.g., the first argument of a conditional(/universal) (*If Jo solved at least 3 problems, she passed*. **(Polarity sensitivity 2)** And their acceptability in the first argument of a conditional(/universal) varies with the lexical/conventional/grammatical polarity of the SMN (*If Jo solved # at most 3 problems, she passed*), of the predicates in the first/second argument (*If Jo solved at least 3 problems, she # failed*), and of the first/second argument itself (*If Jo # didn’t solve at least 3 problems, she passed*). I derive these patterns from silent exhaustification via O(nly) and E(ven). **O** operates on the ***non-entailed*** (scalar and) **subdomain alternatives** to yield (scalar implicatures, ignorance, and) **polarity sensitivity 1**. **E** operates on the ***entailed* scalar alternatives** to yield **polarity sensitivity 2**. Overall, SMNs emerge as items that want all their alternatives to contribute to their strengthening, and recruit both O and E to achieve that.