At/With/On Short Notice
Solution 1:
All three are common and idiomatic.
Based on my resourses, "at short notice" tends to be British English - so perhaps "on short notice" is more American.
"With short notice" is, as I said, correct and to me personally there is nothing wrong with using all of them interchangeably. But you should ask your teacher or mentor which style of the interpretation they prefer.
Dictionaries may not consider "with short notice" a well-established phrase but that doesn't necessarily mean it's wrong.
- Expressions with the same meaning: on/at/with a moment's notice.