when do you say amen

Question

Can you say amen to a bracha if you hear the last part, see a gesture of ending, or is it only if you hear all of the brachah.

Answer 1

The Mishnah (Berachos 8:8) states that we answer Amen even after hearing a partial berachah from a Jew, but not from a Cuthean (who is suspect of having addressed the blessing to Mt. Gerizim, the site of their place of worship).

This is codified as halachah in Shulchan Aruch (Orach Chaim 215:2). Mishnah Berurah there (subsection 6) records variant opinions as to whether this applies only when one heard everything from Hashem's name onwards (i.e., basically the entire blessing except for the words "baruch atah"), or if it is also when one hears just the very end of the blessing (e.g., "borei minei mezonos").

Answer 2

To support Alex's point there is a Gemara in Yoma among other places that talks about the Shul in Alexandria that had flags which helped people indicate when to say Amen