Hit upon

He hit upon all major concerns during the presentation.

Source: wiktionary

So next day the hunting began. I did not know how to shoot, but I proceeded to learn. And when I had expended some thirty shells for three seals, I decided that the ammunition would be exhausted before I acquired the necessary knowledge. I had used eight shells for lighting fires before I hit upon the device of banking the embers with wet moss, and there remained not over a hundred shells in the box.

Source: wiktionary

They hit upon the idea of a site that would help users exchange video files.

Source: wiktionary