How the president ________ this effective solution to the problem remains unknown.
考查短语词义。选项A. put up with（容忍，忍受）；选项B. came up with（想出，提出）；选项C. caught up with（赶上，追上）；选项D. kept up with（紧跟，跟上）。所以根据句意，选B。
【参考译文】总统如何想出解决这个问题的有效办法还不得而知。