A challenging case in web search and question answering are count queries, such as"number of songs by John Lennon''. Prior methods merely answer these with a single, and sometimes puzzling number or return a ranked list of text snippets with different numbers. This paper proposes a methodology for answering count queries with inference, contextualization and explanatory evidence. Unlike previous systems, our method infers final answers from multiple observations, supports semantic qualifiers for the counts, and provides evidence by enumerating representative instances. Experiments with a wide variety of queries show the benefits of our method. To promote further research on this underexplored topic, we release an annotated dataset of 5k queries with 200k relevant text spans.