At noon and midnight the hour and minute hands are exactly coincident with each other. How many other times between noon and midnight do the hour and minute hands cross?

The hour and minute hands coincide at noon (12:00) and midnight (0:00). Between noon and midnight, they cross 10 more times. This happens approximately every 65 minutes when the minute hand catches up to and passes the hour hand. The 11 crossings between noon and midnight occur at times like ~1:05, ~2:11, ~3:16, etc., with the 11th crossing happening at 12:00 (midnight).