1. How many times do the second hand and the minute hand form a $45^{\circ}$ angle between 0 and 12 o'clock?
【Answer】1416
【Analysis】Clock problem
Every hour, the minute hand moves 1 round, the second hand moves 60 rounds, the second hand moves 60-1=59 (rounds) more than the minute hand, so they overlap 59 times, and before and after each overlap, there is one time when they form a $45^{\circ}$ angle, so there are $59 \times 2=118$ (times) per hour, from $0-12$ hours, which is 12 hours, $12 \times 118=1416$ (times)