4. Kolya started playing $W o W$ at the moment when the hour and minute hands were opposite. He finished playing after an integer number of minutes, and at the end, the minute hand coincided with the hour hand. How long did he play (if it is known that he played for less than 12 hours)
Solution: The minute hand catches up with the hour hand at a speed of $\frac{11^{\circ}}{2}$ /min. For them to coincide, the difference in their angles of rotation should be $180+360 k$. This value is a multiple of 11 when $k=5,16, \ldots$. According to the problem, only $k=5$ fits, which gives us 6 o'clock.