2. (1 mark) A clock has an hour hand of length 3 and a minute hand of length 4. From 1:00 am to $1: 00 \mathrm{pm}$ of the same day, find the number of occurrences when the distance between the tips of the two hands is an integer.
(1 分) 一時鐘的時針長為 3 , 分針長為 4 。問在同一天上午一時至下午一時的一段時間内, 時針與分針的端點的距離為整數多少次？
2. Between 1:00 am and 1:00 pm, the hands overlap 11 times. Between two overlappings there are 11 times when the distance is an integer (2 times for distances equal $2,3,4,5,6$, and 1 time for distance equals 7). After the last overlapping (12:00 noon), and before 1:00 pm, again 11 times when distances are integers. Thus altogether $11+11 \times 10+11=\underline{\underline{132}}$ times that distances are integers.