Between the early-morning time on clock A and the time on clock B just after noon, how many times do the hands point in exactly opposite directions?

A shows 5:50 a.m. and B shows 12:40 p.m. Opposite positions occur every $65\frac{5}{11}$ min, at about 6:00, 7:05, 8:10, 9:16, 10:21, 11:27 and 12:32: 7 times. (6:00 is just after 5:50, so it counts; 6 forgets it.)