How many times are the hands exactly 45° apart between the time on clock A and the time on clock B, the same afternoon?

A shows 1:00 and B shows 4:00. A 45° angle occurs with the minute hand 45° behind or 45° ahead: at 1:00 the gap is 30°, so between 1 and 2 only the 45°-ahead time (1:13 7/11) occurs, as the next 45°-behind time is at 2:02 8/11. Between 2 and 3: 2:02 8/11 and 2:19 1/11. Between 3 and 4: 3:08 2/11 and 3:24 6/11. Total 5. (6 assumes two per hour; 4 misses the first one after 2:00.)