A wall clock in Rohan's study shows the time as 3:40. Rohan is curious about the angles formed between the clock's hour and minute hands at this and several other times throughout the day, and works these out using the standard rule that the minute hand moves 6 degrees per minute, measured from the 12 o'clock position, while the hour hand moves 0.5 degrees per minute, also measured from the 12 o'clock position.

Separately, Rohan has also noticed that the hour and minute hands of a clock coincide, pointing in exactly the same direction, at certain repeating intervals throughout each 12-hour period, and he wants to work out exactly how often this happens and at what specific times, using the same movement rules for both hands.