How many times in a day the hands of a clock are straight?

44

The hands of a clock (the hour hand and the minute hand) are considered "straight" in two different positions:

1. When they are overlapping (coincident / $0^{\circ}$ angle)
2. When they are opposite to each other (pointing in exactly opposite directions / $180^{\circ}$ angle)

The Breakdown:

• In a 12-hour period:
• The hands overlap exactly 11 times.
• The hands point in opposite directions exactly 11 times.
• Total straight positions in 12 hours = $11 + 11 = 22$ times.
• In a full day (24 hours):
• Total straight positions = $22 \times 2 = 44$ times.