Straight line (0° or 180°) each day: How many times in a day are the hands of a clock in a straight line (either overlapping or opposite)?

Introduction / Context:
A “straight line” means either 0° (overlap) or 180° (opposite). In 12 hours, the hands overlap 11 times and are opposite 11 times. Over a full day (24 hours), each of these occurs twice as often, totaling 44 straight-line occurrences.

Given Data / Assumptions:

• Uniform hand motion; standard 12-hour analog clock.
• Co-linear events comprise both overlaps and oppositions.

Concept / Approach:
Known counts per 12-hour cycle: 11 overlaps and 11 oppositions. Multiply by 2 for 24 hours.

Step-by-Step Solution:

Verification / Alternative check:
The average spacing between overlaps is ~65 5/11 minutes; doubling counts for 24 h yields the standard results used in clock problems.

Why Other Options Are Wrong:
24/22/42 are partial counts; 44 uniquely includes both types for the entire day.

Common Pitfalls:
Counting only overlaps or only oppositions, or assuming one per hour.

Final Answer:
44