A clock strikes 1 at 1 o'clock, 2 at 2 o'clock, …, 12 at 12 o'clock. How many total strikes occur in 24 hours?

Introduction / Context:This classic tally problem counts the total number of bell strikes over a day when a clock strikes n times at n o'clock.

Given Data / Assumptions:

• In 12 hours the clock strikes 1+2+...+12.
• Pattern repeats every 12 hours.

Concept / Approach:Sum of the first 12 natural numbers, then double it for 24 hours.

Step-by-Step Solution:Sum S = 1+2+...+12 = (12*13)/2 = 78.In 24 hours: 2*S = 156.

Verification / Alternative check:List small segments (e.g., 1–3 o'clock) to see the pattern, then scale.

Why Other Options Are Wrong:78 is only half day; 136 and 196 do not match doubling the 12-hour sum.

Common Pitfalls:Forgetting to double; mis-summing 1–12.

Final Answer:156 strikes