If a clock tower strikes once at one o'clock,twice at two o'clock,thrice at three o'clock,then how many times does the clock strike altogether in 24 hours?
Assuming a 24-hour clock and chime, that would be
24/2 (2+23)
If it starts over again with one chime at 1:00, then the sum is
2*12/2(2+11)
the answer is 156
To determine how many times the clock strikes in 24 hours, you need to consider the pattern. The clock tower strikes the number of times corresponding to each hour.
From the given information, we know that the clock tower strikes once at one o'clock, twice at two o'clock, and thrice at three o'clock.
Therefore, for every hour after three o'clock, the clock tower will strike the same number of times as the hour itself. For example, at four o'clock, it will strike four times, and at five o'clock, it will strike five times.
In a 24-hour duration, we need to count the number of times the clock strikes from one o'clock to twelve o'clock and then add the count from one o'clock to twelve o'clock again.
Let's break it down step by step:
1. Count the strikes from one o'clock to twelve o'clock:
- The clock tower strikes once at one o'clock.
- The clock tower strikes twice at two o'clock.
- The clock tower strikes thrice at three o'clock.
- For each hour from four o'clock to twelve o'clock, the clock tower strikes the same number of times as the hour itself.
So, to count the strikes from four o'clock to twelve o'clock, we can sum the numbers 4, 5, 6, 7, 8, 9, 10, 11, and 12.
Using the formula for the sum of the first n natural numbers (n * (n + 1) / 2), we can calculate this sum:
Sum = 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = (9 * (9 + 1)) / 2 = 9 * 10 / 2 = 45.
Therefore, the number of strikes from one o'clock to twelve o'clock is 1 + 2 + 3 + 45 = 51.
2. Multiply the result by 2 to account for both the first twelve-hour cycle and the second twelve-hour cycle: 51 * 2 = 102.
Hence, the clock strikes a total of 102 times in 24 hours.