SOLUTION: A very annoying clock at your house chimes at the beginning of nth hour, 2n times. ( For example, at 8:00A.M. the clock chimes 16 times and at 2:00P.M. the clock chimes 28 times)

Algebra ->  Probability-and-statistics -> SOLUTION: A very annoying clock at your house chimes at the beginning of nth hour, 2n times. ( For example, at 8:00A.M. the clock chimes 16 times and at 2:00P.M. the clock chimes 28 times)       Log On


   



Question 472129: A very annoying clock at your house chimes at the beginning of nth hour, 2n times. ( For example, at 8:00A.M. the clock chimes 16 times and at 2:00P.M. the clock chimes 28 times) The clock also chimes three times at half-past every hour. Determine how many times in total the clock chimes in one full day.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I will start the day at 1 AM
The clock chimes +2%2A1+=+2+ times
The number of on the hour chimes are:
+2%2A1+%2B+2%2A2+%2B+2%2A3+%2B+2%2A4+ . . . to +2%2A24+
+2%2A%28+1+%2B+2+%2B+3+%2B+4+%29+ etc.
The formula for the sum of digits 1 through n is
+%281%2F2%29%2An%2A+%28n%2B1%29+
When +n+=+24+
Twice the sum = +2%2A%281%2F2%29%2A24%2A25+
+24%2A25+=+600+
3 chimes each half hour, from 1:30 AM to 11:30 PM is +23+ chimes
+23%2A3+=+69+
Total = +600+%2B+69+=+669+ answer
Hope I got it