Ship's Bells

Number Theory Level pending

A ship’s bell ringer rings/strikes a certain amount of bells every half hour of a 4-hour period. After the first half hour he strikes 1 bell. After the second half hour he strikes 2 bells, and so on until he strikes 8 bells at the end of the 4 hour period. He then begins a new 4-hour period. This goes on for25 years. Each consecutive year the amount of bells rung at each time interval in each 4-hour period is multiplied by 3. However, given the bell ringer is very lazy and sleeps on the job, the first year the ship’s clock does not ring for 1 month. The next year, it does not ring for 1/3 of a month. The next year 1/9 of a month, and so on and so forth. Assume that all months are 30 days and that there are no leap years. There are 12 months in a year.

How many bells did the bell ringer miss in the 25 years?

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