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Your Piggy Bank

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Dad gives you money every day to put in your new piggy bank. He gives money to you in such a way that the money in the piggy bank doubles with each passing day.

If you already have 1 cent in the piggy bank and Dad gives you 1 cent the first day, 2 cents the second day, 4 cents the third day and so on, then your piggy bank gets full on the 9th day.

1. On which day will your piggy bank be half-full?
For example, type 6 if your answer is 6th day.
Answer: 8

2. In addition to Dad's contributions, if Mom also gave you 1 cent the first day, 2 cents the second day, 4 cents the third day and so on, then on which day would your piggy bank be about half-full?
For example, type 6 if your answer is 6th day.
Answer: 7

Solution:

1. Since the money in the piggy bank doubles with each passing day, the piggy bank will be half-full the day previous to the one on which it gets full. Thus, the piggy bank will be half-full on the 8th day.

2. If both Mom and Dad contribute equal amounts to your piggy bank, then each needs to only make your piggy bank quarter-full. When both Mom and Dad contribute, the piggy bank will be half-full two days prior to the day it would be full when only Dad contributes. Thus, the piggy bank will be full on the 7th day when both Mom and Dad contribute.

Food for thought:

If Dad contributed to your piggy bank in this manner for 30 days, how much money would Dad have given you?
Would it be (230 − 1) cents, i.e., 1,073,741,823 cents or over 10 million dollars? Unbelievable!?

Doubling a number leads to a geometric progression and fantastic growth rates.


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puzzle : image for piggy bank

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