The Power Of Multiplication

Here is just something to think about.

Most people remember the classic example used in school to illustrate the surprising power of successive multiplication. Suppose a laborer did some work for someone for a month. The employer asks the laborer how much he would like to be paid. The laborer answers " a penny on the first day doubled every day so that I would be paid two cents on the second day and four cents on the third day and so on and I must be scheduled for at least thirty days.

"Wow, what a bargain this is" thought the employer as he agreed to pay the laborer as he requested. However, the employer did not stop to consider the power of successive multiplication and had to pay the laborer over ten million dollars (or pounds, euros, rupees, etc,) for thirty days work.

One day while messing around with a scientific calculator I discovered what I consider as a more space age example of the power of successive multiplication. Consider a roll of pennies that is stored in cash registers. There are fifty pennies in a roll, or we could just take any stack of fifty coins. We could vary the position of the pennies in the roll and also flip each penny so that the heads side is facing one way and tails the other or vice versa.

I calculated that in this roll of pennies, there are more possible combinations than there are atoms in the entire universe.

The number of atoms in the universe is believed to be about 10 (79) or a 1 followed by 79 zeroes. If we take the factorial of 50 (50!), which is 50 x 49 x 48... back to 1, it will give us the number of possible combinations in the sequence of pennies in the roll. I come up with 3.04140932 x 10 (64).

Remember that we can also flip each penny in the sequence for heads or tails to face in a given direction. So, we would take 2 multiplied by itself fifty times and multiply it by the first number. We get 1.125899907 x 10 (15). This gives us a total of 3.42432247 x 10 (79). In other words, within our roll of pennies, there are three possible combinations for each and every atom in the entire universe.