The U.S. Government has discontinued making pennies. This reminds me of what I consider as the best example of the power of successive multiplication.
Consider a roll of fifty pennies that is stored in a cash register. This could also be a stack of fifty pennies or any set of fifty coins that has two different sides, such as heads and tails. We could vary the positions of the pennies in the roll, and also flip each penny so that heads is facing one way and tails the other or vice-versa.
I calculated that, in this roll or stack of pennies or other coins, there is a possible combination for every three atoms in the entire universe.
The number of atoms in the universe is believed to be about 10 (80), or a 1 followed by 80 zeros. 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. 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 these two possibilities multiplied by itself fifty times, and then multiplied by the first number. We get 1.125899906 x 10 (15). This gives us a total of 3.42432247 x 10 (79). In other words, there is a possible combination for about every three atoms in the universe.
If we wanted to add more combinations, far more than the number of atoms in the universe, we would only need to add another penny to the sequence.
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