How many phone numbers are there?

Dear Editor:

I would like to address the issue of bringing in another area code. It seems like technology is going backwards. When I was a kid, we had a short number like 859J. Then it got longer and went to RA3-4209 and then to 723-4209. Now they want to make it longer yet. Why is this?

I would like to call the attention to mathematicians and math teachers about this issue. I cannot believe that all numbers going with 814 are exhausted. Unless I am mistaken, it seems like there would be a lot more number combinations than there are phones in the 814 area code.

I break down a phone number into 3 parts- area code, office code and number.

Let’s analyze this. 814 would be the constant in this.

So you move to the office code. How many combinations are there in this 3 digit number. You have to add in the duplicates. For example, using two 2’s, you would have 221 or 220 or 122 or 212 or 202 or 222. How many combinations are there with just the 3 digit numbers from 0-9?. Then you move on to the 4 digit numbers. There are many combinations of these. Then when you hook all of the 3 number combinations to the 4 digit combinations, I believe it would be in the thousands and far more than the total number of phones.

If I am not mistaken, factorial would come into some of this but you have to consider the number of different combinations when hooking the office code and the number together in different combinations.

I have never heard of phone office codes that begin with or 000 or 111 and up the line.

I would love for a math person to calculate how many number combinations there are in all of the possible scenarios there are for the office codes and the numbers. It seems to me that the number of them would far exceed the number of phones out there. Is anyone up to the task? Feel free to email me at blkkk@yahoo.com in case you do not wish to send your solution to this column.


Barry Keller



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