Telephone Numbers Day - October 26

Happy Telephone Numbers Day!

You may be surprised to learn that these aren't the telephone numbers associated with our individual telephones, but instead represent the number of ways that n number of telephones can be connected to each other for 2-way calls.

For example, if you have 0 phones or 1 phone, there only 2-way "connection" possible is no connection at all. But if you have 2 phones, there are now 2 possibilities: no connection at all or the 2 phones connected to each other. This table shows the number of combinations possible when you have very few phones:

You might notice that the number of combinations starts very small but then grows pretty quickly. This is one reason why it's impractical to set up a telephone network with equipment dedicated to every possible phone call combination. Actually writing and counting all those combinations would get tedious pretty quickly; fortunately there's a formula for that:

Applying this formula, you can see just how quickly the numbers in the telephone number sequence increase:

We celebrate telephone numbers today because 10 and 26 are the largest telephone numbers that comprise a date: 10/26 or October 26.