You are here:

- Home
- Science
- Mathematics
- Number Theory
- Enumerating call letters

Advertisement

Radio stations in the United States that are east of the Mississippi River have call letters consisting of a W followed by three letters (W can be used again). How many different call letters of this type are possible? My book says 17,576 but does not break it down, nor does it provide a similar practice problem. I figure the alphabet has 44 letters and I got stuck after that. Can you explain the logic (if any) in getting this answer? Thank you.

I'm not sure where the 44 came from, but the alphabet, A to Z, only has 26 letters.

Since 26*26 = 520 + 156, and that is 676, that is the number for two letters.

Since 26*676 = 13,520 + 4,056 = 17,576, that is the number for three letters.

The first few powers of 26 are

26

676

17,576

456,976

11,881,376

308,915,776

8,031,810,176

208,827,064,576

5,429,503,678,976

I find it interesting that one 26 squared, all of the rest of the powers end in 76.

I can answer almost anything that is sent in. If I can't, I'll let you know, but I don't expect that to happen much.

I have known about number theory since the mid 80's. I have answered over 250 questions on Number Theory with this software. Altogether, I have answered over 8,500 questions in mathematics.**Publications**

You're looking at it ... I've answered over 8,500 quesitons in mathematics right here.
**Education/Credentials**

My credentials are an MS in Mathematics at Oregon State in 1986;
I received a BS in Mathematics at the same place in 1984.**Awards and Honors**

I graduated with honors in Mathematics when getting my BS degree and my MS degree.
**Past/Present Clients**

I have assisted many students in mathematics at OSU.
Perhaps I have assisted one of you're friends in math on a computer somewhere else,
but you don't even know... That would be late last night, perhaps with thousands of miles between us ...
Then again, if you're in Washington, so am I ...