###### Asked in Math and Arithmetic

# How do you find How many numbers are there between 200 and 300 in which 9 occurs only once?

## Answer

###### Wiki User

###### August 02, 2012 11:38AM

There are three digits. The numbers are between 200 and 300 so a 9 cannot occur in the first digit.

So there are three possibilities:

A: it appears ONLY in the second digit,

B: it appears in the second AND third digits

C: it appears only in the third digit.

You want to know the number of occurances of A and C but not B.

A: These are numbers of the form 29x where x can be any number other than 9 (in that case it would be type B). So there are 9 possible values of x in A.

C: These are numbers of the form 2y9 where y can be any number other than 9 (in that case it would be type B). So there are 9 possible values of y in C.

Incidentally, although you don't need it,

B: There is only one number, and that is 299. So there is 1 possible values in B.

So, number of type A + number of type B = 9 + 9 = 18.