Reference no: EM13588346

Consider the integers from 0 to 999,  written in the normal  way. We will ask several questions about these  numbers, and then ask you some questions about the questions.

a) How many of these numbers contain exactly one  digit 0?

b) How many of these numbers contain at least one digit 0?

c) What is the total number of digits 0 that appear in all these numbers?

Now, sometimes the numbers from 0 to 999 have to be written with three digits no matter what, for  instance, in  marking answers on a computer  scan  sheet  for the  AIME  exam. In  such cases, 0 is  written as 000 and 23  is  written  as  023.  Answer  a)-c)  again  for  the  numbers  from 000 to  999 written this way. That  is, answer

a) How many of these specially written numbers contain  exactly one digit 0?

b) How many of these specially written numbers contain  at least one digit 0?

c) Which  set of questions,  a)-c) or a′)-c′),  did  you  prefer? Why?

d) Of  your six solutions, which did you like best? Why?