Question

If we listed all numbers from 100 to 10,000, how many times would the digit 3 be printed?

Answer 1

Answer:

990

Step-by-step explanation:

Imagine writing all the numbers from 0 to 9999, but always using 4 digits, so the smaller numbers have 0s on the left.  So we have a list of numbers like this:

0000

0001

0002

....

9998

9999

Each digit gets used equally often.  There are 10000 numbers in this list and there are 10 digits, so each digit appears 1000 times.

Similarly, in the list of 2 digit numbers (allowing them to start with 0)

00  01  02  ...  98  99

each digit is used 100 / 10 = 10 times.

So the number 3 appears 1000 times in the first list and 10 times in the second list, meaning that it turn ups 1000 - 10 = 990 times when listing the numbers from 100 to 10000.