The total number of times, the digit 3 will be written, when the integers having less than 4 digits are listed is equal to

- - 3- 3 -3 - -- 3 33 3 -3 - 3Any place other than 3 is filled by 9 ways as 0 can appear anywhere which gives all types of numbers such as single digit, two digits, etc. Alternate solution: Three-digit numbers from 000 to 999 means 1000 numbers, each number constituting 3 digits. Hence, the total numbers of digits which we have to write is 3000. Since the total number of digits is 10 (0 to 9) no digit is filled preferentially. Therefore, number of times we write 3 is 3000/10 = 300.