Question

Write (i) the smallest (ii) the largest 6 digit numbers having four different digits.

Answer 1

(i) Four smallest digits are 0, 1,2 and 3. In order to generate the smallest 6-digit number using digits 0, 1, 2 and 3, we write the smallest non-zero digit at the place having the highest place value and the largest digit at the place having least place value. Thus, we put 1 in the left-most place and 3 in the right-most place. Digit 2 is put at ten's place and at all other places we write zero.
Hence, the required number = 100023.

(ii) To write the greatest 6-digit number having four different digits, we will have to use four largest digits. Clearly 9, 8, 7 and 6 are four largest digits. In order to write the largest 6-digit number using digits 6, 7, 8 and 9, we put the largest digit 9 at the place having the highest place value. The smallest digit 8 is put at the hundred's place, the smallest digit 6 is put at the right most place i.e. at unit's place and the digit 7 is put at the ten's place. All other places are filled by 9.
Hence, the required number = 999876.