# Number System 3

### From Homeworkwiki

**1. Write the smallest 4-digit number of four different digits.**

**Solution:** The smallest 4 different digits are 0,1,2 and 3.

Thus, the required number is the smallest 4 digit number formed by using the digits 0,1,2 and 3, which is 1023.

**2. Write the greatest 4 digit number of four different digits.**

**Solution:** The greatest 4 different digits are 9,7,8 and 6.

Thus, the required number is the greatest 4 digit number formed by using the digits 9,8,7 and 6, which is 9876.

**3. Write the smallest 6 digit number using three different digits.**

**Solution:** The smallest 3 different digits are 0,1 and 2.

Clearly, we have to form the smallest 6 digit number using the digits 0,1 and 2, which is possible only if we repeat the smallest digit i.e. 0.

So, the required number of times i.e. 4 times.

Clearly such a number is 100002.

**4. Write the greatest 6 digit number using three different digits.**

**Solution:** The smallest 3 different digits are 9,8 and 7.

Thus, the required number is the greatest 6 digit number formed by using the digits 9,8 and 7 which is possible only if we repeat the greatest digit

i.e. 9 the required number of times i.e. 4 times.

Clearly, such a number is 999987.