Question

Find the sum of the four-digit greatest number and the five-digit smallest number, each number having three different digits

Answer 1

Step 1: Finding largest four-digit number with three different digits

1. Collect the three largest digits (which are $7$, $8$ and $9$)
2. Arrange them in descending order (i.e., $978$)
3. Add the largest among them to the left-most position until the required length (four in this case) is reached (i.e., $9978$)

Thus, the largest four-digit number with three different digits is $9978$

Step 2: Finding smallest five-digit number with three different digits

1. Collect the three smallest digits (which are $1$, $2$ and $3$)
2. Arrange them in ascending order (i.e., $123$)
3. Fill the remaining required places with the smallest number that is that many digits long ($10$ in this case)

Thus, the smallest five-digit number with three different digits is $10123$

Step 3: Finding their sum

Their sum is, $10123+9987=20110$

Therefore, the sum of the four-digit greatest number and the five-digit smallest number, each number having three different digits is $20110$