Problem: The estimated difference between the largest and smallest 3 digit numbers formed by given digit is found to be 220. Which of the following sets of 3 digits satisfy the above given condition?

Solution:
To find the solution to this problem, we need to first understand what is meant by the term "3 digit numbers formed by given digit."

Understanding the problem:
The problem statement mentions that we need to find the difference between the largest and smallest 3 digit numbers formed by a given digit. Let's assume that the given digit is 'x.'

To form a 3 digit number using the digit 'x,' we can place the digit in any of the three places - hundreds place, tens place, or ones place. Let's consider all the possible combinations of 'x' in these three places.

- If 'x' is placed in the hundreds place, then the other two places can be filled with any of the 9 digits (excluding 0 and 'x'). So, there are 9 x 9 = 81 such 3 digit numbers.
- Similarly, if 'x' is placed in the tens place, then the hundreds and ones places can be filled with any of the 9 digits. So, there are again 9 x 9 = 81 such 3 digit numbers.
- If 'x' is placed in the ones place, then the hundreds and tens places can be filled with any of the 9 digits. So, there are again 9 x 9 = 81 such 3 digit numbers.

Therefore, the total number of 3 digit numbers formed by the digit 'x' is 81 + 81 + 81 = 243.

Next, we need to find the difference between the largest and smallest 3 digit numbers formed by 'x' such that the difference is 220.

Calculations:
Let the three digits be a, b, and c. We need to find the values of a, b, and c such that the difference between the largest and smallest 3 digit numbers formed by these digits is 220.

- The largest 3 digit number formed by these digits is abc (in descending order)
- The smallest 3 digit number formed by these digits is cab (in ascending order)

The difference between these two numbers is (100a + 10b + c) - (100c + 10a + b) = 99a - 99c = 99(a - c).

Since we know that the difference is 220, we can write the equation as:

99(a - c) = 220

Solving for (a - c), we get:

a - c = 220/99

This is not an integer value, so we cannot find a, b, and c that satisfy the given condition.

Therefore, there are no sets of 3 digits that satisfy the given condition.

Conclusion:
The given problem requires us to find the sets of three digits such that the difference between the largest and smallest 3 digit numbers formed by these digits is 220. We found that there are no such sets of digits that satisfy this condition.