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- Hint: If digit at hundredth place of any 3-digit number is greater than digit at hundredth place of another 3-digit number than it is greater than the other number. Same will hold for the digit at tenth place only if the digit at hundredth place is the same for both.

For the greatest number we will make a digit at its hundredth place greatest which is 9. So the digit at its hundredth place will be 9. Now we cannot use nine as we are given in question to use different digits, so the digit at tens place will be 8. And as the digit at unit place is given 6.

Our greatest 3 digit number is 986.

For the smallest number we will make a digit at its hundredth place smallest which is 0, but we cannot use the first digit of a number 0 so we have to use the next smallest digit i.e. 1. So the digit at its hundredth place will be 1. Now the digit at the tens place will be 0. And as the digit at unit place is given 6.

Our smallest 3 digit number is 106.

Note: You have to make sure for the smallest number you do not use the first digit or digit at its hundredth place 0, as it will make the number a 2 digit number. Also remember to make a digit at tens place 0.

__Complete step-by-step solution__-For the greatest number we will make a digit at its hundredth place greatest which is 9. So the digit at its hundredth place will be 9. Now we cannot use nine as we are given in question to use different digits, so the digit at tens place will be 8. And as the digit at unit place is given 6.

Our greatest 3 digit number is 986.

For the smallest number we will make a digit at its hundredth place smallest which is 0, but we cannot use the first digit of a number 0 so we have to use the next smallest digit i.e. 1. So the digit at its hundredth place will be 1. Now the digit at the tens place will be 0. And as the digit at unit place is given 6.

Our smallest 3 digit number is 106.

Note: You have to make sure for the smallest number you do not use the first digit or digit at its hundredth place 0, as it will make the number a 2 digit number. Also remember to make a digit at tens place 0.

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