Determine the smallest even three-digit number that can be formed using all the digits 1, 6, and 9.
Since the number is even, the digit in the units place must be 0, 2, 4, 6, or 8. So, use the digit 6 in the units place.
Since we want the number to be as small as possible, use the smallest number in the hundreds place: 1.
The remaining number (9) belongs in the tens place.
Therefore, the number 196 is the smallest even three-digit number formed with all the digits 1, 6, and 9.