Possible student responses

• The hundreds digit must be 9.
• The units digit must be 0, 2, 4, 6, or 8.
• If the units digit is 0, the number could be 930 or 990 because 9 + 3 + 0 is divisible by 6, as is 9 + 9 + 0.
• If the units digit is 2, the number could be 912 or 972, because the sum of the digits must be either 12, 18, or 24.
• There are only 5 other possibilities: 954, 936, 996, 918, and 978.
• The tens digit must be odd.
• If another clue was added, such as “The number I’m thinking of is the smallest number possible that can be made this way,” then a single number can be selected.