Even Nine

A number is divisible by 9 only if its digits sum 9, or a multiple. Due to no sum of numbers of the same parity gives as a result an odd, we look for the smallest even multiple of 9, which is 18. Then, we look for the combination of smallest digits that gives this sum, which are 2, 8 and 8. Hencefore, the number is 288

Any number is divisible by $9$ only if the sum of its digits is $9$ or a multiple of $9$ . The smallest even multiple of $9$ is $18$ , hence we need to find the smallest numbers whose sum of digits is $18$ . In this way, we get the number $288$ as the solution.

The sought number should be a multiple of 18. There are five 2-digit multiples of 18: 18, 36, 54, 72, 90. Each has one odd digit. The 3-digit numbers that start with 1 are those that exceed 99​ but are below 200. Evidently, their first digit is odd. So, we need to look further up. The sum of the digits of such a number is an even multiple of 9. The sum is then divisible by 18. For numbers below 300, the sum is bound to be 18. Excluding the first digit, the sum is 16. The only two digit number with even digits that add up to 16 is 88. Thus, the answer to the problem in 288.