$14.28 \star \star$ What is the largest even number that cannot be written as the sum of two odd composite numbers?
Odd composite numbers less than 38 are $9,15,21,25,27,33$. 38 cannot be expressed as the sum of any two of them. However, for even numbers $A$ greater than 38, all can be expressed as the sum of two odd composite numbers: when the last digit of $A$ is 0, $A=15+5n$; when the last digit of $A$ is 2, $A=27+5n$; when the last digit of $A$ is 4, $A=9+5n$; when the last digit of $A$ is 6, $A=21+5n$; when the last digit of $A$ is 8, $A=33+5n$. Here, $n>1$ is an odd number. Therefore, 38 is the answer.