List numbers that leave remainder 4 when divided by 9, then check which also leaves remainder 1 when divided by 3.<br><br>
&bull; Numbers of the form 9k + 4: 13, 22, 31, 40, ...<br>
&bull; Check 13: 13 &divide; 3 = 4 remainder 1 &#10003;<br>
&bull; Check 13: 13 &divide; 9 = 1 remainder 4 &#10003;<br><br>
The smallest possible number is 13.<br>
Final Answer: 13