<PRE><B>Question 1210212</B>
&lt;br&gt;
sum of digits is 6
at most one even digit (i.e., either one or none)
strictly decreasing digits&lt;br&gt;
(1) first digit 6&lt;br&gt;
Clearly there is only one such string with first digit 6: 6&lt;br&gt;
(2) first digit 5&lt;br&gt;
The sum of the remaining digits must be 1, and the digits must be strictly decreasing.  There are, simply, two such numbers: 51 and 510.&lt;br&gt;
(3) first digit 4&lt;br&gt;
The sum of the remaining digits must be 2; we can&#39;t have another even digit; and the digits must be strictly decreasing.  Simple observation shows there are no such numbers.&lt;br&gt;
first digit 3&lt;br&gt;
The sum of the remaining digits must be 3, and the digits must be strictly decreasing.  Also trivially, there is one such number: 321.&lt;br&gt;
Clearly there are no other numbers that satisfy all the conditions.&lt;br&gt;
ANSWER: 4 (6, 51, 510, 321)&lt;br&gt;
</PRE>