Tiger, I would say with all of your thinking you may have developed a new way to look at the problem. Most people look at the "odd amount" and immediately think odd number and when you say 1 cube it is accurate in that manner. I would agree with you that an even distribution of the cubes across all three cups would also qualify as an odd amount. I don't think there is one correct answer when you are trying something like this, but 34 cubes does drive home the point reasonably well.