Yes. You missed something. Keep in mind that the odds of success for the commoner hoping to get the dowry, is only 37%, even with the best strategy. Also, clearly the Sultan can defeat this strategy very easily if he wishes, just by sending in the daughter with the highest dowry, first.
The idea is that you learn something about the range of data, by seeing some of it, first. When you start meeting the daughters, you would have (according to the problem, at least), no idea at all of what the dowry's might be - 10 grams of gold, or 10,000 kilo's of gold, you just have no idea. So any choice you make is going to be 1/n, initially. But after you see the dowrys, and say they're something like: 4 kilo's, 3.75 kilo's, 5.6 kilo's, 4.2 kilo's, etc., so you get the idea you need a dowry greater than 5.6 kilo's. After you've seen about 1/3 of the daughter's and learned something about the range of dowry's, when the next daughter comes in to meet you, and she has a dowry > 5.6 kilo's, then she's the one you want to choose. Keep in mind that your chances of success choosing the daughter with the highest dowry is never better than 37%, and in some cases, slightly less. And of course, the Sultan can defeat this scheme, if he wishes, very easily. (which isn't a part of the problem as stated, but does smack me in the face like a dead fish). Dave
