[Gator]

Big - You post the original answer as being greater then 30% (in the case of 1,000 numbers). I always understood the answer to be >25% (I'm not doubting you - your answer is more precise). My solution was based on the concept that I only care about two numbers (the highest and the second highest - call them X and Y). I let you read half the numbers (500 in the case of 1,000 - 1/2 billion in the case of a billion). I hope that Y is in the first half. Then, once you read half the numbers, I stop you as soon as you read a higher number. The chance of X being in the first half and Y in the second is 25% and I win every time that happens. There are additional ways to win that put my chances at greater then 25%. Two questions - one is, based on 1,000 numbers, how many should I let you read (I always thought exactly half, but you equation suggests a different number) and second - am I correct that the more numbers you have (i.e. a billion vs. 1,000) the correct answer asymtomically -- sorry about spelling -- approaches 25%?