My thought process would go like this, 999 is the number that will win this contest. This is common knowledge, others might also be choosing the same and hence likely to be eliminated. The next number I should choose is 998. But this is common knowledge too, others might also be thinking on similar lines. 998 is likely to be eliminated. So, I should go back to 999. But, what if this is common knowledge too? So, to win I need to eliminate both, 999 and 998, and go with the next number 997. But, what if? This can spiral down all the way to 1. By this reasoning, is it better to stick with 999?