A company has a competition to win a car. Each contestant needs to pick a positive integer. If there’s at least one unique choice, the person who made the smallest unique choice wins the car. If there are no unique choices, the company keeps the car and there’s no repeat of the competition. It turns out that there are only three contestants, and you’re one of them. Everyone knows before picking their numbers that there are only three contestants. How should you make your choice?
Thoughts: Since there's no strategy you can adopt that the others cant, you need to aim for the situation where the other 2 pick the same number so you need to avoid them, so perversely aim high. However the other 2 can do the same as well, so do you aim lower of the high numbers, or does it make no difference?
I understand the answer is not: pick 12, but once you've gone beyond the strategy of getting the other 2 to match, do you hedge your bets somewhat by keeping it low, or do you maximise your chances of your strategy working by going insanely high (utilising exponentials etc.).