boot camp day 12

well, it's the end of another week of boot camp. today, people hung out and had a bbq outside of the weyburn apartments... i joined, and it felt very typical as we discussed several good logic puzzles. later i talked to some people for a while that i had not met before. for the sake of writing something down, i'll describe one of the logic puzzles i was introduced to:

there are 10 prisoners in a prison and the guards decide to play a sadistic game. the guards describe their game to the prisoners: "each of you will be blindfolded, and then given a hat, either white or black, to wear. we will then line you up one in front of the other; then everyone will remove the blindfold, so that every one of you can see all prisoners (and their hats) that are in front of you but none that are back behind you. then, starting at the back of the line, we will ask each of you in order what color hat you are wearing: if you say the correct answer, you survive; if you answer incorrectly we will shoot you in the head. we continue this with each of you until we reach the front of the line. then our game is over. fortunately, you're not completely out of luck, as before we apply the blindfolds and hand out hats, you will have the opportunity to strategize as a group." the question is: if possible, come up with a strategy that maximizes the number of surviving prisoners. in particular, what is the maximum number of prisoners that can be sure to survive, given the right strategy?

thanks for reading!