6 ms·
Right, that's a valid example case with n=0, though such cases are of measure zero in the same way the rational numbers are of measure zero in the real numbers.
by rwallace 12y ago
Right, that's a valid example case with n=0, though such cases are of measure zero in the same way the rational numbers are of measure zero in the real numbers.
Here's a counterexample: give all the prisoners white hats. Now the same strategy produces no prisoners going home.
In fact, if the population of hat distributions is restricted to {all black, all white}, this still suffices to show that there is no strategy that guarantees all prisoners will go home after some finite standard number.
- ColinWright 12y ago> ... if the population of hat distributions is > restricted to {all black, all white}, this still > suffices to show that there is no strategy that > guarantees all prisoners will go home ... The strategy given in the submitted article is such that if all prisoners are given the same color hat then they will all go home, so I'm not sure what you're saying here.
- rwallace 12y agoI'm saying the strategy in the article does not actually do this at all, and it's easy to prove this by noting that a strategy that has them all going home with black hats has none of them going home with white hats.
- hyperpape 12y agoYou're confused about what the strategies are. A strategy is not "all say black" or so on. The prisoners will make different choices depending on the infinite sequence of hats they see in front of them.
- ColinWright 12y agoI've worked through the strategy, and what you say seems simply to be false. As I work through the strategy I find that if they all have black hats the strategy has them all saying "Black", and if they all have white hats then the strategy has them all saying "White." I don't understand why you claim otherwise.