Rav Huna and Rav Chisda disagree as to whether a person lost in the desert with no idea when Shabbos is, no sense of time, should observe one day as Shabbos and then treat the six following days as chol or keep six days as chol followed by one day of Shabbos (Shabbos 69b). We pasken like Rav Huna that six days of chol are counted followed by Shabbos. However, all this means is that kiddush and havdalah are recited on the day arbitrarily designated as Shabbos. Melacha necessary to remain alive is permitted on every day, including that Shabbos day --one cannot prepare on one day for the next and then take a day off. Rava explains why. Each day has exactly the same liklihood as any other of being the real Shabbos. Since one cannot prepare on Shabbos for chol, one cannot do melacha on any day in preparation for the next given the 1/7 chance that one might be doing extra work on the real Shabbos in preparation for chol.
There are a number of interesting issues the Achronim discuss regarding this din. The Mishna Berura (Biur Halacha, 344) points out that were the person trapped in the desert to do whatever melacha needed for the entire upcoming week on only one day, the odds of that day being Shabbos, the odds of the person being mechalel Shabbos, are only 1/7. By not allowing the person to prepare from one day to the next and having the person do melacha on every single day (as needed), the odds of chilul Shabbos are now 7/7, or 100%! Why is this outcome prefarable to the first?!
This is just to get the brain warmed up - more to come bl"n.