lemmingllama Posted April 8, 2012 Report Share Posted April 8, 2012 So once again I will bring us to a puzzle that contains multiple answers, with each being just as correct as the others.So now we have Sleeping Beauty, who loves to sleep and will sleep forever unless woken up. Since Sleeping Beauty loves games and sleep, Prince Charming devised a game to entertain her that would combine both sleep and fun. However, this game will also make her think. So Prince Charming tells her that she will be put to sleep. Once she is asleep, he will flip a coin. If the coin lands on heads, then he will wake her up halfway through the week for 10 minutes. If the coin lands on tails, then he will wake her up every day of the week for 10 minutes each day. When he wakes her up, Sleeping Beauty must guess whether the coin landed on heads or tails. However, there is a twist to make this game more entertaining. Every time that Sleeping Beauty wakes up, she will then forget about her 10 minutes of wakefulness upon falling asleep again.So how should Sleeping Beauty decide on which option? Additionally, should her answer vary if they played this game each week rather than just for a single week? Quote Link to comment Share on other sites More sharing options...
KaoclazmMJR Posted April 8, 2012 Report Share Posted April 8, 2012 She could have Prince Charming shave on the first day and then depending on how much facial hair he has when she is woken up she can decide? Quote Link to comment Share on other sites More sharing options...
lemmingllama Posted April 8, 2012 Author Report Share Posted April 8, 2012 She could have Prince Charming shave on the first day and then depending on how much facial hair he has when she is woken up she can decide? I was hoping that the answers would have a bit more rationalization... Also, Sleeping Beauty didnt have facial hair, so your plan wouldnt work either way Quote Link to comment Share on other sites More sharing options...
Dark Spy Posted April 8, 2012 Report Share Posted April 8, 2012 both have the same probability Quote Link to comment Share on other sites More sharing options...
KaoclazmMJR Posted April 8, 2012 Report Share Posted April 8, 2012 I was hoping that the answers would have a bit more rationalization... Also, Sleeping Beauty didnt have facial hair, so your plan wouldnt work either waywhen did I ever say that she did? Quote Link to comment Share on other sites More sharing options...
Dark Spy Posted April 8, 2012 Report Share Posted April 8, 2012 when did I ever say that she did?It seems like a huge misunderstanding happened here Quote Link to comment Share on other sites More sharing options...
†Mute point Posted April 8, 2012 Report Share Posted April 8, 2012 If they have a calendar on the wall, then she can look at that, if it's sunday, monday, tuesday, thursday, friday, or saturday, then the coin landed on tails. If it's wednesday, she would have to guess.Another way would depend on what time of day she is being woken up, and what the time of year is, because if it were at night, and she knew enough about astronomy, she could determine what day by the position of the stars if she was woken up at exactly the same time every day.Or she could hide a pebble beneath her pillow each time he woke her up. If there were more than one, then it was tails. Quote Link to comment Share on other sites More sharing options...
Dark Spy Posted April 8, 2012 Report Share Posted April 8, 2012 A pebble is a clast of rock with a particle size of 4 to 64 millimetres based on the Krumbein phi scale of sedimentology. Pebbles are generally considered to be larger than granules (2 to 4 millimetres diameter) and smaller than cobbles (64 to 256 millimetres diameter). A rock made predominantly of pebbles is termed a conglomerate. Pebble tools are among the earliest known man-made artifacts, dating from the Palaeolithic period of human history.so that what pebble is Quote Link to comment Share on other sites More sharing options...
KaoclazmMJR Posted April 8, 2012 Report Share Posted April 8, 2012 Ahh geology if only Sheldon where to acknowledge you as a real science Quote Link to comment Share on other sites More sharing options...
lemmingllama Posted April 8, 2012 Author Report Share Posted April 8, 2012 Ok, so now let me propose my answer to see if you guys can be rational. I do like mute's ideas, but there is an even easier way to solve this, based purely on probability.both have the same probabilityThe above statement is partly true, and yet at the same time it is false. This is simply because Sleeping Beauty will be woken up more times if it is tails. As such, she will be woken up more frequently, and so by guessing tails, she has a higher chance of getting it right. Quote Link to comment Share on other sites More sharing options...
KaoclazmMJR Posted April 8, 2012 Report Share Posted April 8, 2012 Answer dosen't change if played every week numerator and denominator both grow Quote Link to comment Share on other sites More sharing options...
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