On New Year’s Eve 2008 the evil sorcerer Gargamel captures 100 Smurfs and locks them up in his completely dark cellar. In there, he removes their white hats and randomly puts each Smurf a hat on from his collection of 10 red and 90 white hats. When finished, he tells them one or more Smurfs now wear a red hat and they have to find out who do, but they have to obey the following rules.
From now on they are strictly forbidden to talk, to take off their hats, or to give any other signals to each other. They will be allowed to go outside for 3 minutes the next morning (January 1, 2009) and have to sit down in a circle so that they can see the colour of all hats but their own hat. Only if all red hatted Smurfs manage to simultaneously stand up, Gargamel will immediately free all Smurfs. However, if not all red hatted Smurfs stand up or any white hatted Smurf stands up, Gargamel will kill them all. If nobody stands up within those 3 minutes, all Smurfs will have to get back into the dark cellar and they may give it another try the next morning.
How can the Smurfs survive and on what date will the 10 red hatted Smurfs stand up?
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