One day, the chief of the dwarves decided he wanted to test his tribe. So that night, he told the dwarves that he would paint on each dwarf's back a dot colored either red or blue. Each dwarf will know everyone else's dot color, but not their own.
Every dwarf with a red dot on his or her back is to go to the dining hall on the Nth day, where N is the number of dwarves with a red dot on their backs. The presence of any blue-dotted dwarves at the dining hall on the Nth day constitutes a failure.
Furthermore, after the dwarves get their backs painted, they are not allowed to communicate using any means, including (but not limited to) speaking, punching, and holding mirrors. No dwarf is allowed to know what color he is until after the trial is over. They do not also get to know if someone went to the hall on any of the 1 to N-1 days.
The dwarves can meet on the day before the trial in order to talk strategy. What strategy should they use?
Note the question is not the same as the blue-eyes puzzle . In the blue eyes puzzle, one would get get to know if someone went to the hall on days 1 to N-1 .Here, nobody gets to know this. This is a crucial difference.