Puzzle the first, I assume you have heard this one, but I'll repeat it in case you haven't.
Suppose a hundred people are buried in the sand one in front of another so each can see all the people in front but none of the people behind. An Evil Dictator (TM) places a red or blue hat on each of them. He goes along the line from the back asking each person what colour their hat is, and at the end kills everyone who gets it wrong.
They're allowed to discuss strategy beforehand, but the dictator listens and doesn't allow them to come with any tone-of-voice signals or the like, information can only be conveyed by saying "red" or "blue" when asked.
What strategy is sure to save the most people? If the hats are colored randomly What strategy has the best Expectaion of number saved? For instance the first person is always at risk because NO-ONE knows anything about his hat at all, so no solution can do better than 99 guaranteed saved or 99.5 expected saved.
( Solution )
Puzzle the second. What if the line was (semi) infinite?
( Solution )
Suppose a hundred people are buried in the sand one in front of another so each can see all the people in front but none of the people behind. An Evil Dictator (TM) places a red or blue hat on each of them. He goes along the line from the back asking each person what colour their hat is, and at the end kills everyone who gets it wrong.
They're allowed to discuss strategy beforehand, but the dictator listens and doesn't allow them to come with any tone-of-voice signals or the like, information can only be conveyed by saying "red" or "blue" when asked.
What strategy is sure to save the most people? If the hats are colored randomly What strategy has the best Expectaion of number saved? For instance the first person is always at risk because NO-ONE knows anything about his hat at all, so no solution can do better than 99 guaranteed saved or 99.5 expected saved.
( Solution )
Puzzle the second. What if the line was (semi) infinite?
( Solution )