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## "Black" Riddles - Next 10 of 88.

Riddle: Sometimes I am black, sometimes I am white sometimes you can see me at night. I have friends that are with me that are much smaller. Some of you have walked on me but not all. What am I?
Riddle: Before he turned physics upside down, a young Albert Einstein supposedly showed off his genius by devising a complex riddle involving a stolen exotic fish and a long list of suspects. Can you resist tackling a brain teaser written by one of the smartest people in history? Dan Van der Vieren shows how.
Answer: The key is that the person at the back of the line who can see everyone else's hats can use the words "black" or "white" to communicate some coded information.  So what meaning can be assigned to those words that will allow everyone else to deduce their hat colors?  It can't be the total number of black or white hats.  There are more than two possible values, but what does have two possible values is that number's parity, that is whether it's odd or even.  So the solution is to agree that whoever goes first will, for example, say "black" if he sees an odd number of black hats and "white" if he sees an even number of black hats.  Let's see how it would play out if the hats were distributed like this.  The tallest captive sees three black hats in front of him, so he says "black," telling everyone else he sees an odd number of black hats.  He gets his own hat color wrong, but that's okay since you're collectively allowed to have one wrong answer.  Prisoner two also sees an odd number of black hats, so she knows hers is white, and answers correctly.  Prisoner three sees an even number of black hats, so he knows that his must be one of the black hats the first two prisoners saw.  Prisoner four hears that and knows that she should be looking for an even number of black hats since one was behind her.  But she only sees one, so she deduces that her hat is also black.  Prisoners five through nine are each looking for an odd number of black hats, which they see, so they figure out that their hats are white.  Now it all comes down to you at the front of the line.  If the ninth prisoner saw an odd number of black hats, that can only mean one thing.  You'll find that this strategy works for any possible arrangement of the hats.  The first prisoner has a 50% chance of giving a wrong answer about his own hat, but the parity information he conveys allows everyone else to guess theirs with absolute certainty.  Each begins by expecting to see an odd or even number of hats of the specified color.  If what they count doesn't match, that means their own hat is that color.  And every time this happens, the next person in line will switch the parity they expect to see.
Riddle: You are about to be executed, but the king gives you a chance. He says that he will divide 100 marbles in half. 50 of them are black and 50 are white. You can arrange them however you like into two bowls, but you must use all the marbles. The king will then blindfold you and switch them around. Then you choose a single marble from whichever bowl you put your hand randomly in. If you choose a white marble you can live, but if you choose a black one you die. How do you divide the marbles so there is a 50-50 chance you will live?
Answer: You need to put one white marble in one of the bowls. Then the remaining 49 go with the 50 black marbles. Then you will have a good chance of living.
Riddle: Blacker than black, colder than cold, some things out here are worth more than gold. What is it?