

Ask HN: What are your favorite brain teasers? - huangm

The other day I encountered an interesting problem:
<i>You have two fair, six-sided die with positive-integer-valued faces. You roll the die, and take the sum S of the numbers you roll. S will have some frequency distribution. For standard die, theres 1 way to roll a 2, 2 ways to roll a 3, etc. Are there any other pairs of die (the dice need not be identical) that generate this same frequency distribution?</i><p>It turns out this problem has a unique solution, and a nice name: http://en.wikipedia.org/wiki/Sicherman_dice<p>I encounter pretty cool problems like this on a regular basis, but they are always by way of a random friend or blog post - there doesn't seem to be a good central resource for such things. This may be because any problem that enough people know about is no longer novel or interesting (think of all the tired brainteasers you know of).<p>Nonetheless, I'd be interested to hear of other peoples' fun brain teasers. What are some of your favorites?
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rottencupcakes
This one's my favorite. Good luck. I'll buy a 6-pack for the first person to
solve it:

 _A hundred prisoners are each locked in a room with three pirates, one of
whom will walk the plank in the morning. Each prisoner has 10 bottles of wine,
one of which has been poisoned; and each pirate has 12 coins, one of which is
counterfeit and weighs either more or less than a genuine coin. In the room is
a single switch, which the prisoner may either leave as it is, or flip. Before
being led into the rooms, the prisoners are all made to wear either a red hat
or a blue hat; they can see all the other prisoners' hats, but not their own.
Meanwhile, a six-digit prime number of monkeys multiply until their digits
reverse, then all have to get across a river using a canoe that can hold at
most two monkeys at a time. But half the monkeys always lie and the other half
always tell the truth. Given that the Nth prisoner knows that one of the
monkeys doesn't know that a pirate doesn't know the product of two numbers
between 1 and 100 without knowing that the N+1th prisoner has flipped the
switch in his room or not after having determined which bottle of wine was
poisoned and what color his hat is, what is the solution to this puzzle?_

~~~
Lahtnesor
I almost got it, but given that a six-digit prime number is odd, which half of
the Monkeys lie again?

