This one is real bad for productivity

A friend sent me a very interesting puzzle page:

http://www.weffriddles.com/

Check it out. I've found it to be fairly addictive and incredibly fun / interesting. Let me know what you think over email or IM.

Useless Strangers

At a fork in the road between two cities, you see 2 people. One always tells the truth, and comes from the city of safety. The other person always lies and comes from the city of cannibals, where they will eat you. They both look exactly the same. You must choose one of the persons, and ask him one and only one question (no compound questions either, such as "is this shirt red and which way to safety?"). What question could you ask to find out which path leads to the city of safety?

You know you love number sequences

What is the next number in the sequence?

1
11
21
1211
111221
312211
13112221
?

Going nowhere fast

How many points on the Earth are there where you can walk 1 mile south, then 1 mile west, then 1 mile north and end up in the same place?

And trust me, you can't go anywhere but north from the south pole.

Dominos

You are given an 8×8 chess board and a set of 31 dominos, such that each domino covers exactly two adjacent squares on the chess board. Two diagonally opposite corners are cut away from the chess board (so that it has a total of 62 squares left). Your task is to cover the remaining chessboard with dominos, such that it is completely covered and no dominos
overflow from the sides of the modified chess board. If you think you can do it, tell me how. If you think you can't, tell me why.

Los ratones estan borrachos

Suppose some guy has 1000 bottles of wine. He finds out that 1 bottle is poisoned. Fortunately, he has 10 mice which he can use to check which bottle is tainted. It takes a day though to find the result of the test (i.e. if mouse drinks bad wine, it dies in 24 hrs). The dude is throwing a big party the next night. If he runs optimal tests with his mice, how many of the 1000 bottles can he served at the party? E.g. he could have each mouse drink from a bottle. If they all live, he knows that 10 bottles are safe. All mice have to be assigned to bottles right away, because there’s only 24 hours to the party.

Half a Glass of Water

Suppose you're naked in a bare room with nothing but a glass of water. The glass is a right cylinder and seems to be about half-full. But, because you have NOTHING else to do (given that you're naked in a bare room...not the most exciting place in the world) you want to know if the glass is more than half-full, exactly half-full, or less than half-full. What do you do?

First Post

So hopefully this will be the only non-puzzle post for awhile. I've decided that instead of posting a puzzle to my gtalk away message every week, I'll just post them on here. That way you guys can keep looking them up and working on them.

Although the title is "Puzzle of the Week", I'm actually gonna start posting once every two weeks to begin with. I've got some interesting ideas for stuff to do on here, so bear with me if it's slow in the beginning. As per some previous feedback, I'm gonna try to broaden the types of puzzles that I post so that there's something for everyone.

I've disabled comments (hopefully) because I don't want anyone giving away answers and ruining everyone's day. Answers aren't going to be posted either, but you can email me your guesses at bigwilliestyle+potw@gmail.com or just drop me a gtalk message. Other than that, look for improvements coming soon!