A nice number theory puzzle based on one I heard on Car Talk.
In the secret lab of a mad scientist, you find thirteen vials of liquid. One of the vials contains a deadly poison that will kill you instantly. If you drink all of the other twelve vials, you will gain a pleasant variety of super-powers. Luckily, there are some petri dishes which will, in one hour, determine if any poison has been placed in them. Unluckily, there are only four to use, and you only have one hour before the mad scientist returns. How can you determine which of the thirteen vials you should definitely not drink?
Car Talk Puzzler - sometimes automotive, sometimes more math/logic based.