[pjc50]

It's an offer, which can be accepted by someone complying with the terms. At that point it constitutes a contract.

http://www.bailii.org/ew/cases/EWCA/Civ/1892/1.html CARLILL v. CARBOLIC SMOKE BALL COMPANY; admittedly that's English law rather than German, but the principle holds. That case also deals with rewards, diseases and pseudoscience.

[schoen]

There also seem to be a number of U.S. cases enforcing unilateral reward offers as contracts; a theme seems to be that they intended to get other people to do work and those people reasonably relied on the offer and did the requested work (most often going out and finding a missing person or item).

[icebraining]

I believe the doctrine is called Promissory Estoppel: http://en.wikipedia.org/wiki/Estoppel#Promissory_estoppel

[schoen]

Yeah, it looks like that's the theory.