I'm collecting advanced exercises in geometry. Ideally, each exercise should be solved by one trick and this trick should be useful elsewhere.

If you have a problem like this please post it here.

Remark:

• I'm collecting such problems for many years. The current collection is here, it is about 80 problems. At the moment, I have just few problems in topology and in geometric group theory and just one in algebraic geometry.

• Thank you all for nice problems --- I gave bounty to one, but would give it to 4 problems if I could :). Some of them are in the collection by now --- please post more...