OPM 2001

The trapezium $[ABCD]$ has bases $[AB]$ and $[CD]$ (with $[AB]$ being the largest base). Knowing that $BC = 2 DA$ and that $\angle DAB + \angle ABC =120^o$ , determines the measure of $\angle DAB$ .

How many consecutive zeros are there at the end of the number $2001! = 2001 \times 2000 \times ... \times 3 \times 2 \times 1$ ?

Let $n$ be a natural number. Prove that there is a multiple of $n$ that can be written only with the digits $0$ and $1$ .