EE-MO 2002

Points $K$ and $L$ are taken on the sides $BC$ and $CD$ of a square $ABCD$ so that $\angle AKB = \angle AKL$ . Find $\angle KAL$ .

Do there exist distinct non-zero digits $a, b$ and $c$ such that the two-digit number $\overline{ab}$ is divisible by $c$ , the number $\overline{bc}$ is divisible by $a$ and $\overline{ca}$ , is divisible by $b$ ?

Let $a_1,a_2,...,a_n$ be pairwise distinct real numbers and $m$ be the number of distinct sums $a_i +a_j$ (where $i \ne j$ ). Find the least possible value of $m$ .