NL-NWO 1979

A cent, a stuiver ( $5$ cent coin), a dubbeltje ( $10$ cent coin), a kwartje ( $25$ cent coin), a gulden ( $100$ cent coin) and a rijksdaalder ( $250$ cent coin) are divided among four children in such a way that each of them receives at least one of the six coins. How many such distributions are there?

Solve in $N$ : $$\begin{cases} a^3=b^3+c^3+12a a^2=5(b+c) \end{cases}$$

Define $a_1 = 1979$ and $a_{n+1} = 9^{a_n}$ for $n = 1,2,3,...$ . Determine the last two digits of $a_{1979}$ .

Given is the non-equilateral triangle $A_1A_2A_3$ . $B_{ij}$ is the symmetric of $A_i$ wrt the inner bisector of $\angle A_j$ . Prove that lines $B_{12}B_{21}$ , $B_{13}B_{31}$ and $B_{23}B_{32}$ are parallel.