Eggstreme

Awash with chocolate eggs and gift bags, confectionery delirium sets in and your mind starts to wander... Given you have 20 bags, what is the minimum number of eggs needed so that you have a different number of eggs in each bag? 
This puzzle and solution can be found here.
There is an interesting non-obvious (quite mischievous) solution which nicely illustrates what mathematicians can do when the rules are not overly defined.

Gauss Triangular Array Problem

This is from the Gauss (2012) competition.
Solution here.

After solving the problem look for other patterns in this triangular array, or ask other mathematically interesting questions. Write your own problem based on the design of this array (or one like it).