Order of operations

6÷2(2+1)= ?

This problem turned up on my Facebook feed and generated a nice little conversation. We googled it, we tried it out in Wolfram Alpha - same answer came back. Why does this problem (potentially) cause difficulty? What does it tell us about necessary and arbitrary parts of mathematics? What other equivalent expressions could be written?

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).  

Counting dots and squares

This was inspired by a similar problem in the Canadian Math Kangaroo Parent paper (2014).
You can see that paper here.

Identical Coloured Nets

Net Problem from UKMT Senior Math Challenge (2014)
Solution here.

Regular Star Polygon made of Trapezia

Angle/Polygon Problem from UKMT Senior Math Challenge (2014).
Solution here and extended solution together with note on original inspiration for problem here.

Tetrahedral Die Problem

Patterning Problem from the UKMT Junior Mathematics Challenge (2014).
Solution here, extended solution and suggested investigation here.

Quadrilateral Areas Problem

Area Problem from the UKMT Intermediate Mathematical Challenge (2015).
Solution here and extended solution here.