Age 16 to 18
Glue three cubes together to make a cuboid of dimensions $3$ by $1$
by $1$. Label $4$ points on the cuboid with coordinates $A =
(0,0,0)$, $B=(1,1,1)$, $C=(2,1,0)$ and $D=(3,1,0)$. Now the
challenge is to find at least two different ways to calculate the
angles $\angle ABC$ and $\angle ABD$.