In how many ways can you fit all three pieces together to make shapes with line symmetry?
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.
Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?
Explore the transformations and comment on what you find.
Original text of NRICH problems, as featured in Charlie and Alison's BCME session 2018.