This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.)
Imagine the central square in a big city and its paved with large square tiles. It may be rectangular rather than squrea! You are going to go straight from one corner, diagonally across to the other corner. You may be walking, cycling, skate boarding or using roller blades. Which ever way you travel you will go absolutely straight.
In the picture above showing a very, very small example (a $4$ by $3$ rectangle) you see that the blue line of travel goes through six of the square tiles. Maybe there are other small rectangles that would need you to cross six square tiles.
Your challenge is to find what different sizes of rectangles would mean you travelled across $36$ tiles?
Can you find a generalization that would enable you to find solutions more easy?