Imagine the central square in a big city is paved with large square tiles. It may be rectangular rather than square! You are going to go straight from one corner, diagonally across to the other corner. You may be walking, cycling, skateboarding or using roller blades. Whichever way you travel you will need to go absolutely straight from corner to corner.

You see in the picture above that shows a very, very small example (a 4 by 3 rectangle). The blue line of travel goes through six of the square tiles. Maybe there are other small rectangles other than this one that crosses 6 tiles.

Your challenge is to find what different sizes of rectangles would mean you travelled across 10 tiles. 

Your extra challenge is to find a set of answers for 12 tiles being crossed. There are probably more than you first discover!

Can you find a generalization/pattern/system from the ones you've done that would enable you to find solutions more easy to other numbers of tiles being crossed?