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This activity has been particularly created for the highest attainers. (The pupils that you come across in many classrooms just once every few years.) It is seen as a possible follow on from Tiles in the Garden.
This activity takes "Tiles in the Garden", much further. We can keep the main ideas the same -
So this one used $26$ and the slope was generated by going along $1$ and up $5$.
This time let's put on a limit of using less than $100$ tiles.
What sizes of rectangles could be filled obeying the three rules?
How many tiles for each rectangle you find?
Are there any numbers of tiles between $10$ and $100$ for which there cannot be a rectangle?