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In the diagram below can you go from A to Z right through the alphabet? You must go to every letter in order, visiting every hexagonal cell once and once only, without crossing the path you are making.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.
If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?