Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
When you try to draw a star, one way to begin is to join the
first dot to the third dot i.e. miss out one dot each time as you
go around. Why can't you draw a 6-pointed star in this way?
Now think about another way to draw the star. Does this work for
a 6-pointed star?
Try to apply this to stars with more points and you should see