Here are the numbers 1 to 6 drawn using coloured squares:
We can call these numbers squares, rectangles or sticks.
1 is a square but just a single one.
We can't make 2 into a square so 2 is a stick.
We can't make 3 into a square or a rectangle so 3 can only be a stick.
We can make 4 into a square.
We can't make 5 into a square or a rectangle, so 5 can only be a stick.
We can't make 6 into a square, but we can make 6 into a rectangle.
If you had 7 yellow squares, what could you make them into? A square, a rectangle or a stick? How about 8 squares?
Try this with the numbers up to and including 20.
Which ones can only be sticks?
Which ones can make rectangles?
Which ones are squares?
What do you notice?
This problem was inspired by a session at an ATM conference, led by Tandi Clausen-May.