You may also like

problem icon

Counting Counters

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

problem icon

Cuisenaire Rods

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

problem icon

Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Fault-free Rectangles

Age 7 to 11 Challenge Level:

This rectangle is made from six 2 by 1 rectangles:
A rectangle with a fault line
You can see it has a line going through the middle from the top edge to the bottom edge. This means that the rectangle could be broken into two and so the line is called a fault-line.

Can you make a rectangle without a fault-line (a "fault-free" rectangle) with one white and four red rods?

What do you notice about the way you have made the shape?

Can you use what you have noticed to make a fault-free rectangle with red and light green rods?

Can you make any similar fault-free rectangles with rods of other colours?

Can you find the smallest fault-free rectangle that can be made using 2 by 1 rectangles?

Full Screen Version
If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.

We would like to thank Geoff Faux for introducing us to the idea of fault free rectangles.