You may also like

problem icon

Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

problem icon

Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

problem icon

Bendy Quad

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

Always Perfect

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Have you tried some simple cases to see if there is a pattern?

If you have a number "$x$" the next number is "$x +1$". How could you write four consecutive numbers?

If you can express $x^4 + \ldots + 16$ as a perfect square, the two factors will be of the form $(x^2 +\ldots + 4)$.