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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?

Archimedes and Numerical Roots

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

Time to Evolve

How many generations would link an evolutionist to a very distant ancestor?

More or Less?

Age 14 to 16
Challenge Level

In each question there will be some way of relating the quantities referred to. You will need to think what equations from science to use.

Once you have the equations, what quantities don't you know? Could you substitute sensible values for one of these?

Don't forget to use physical intuition. For example, an apple floats in water. What does that tell you about its density?