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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?

More or Less?

Are these estimates of physical quantities accurate?

Time to Evolve

Age 14 to 16 Challenge Level:

Estimate lifespan and time to first offspring from those for the modern day equivalent creature.

Think about the point in the lifespan of a descendant at which the next descendant might have been produced.

Don't forget that this is an exercise in estimation and approximation: there is no 'right' answer, so try to put sensible guesses in the table.