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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?


A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

Gift of Gems

Four jewellers share their stock. Can you work out the relative values of their gems?

Mixed up Mixture

Age 14 to 16 Challenge Level:


A standard calibration for a spectrophotometric assay for lysozyme was created by diluting some initial concentrations of the reagents Tris HCl buffer, NaCl, Lysozyme and a Micrococcus lysodeikticus suspension.The final volume was 5ml.

The numbers in the calculation have become mixed up. Can you work out how consistently to drag them back into the table? There will be two numbers left over. What will these represent?