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This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.


This activity investigates how you might make squares and pentominoes from Polydron.

Multilink Cubes

If you had 36 cubes, what different cuboids could you make?

Fake Gold

Age 7 to 11
Challenge Level

The solutions to both parts of the problem were explained very well by Robert (Moorgate C P School, Staffordshire), Jack and Jesse (Tattingstone School), Daniel (Anglo-Chinese School, Singapore), Samantha, Julie (The Abbey) and Ashley.

This solution to the four bar problem is from Laura (St Ives School, Haslemere)

My solution to the four bars of gold Find the fake is:
The man weights two bars of gold in either of the scales - one side will be lighter, that will have the fake in it. Split the two bars and weigh it again, the lighter will be the fake.

This answer for the 9 bar problem comes from Caroline, Sarah and Ellie (The Mount School, York),

  1. Place 3 bars on each side. If they balance then the fake is in the other 3. If they don't balance then the fake is in the lighter side.
  2. Take the 3 bars which the fake is in and weigh 2 of them against each other. If they balance it's the one left over and if they don't balance it is the lighter one.