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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?

Professional Circles

Age 7 to 11
Challenge Level

Wong Jing and Wan Paul, River Valley High School, found both solutions to this problem as did Anne from Madras College, St Andrews. One or other of the solutions was found by Maria, Madras College; Caroline, Sophie, Laura and Emma, The Mount School, York; Henry, New College School, Oxford; Prav, Sheli and Ruoyi, from North London Collegiate School Puzzle Club; Becky, Richard, Chris and Richard all from Bourne Grammar School; Ashley, Mansfield, Australia and Isobel and Lottie.

Six friends sat around a circular table. Ann (who is not the banker) sat opposite the consultant. Bob sat opposite Fred. Celia sat on the doctor's right. Dave (who is not the consultant) sat opposite the accountant. Emily sat opposite the engineer and next to the financier. Fred sat on Ann's right.

1 st solution

2 nd Solution