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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?

Seating Arrangements

Age 7 to 11
Challenge Level

Syed (Foxford School and Community College, Coventry) has supplied a diagram of a solution:

Joshua (Brooklands Primary, Suffolk) explained his thinking well:

From clue 1, two girls sit next to each other, and from clue 4, Carol did not sit beside Annie or Ellen - so Ellen and Annie must sit next to each other. From clue 5, Felix sat opposite Ellen.

So far

From clue 2, David sat opposite Bert, so I put them on the two ends of the table. Which means Carol sits next to Felix - which fits in with clue 3 (Felix sat to Carol's left).

Final answer:

Samantha (Nanyang Primary School, Singapore) realised that Bert and David could swap seats and still fit all the clues.

Josh (Ampthill, Bedfordshire) gives an excellent description:

David is sat at the left end of the table and Bert is sat facing him at the right end.
Carol and Felix are sat next to each other along one side, with Carol at David's end.
Annie and Ellen are sat along the other side, with Annie at David's end so she is sat across from Carol and Allen at Bert's end so she is sat across from Felix.

Sally (Tattingstone Primary, UK) thought about the problem in a similar way to Josh.

Jason (Lark Rise Lower School, UK) was the only one to send in a different, but similar, seating arrangement:

Carol Felix


Annie Ellen