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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?

Latin Lilies

Age 7 to 16
Challenge Level

This idea came to our attention as part of the Big Internet Math-Off 2019 and we hope that you’ll enjoy playing the NRICH version of Jorge's game.

This is a game for two players.  


  • Players take turns to place an available number (the lily pads) into any space on the grid (the pond), without repetition in any row or column.
  • The aim of the game is to win columns (which will then be marked with a star) by getting a frog to hop from your side of the pond to the other.
  • This is possible if you can ‘hop’ onto three numbers that increase in size in your direction of travel.  You are allowed to hop over numbers on the way.
  • You start with frog spawn on your side of the pond and as you place numbers that could be used to form your path to the other side, you’ll see different stages of the frog life cycle illustrate how close you are to winning each column.
  • Depending on the previous moves made, it may not be possible to place all of the lily pads into the pond.
  • The winner of a column is the first frog to be able to hop across the pond, even if the final number has been placed by your opponent. So watch out that you don't give your opponent a column by mistake!

Please do share your thinking with us via the Submit a Solution link (in the menu on the left). You might like to include a screenshot of the game in play, or a finished game, to help illustrate your submission.  We will use all of your feedback to help us write up the fully formed activity (complete with Teachers’ Resources) in the spring term 2020.

With thanks to Jorge Nuno Silva whose idea this is, and who kindly gave NRICH his permission to publish our take on it.