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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 14
Challenge Level

Why play this game?

Latin Lilies can be used as an introduction to Latin squares. It offers an engaging context in which students are challenged to plan ahead and devise winning strategies.


Possible approach

Introduce the game using the interactivity with you playing against Computer 1 (the default setting). You could choose to play in silence and invite students to watch the game, and consider what the rules might be. Give them a chance to talk to a partner and then draw everyone together to share suggestions and clarify how to play.

Once the rules have been established, invite students to play in pairs against Computer 1 on a tablet or computer. Once they are confident they can beat Computer 1, they can be challenged to take on Computer 2 and then Computer 3.

If students do not have access to a tablet or computer, they could play the game against each other using paper and pencil.

In the plenary, you could ask students to articulate their strategies, perhaps in the context of offering advice to a friend about how to play the game, and/or invite students to test out their strategies by demonstrating they can beat Computer 3 or by playing against the whole class.


Key questions

Which of the five numbers is it best to place at the start?

How many columns are you going to try and win?

Can you ever block your opponent so that they cannot win that column?


Possible support

The task Three by Three will help students focus on the properties of Latin squares.


Possible extension

Tea CupsNine Colours and Latin Numbers could all be offered as challenging follow-up tasks.