List

Groups Further

Groups of Sets
problem

Groups of Sets

Age
16 to 18
Challenge level
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The binary operation * for combining sets is defined as the union of two sets minus their intersection. Prove the set of all subsets of a set S together with the binary operation * forms a group.
Rose
problem

Rose

Age
16 to 18
Challenge level
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What groups of transformations map a regular pentagon to itself?
Poison, antidote, water
problem

Poison, antidote, water

Age
14 to 18
Challenge level
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Play the game of Poison, Antidote, Water to start to understand the mathematics of associativity and groups.