How can a line of people sort themselves by height? Or by age? It depends on what operations they are allowed to use. One might consider using “swaps” where two people in the line switch position with each other. One might also consider using “cycles” where someone at the end of the line moves to the beginning of the line.

This leads to an investigation of “permutations”, which is a fancy word for rearrangements of a set of objects. Some sets of permutations allow the people in the line to sort themselves in any order they choose, while other sets of permutations don’t.

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Continue reading The secret lives of permutations →

In our first day back at the math circle, we discussed the motions of a shape (such as a triangle, square, pyramid, etc) which return the square to a fixed position. We found that these motions can be composed or “multiplied” like numbers, and investigated the nature of these compositions. Continue reading Shapes and motions →

For this session, we worked on Modular Arithmetic by thinking about a circular number line arranged like a clock.

Continue reading Numbers on Clocks →

## Explore and engage with mathematics