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Here is a way to sort a series of numbers. Proably not suitable for practical use but rather elegant.

Imagine for example we want to sort 3, 4, 2, 1 into ascending order. We set out some beads like so

3     o o o

4     o o o o

2     o o

1     o

Then we let the beads in each column drop vertically, and: hey presto

1    o

2    o o 

3    o o o

4    o o o o

It's not obvious at all that (or how) this works but people have proved it always does. Thinking about it does give an intuitive feel but it's good to have some more solid evidence.

See https://en.wikipedia.org/wiki/Bead_sort