Tag Archives: algorithm

From primitive roots to Euclid’s orchard

Commenter Snowball pointed out the similarity between Euclid’s Orchard… …and this picture of primitive roots I made a year ago: At first I didn’t see the connection, but Snowball was absolutely right. Once I understood it, I made this little … Continue reading

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A few words about PWW #20

A couple commenters quickly figured out what my previous post without words was about. The dots making up the image are at integer grid points , with the center at . There is a dot at if and only if … Continue reading

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Post without words #20

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A new way to read (and print) double-sided paper

Continuing with the theme of reading stacks of paper (see my previous two posts, I have had a marvellous idea (at least I think so; I will let you judge for yourself). Let me take you through my thought process, … Continue reading

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Reading double- and triple-sided paper

In the comments on my previous post there are some nice suggested algorithms for reading a stack of double-sided sheets of paper. The key seems to be that you need to keep track of a distinguished edge of the stack. … Continue reading

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John Conway’s algorithms for counting stairs and reading double-sided paper?

This past week I started reading Siobhan Roberts’s new biography of John Conway, Genius at Play: The Curious Mind of John Horton Conway. I’m enjoying it so far. I’ll have more to say about it later, once I finish it, … Continue reading

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The Steinhaus-Johnson-Trotter algorithm

In a previous post I posed the question: is there a way to list the permutations of in such a way that any two adjacent permutations are related by just a single swap of adjacent numbers? (Just for fun, let’s … Continue reading

Posted in combinatorics, pattern, solutions | Tagged , , , , , | 9 Comments