Monthly Archives: January 2016

M74207281 is prime!

Posted on January 24, 2016 by Brent

I’m a bit late to the party, but the Great Internet Mersenne Prime Search has recently announced a newly verified prime number, , with a whopping 22,338,618 decimal digits! This is now the largest known prime number (though of course … Continue reading →

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The chocolate bar game: losing positions proved

Posted on January 23, 2016 by Brent

In my last post I claimed that the losing positions for the chocolate bar game are precisely those of the form (or the reverse), that is, in binary, positions where one coordinate is the same as the other with any … Continue reading →

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The chocolate bar game: losing positions characterized

Posted on January 20, 2016 by Brent

The evident pattern from my last post is that losing positions in the chocolate bar game appear to be characterized by those where the binary expansion of is the same as the binary expansion of with any number (including zero) … Continue reading →

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The chocolate bar game: losing positions in binary

Posted on January 18, 2016 by Brent

Recall the chocolate bar game from my last post, whose winning and losing positions can be visualized like this: Here’s a list of some losing positions on or above the main diagonal (dark blue squares in the above picture), ordered … Continue reading →

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The chocolate bar game

Posted on January 14, 2016 by Brent

Suppose there is an rectangle. I like to think of it as one of those bars of chocolate made up of squares: Two players take turns. On a player’s turn, she must break the chocolate bar along any one of … Continue reading →

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

Posted on January 8, 2016 by Brent

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

Posted on January 6, 2016 by Brent

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?

Posted on January 4, 2016 by Brent

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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