# Tag Archives: binary

## The chocolate bar game: losing positions proved

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

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

Posted in challenges, games, pattern, pictures | | 1 Comment

## The chocolate bar game: losing positions in binary

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

Posted in challenges, games, pattern, pictures | | 1 Comment

## P vs NP: What’s the problem?

As promised (better late than never), I’m going to begin explaining the (in)famous P vs NP question (see the previous post for a bit more context). As a start, here’s a super-concise, 30,000-foot version of the question: Are there problems … Continue reading

Posted in computation, open problems | Tagged , , , , | 9 Comments

## Math Teachers at Play #21

Math Teachers at Play #21 is up at Math Mama Writes…, and it includes this cute puzzle, which Sue apparently made up herself: The Numberland News runs personal ads. 21 was looking for a new friend and put an ad … Continue reading

## The hyperbinary sequence and the Calkin-Wilf tree

And now, the amazing conclusion to this series of posts on Neil Calkin and Herbert Wilf’s paper, Recounting the Rationals, and the answers to all the questions about the hyperbinary sequence. Hold on to your hats! The Calkin-Wilf Tree First, … Continue reading

## Challenge #12 solution, part II

Yes, that’s right, that Challenge #12, posted one year, five months, and a day ago. You see, I have this nasty habit of starting things and not finishing them… well, better late than never! Question two of the aforementioned challenge … Continue reading

Posted in challenges, counting, induction, pattern, sequences, solutions | Tagged , | 15 Comments

## Challenge #12 solution, part I

I’ll begin by providing an answer to the first of the three questions I posed in a previous post.

Posted in counting, pattern, proof, solutions | Tagged | 8 Comments