Tag Archives: nim

The chocolate bar game: variants

Posted on February 1, 2016 by Brent

Remember the chocolate bar game? Today I want to talk about some variants. Recall that the losing positions for the chocolate bar game can be visualized like this: What if we specify that you win if you end with a … 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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Visualizing nim-like games

Posted on August 16, 2012 by Brent

Inspired by the comments on this post, I’ve had some ideas brewing for a while—I’m just only now getting around to writing them up. The topic is visualizing winning strategies for "nim-like" games. What do I mean by that? By … Continue reading →

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