Here’s an idea for a general tiling game. Start with a set of shapes and 2 (or more) people. Each person takes it in turn to place onto a patch of tiling. The winner is the last person to move.

So here’s the puzzle:

Take the Myer’s polyhex tile:

Can you:

1. Find rules to avoid easy draws (for example wandering off in one direction to infinity).
2. Find a winning strategy?

I personally have no idea, so this is a challenge problem!

If you have access to a Laser Cutter or other fancy computer device the cut files are on Thingiverse.

 

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So, I’m teaching a new course, Math 2033, Mathematical Thought, and it’s going great! I’d like to take a moment to write about it!

(This is one reason the MF has been kinda slow lately; another is that I’m chair) When it’s fully up and running, we’ll have about 150 students in one large section each semester (we’re starting with about 100). In a nutshell, it’s the Math Factor, as a course.

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In Living With Crazy Buttocks  I posed a problem where 20 party guests were each given an unusual book.  These books were placed in identical boxes.  The guests enter the room with the boxes one at a time and are allowed to open half of the boxes.  They leave by a different door and cannot communicate with the other guests.  The room is put back identically before the next guest enters.

If every guest finds their book then the whole group win a trip to Paris.

What is their best strategy?

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Michael Huber discusses the mathematics of the Twelve Labors of Hercules!

 

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Recently I discovered Stan Wagon’s Problem of the Week.  This is a delightful mailing list / site and some of the problems are in the vein of puzzles I post here.  Recent problem 1125 captured the attention of several Math Factor authors so I thought I’d post the puzzle here as an excuse to introduce you all to that list.

You have eight batteries and know that four are good and four are dead, but don’t know which are which.  Your only method of testing them is to insert two into a device that will work if you’ve put in two good batteries and not otherwise.  How many such “tests” are required in order to be sure that you’ve located two good batteries?

As of this posting, the answer to this question is not yet on the POTW website, but if you come to this later, the spoiler may be there, so be careful to avoid spoilers if you want to work this through.

Wayne Winston tells us about his new sports-math book, Mathletics!

 

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