## Puzzle #9: Island of Games

Life is fun on the Island of Games.  The thousand inhabitants enjoy competing at chess, checkers, and contests to solve the Rubik’s Cube puzzle as fast as possible.  The islanders are rated for their skill at each of the three games.  The ratings fall between 0 and 1.

The ratings for each category seem to follow a uniform distribution. For example, here is a histogram for the Chess ratings:

There isn’t much correlation between the skills for the three games:

Correlations between Skills

 Chess Checkers Rubik’s Cube Chess 1.0000 Checkers 0.0530 1.0000 Rubik’s Cube 0.0452 -0.0049 1.0000

The next three charts confirm this lack of correlation.  The first chart compares the ratings for Chess and Checkers, and includes a linear regression:

Here is Chess vs Rubik’s Cube:

And Checkers vs Rubik’s Cube:

The raw data and some statistical analysis can be found here.

All of this looks like pure noise.  But there is a hidden structure.  Can you find it?

See the Answer: Binary Sudoku and the Limits of Visualization

Related Geometric Animations: Melting Fractals

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### 8 Responses to Puzzle #9: Island of Games

1. Win Smith says:

I posted this puzzle to Quant Masters, a LinkedIn group, and Simon Bremer has solved it.

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2. Win Smith says:

I also posted to puzzle to wilmott.com, where it has been solved, leading to an interesting discussion involving monte carlo sampling and fractals.

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3. Wow, very cool puzzle. This is going to take some time for me to work out. I’ve been numbing my brain too much with simple games like Online Checkers. I love puzzles though so I’m looking forward to a challenge.

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4. sumit says:

absolutely awesome, gives a lot to think about, cheers

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