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  1. Mathematical Curio

    If you take any integer and rearrange the digits however you like, the difference between the original number and the rearranged number will always be divisible by 9.

    For example:

    number = 12345
    rearranged = 43215
    difference = 43215 - 12345 = 30870
    difference / 9 = 3430
    

    More generally, you can do the same with numbers ...

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  2. Simulated Annealing

    My initial approach to the tiling problem was to find all the possible configurations, calculate a measure of the distance between same-colour tiles for each, and then select the configuration with the maximum distance. While this does reliably find the optimal solution, it also very quickly becomes infeasible as the ...

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  3. Tiling Problem

    We have a play-mat: eight rubber tiles, two of each colour, that fit together. We had put it together in a 4x2 arrangement, without considering the colours. The result was ... displeasing. Two pink tiles were right next to each other, but all the other pairs were separated. It just looked ...

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