Question

I have an arbitrary array of lego bricks. I also have some figures made of 3 lego bricks. I want to find out how many combinations of figures I can create of the current array of lego bricks.

Anybody have some references for me, so I can solve this problem?

Which algorithms can I use? Any theory I can use?

Thank you in advance for any help you can provide.

/Hans

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Edit: This question was re-asked on the math stack exchange.

Answer 1

Would you believe that problems like this, or at least their general cases, are actually still open research questions? You’re doing real mathematical research here. 😉

Søren Eilers, Mikkel Abrahamsen, and Bergfinnur Durhuus did some work on a LEGO-combination counting problem, namely counting the number of unique ways you can arrange six identical 4×2 lego bricks. You may be able to look at their work (includes Java code) for inspiration.

From a skim over the text, it appears they solved the problem two separate ways:

1. Using a recursive block-positioning and counting algorithm.
2. Using brute force – trying every possible positioning of the six bricks in space (even those for which the bricks don’t touch.)

Hint: The number of possible combinations, even for small numbers of bricks, is large. This is what makes LEGO so fun.