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Long-time puzzler and player Dan from Minnesota asks the following question about our Entrapment Game:

My question is about the strategy game called Entrapment . After playing and solving several of these puzzles over the years I couldn't help notice the occurrence of very difficult and most brilliant puzzles that can take me hours to solve, verses only seconds to solve others, My question is are these randomly generated or are some these more advanced puzzles the result of mischievous talented geniuses?

Hi Dan, believe it or not, all of these games were the result of just one mischief maker. Me. Or, more precisely, my programming. There are almost 7,000 entrapment puzzles on the site, and they were all built by the software using an algorithm I built to create the puzzles at random.

How does it work? Well, the software starts by picking a random location for one of the gray dots, and then randomly picking a location for one of the red dots. Having picked one location, it now knows the location for a second red dot (since it has to be placed in such a way that the gray dot is midway between the two red dots). The software continues on in this way, alternately picking locations for gray dots and red dots, with the proviso that if the software can find a place to put a gray dot which is halfway between two gray dots already on the board, it skips putting another red dot on the board. In this way, the number of gray dots grows larger than the number of red dots.

In the end, the gray dots are removed from the board, leaving just the red ones. Of course, there's no guarantee that there's only one solution, and you've probably noticed that in some cases there are more red dots than are needed. This is because you found a solution that is different than the one the computer found.

Because the process is random, some puzzles end up being more challenging than others, and there's no good way to programmatically evaluate which puzzles are most challenging. Currently we're tracking the average amount of time taken for each puzzle, so that eventually we can break the puzzles into easy/hard/expert categories. But, of course, with 7,000 puzzles on the site, it's going to take a long time to get enough plays on each puzzle that we can confidently categorize them.

In the meantime, thank you for playing, and helping to add to our difficulty calculations!

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