In the game, you deal with robots that come with a tape of binary digits (red and blue dots), and you can build a maze using conveyer belts, branch points (which read a dot from the front of the robot's tape), and things that write dots to the end of the tape. You have tasks to fulfill; they start with easy things like "Accept robots with no red dots", then "Accept robots with the same number of red and blue dots", then "Reverse the input string" (that one is unpleasantly hard), and so on.
In particular, there are some user-submitted levels, and one asks, "Accept if the input number is congruent to 3 mod 7." (Input string is interpreted as a binary number, read left-to-right normally, with blue = 1 and red = 0.) I have a pretty nice solution to that one.
http://www.kongregate.com/games/PleasingFungus/manufactoria
In the game, you deal with robots that come with a tape of binary digits (red and blue dots), and you can build a maze using conveyer belts, branch points (which read a dot from the front of the robot's tape), and things that write dots to the end of the tape. You have tasks to fulfill; they start with easy things like "Accept robots with no red dots", then "Accept robots with the same number of red and blue dots", then "Reverse the input string" (that one is unpleasantly hard), and so on.
In particular, there are some user-submitted levels, and one asks, "Accept if the input number is congruent to 3 mod 7." (Input string is interpreted as a binary number, read left-to-right normally, with blue = 1 and red = 0.) I have a pretty nice solution to that one.