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April 18th, 2015, 11:16 AM  #1 
Newbie Joined: Oct 2011 Posts: 4 Thanks: 0  How do I determine how many sides a shape has?
Hello Mathematicians! I’m hoping you can help a somewhatmathy person with a puzzle which is stumping me. I’m developing a computer program where a person can make shapes from squares on a matrix. They do this on a 6x6 grid, which is composed of 36 squares, and the user has the option to turn a square on or off. The user can create a shape by turning some of these cells on. I suppose this works like a “binary matrix”. What I want to ask the user to do, for example, is create a shape with six sides using four blocks. (They’ll have varied challenges depending on the question, but they’ll involve creating a shape, usually with a certain number of sides, from a certain number of blocks.) They can do this in many different ways, in many positions, and orientations. What I’d like to do is somehow calculate the number of sides a shape has when the user turns on connecting cells. How do I do that though? How do I tell a computer what to count to determine how many sides a shape has? I’m sure the solution is simple and has a distinguishable pattern but this has been stumping me. Any assistance to this logic problem will be much appreciated! Thank you, Brendan 
April 19th, 2015, 10:27 AM  #2 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361 
Some terms (I made them up, if you have any better...): Let a bar be the side of a square, whether the square is colored or not. So a square has four bars and the 6x6 grid has 84 bars. Let a bar be dubious if [one adjacent square to it is selected (by the user)] AND [[the other square is not selected] OR [the other square is not there (the bar is on the edge of the grid).]] Let a side be bars in alignment such that any bar between any two bars on the same line are dubious. You could create a list of all dubious bars created by the user, then identify the bars that form a side and count the sides. Does this help? 

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