Visible/Hidden Sides on Stacked Cubes
Date: 12/12/2001 at 15:33:08 From: robin_spruell Subject: Number Patterns I have been set the task of finding a formula for the number of sides hidden/visible on cubes when put in different arrangements - 1. a line 2. a double line 3. stacked in a 3D way I am having trouble finding out the numbers of sides and finding a formula. Please help!
Date: 12/12/2001 at 22:15:46 From: Doctor Peterson Subject: Re: Number Patterns Hi, Robin. Start with the simple case of a single row; here's a top view: +---+---+---+---+---+ | | | | | | +---+---+---+---+---+ How many sides are there in n cubes? Since each cube has 6 faces, there will be 6n faces in all. How many sides are hidden? There are n bottoms that you can't see (assuming you are supposed to include those); and there are (n-1) places where two cubes touch (5-1 = 4 in my example), each of which hides two faces, one on each cube. So there are n + 2(n-1) hidden faces. You can simplify the expression. That's how you think through this sort of problem: take an example, break it up into parts (bottom and touching faces), write an expression for the number of each kind, and add them up. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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