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Fun JavaScript question: Count the number of cubes filled with paint

黄舟
Release: 2017-02-15 14:49:40
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Suppose I have a cube of iron, and I soak it whole into a bucket of red paint.

Please note that the pigment cannot penetrate into the iron block, which means it can only dye the surface.

Then, I fished out the iron block and cut it.

The iron block has three dimensions as a cube. I made N flat cuts on each dimension to turn it into smaller cubes.

For example, if I cut each face 2 times, I can get 27 small cubes, 3*3*3.

Now the question is, after cutting N times, how many of the small cubes obtained are dipped in red paint? (Things that are dyed on one or more sides are counted)

The idea is very simple:

Require the number of cubes dipped in paint, subtract the undyed cubes from the total number of small cubes The number is available.

Note:

If I did not cut, the result should be 1.

So we have the following code:


	
	var countSquares = function(cuts){
		if(cuts == 0){return 1};
		return Math.pow((cuts+1),3) - Math.pow((cuts-1),3);
	}
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