+199 A wooden block is 4 inches long, 4 inches wide, and 1 inch high. The block is painted red on all six sides and then cut into sixteen 1 inch cubes. How many of the cubes each have a total number of red faces that is an even number?
The block has a total of 24 faces, and each cube has 6 faces. If a cube has an even number of red faces, then it must have 2, 4, or 6 red faces. There are 8 cubes with 2 red faces, 4 cubes with 4 red faces, and 4 cubes with 6 red faces. Therefore, there are 16 cubes with an even number of red faces.
+1239
A wooden block is 4 inches long, 4 inches wide, and 1 inch high. The block is painted red on all six sides and then cut into sixteen 1 inch cubes. How many of the cubes each have a total number of red faces that is an even number?
Draw a 4 x 4 grid on a sheet of paper, as a guide.
You can mentally visualize the third dimension.
Here's what I count:
The 4 corner blocks 4 red sides each
The 8 outside edge blocks
excluding the corner blocks 3 red sides each
The 4 inside blocks 2 red sides each
So, it looks like the cubes that have an even number
of red sides are the 4 on the corners and the 4 inside.
That comes to a total of 8 cubes that have an even number of red sides.
No cube can ever have all 6 sides red, because the side(s) where a
cube was butted up against another cube wouldn't have got painted.
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