Grades 1-2 Video Solutions 2025-2025_1-2

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Problem number 22. There are 13 cubes stacked in the corner of a room. Each is colored gray or white.  Directly below each gray cube is a white cube, and directly below each white cube is a gray cube. How many white cubes are in the stack?  To solve this problem, we can imagine looking at the shape layer by layer. In the first layer, there is a single white cube.  In the second layer, there are four cubes arranged in the pattern shown. And in the bottom layer, there are eight cubes in the pattern shown.  To figure out the colors of the hidden cubes, we can use the problem which says that below each gray cube is a white cube, and below each white cube is a gray cube.  For example, the gray cube in the second layer will have a white cube in the third layer below it,  and the white cube in the second layer will have a gray cube in the third layer below it. You can do that for all the hidden cubes to figure out what the layers will look like.  To solve this problem now, we just need to count how many white cubes there are. We can do that as follows.  The first layer has one white cube, the second layer has one white cube, and the third layer has five white cubes.  Therefore, the total number of white cubes is 1 plus 1 plus 5 equals 7. So the answer is C, 7.

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