Grades 9-10 Video Solutions 2022-2022_9-10

Video Transcription

Question 24. The squares on the surface of a 2x2x2 cube have one of three shapes on them. The shapes are a circle, a square, or an X. Any two squares that share a common side have  different shapes on them. The picture shows one such possibility. Which of the following combinations of shapes is also possible on such a cube? If we look at the three squares  touching any given vertex, we must realize they all have to be different from each other, since each pair of them share a side, and therefore are different. So we know since  there are eight vertices for each vertex, all three shapes must be present. We know there must be eight of each shape. So with that, we know that the answer will be E, none  of the above.

Video Summary

The problem involves a 2x2x2 cube with squares on its surface, each featuring a circle, a square, or an X. Adjacent squares must have different shapes, meaning at every vertex, the three touching squares must all display different shapes. Given the constraints, with every vertex needing representation by all three shapes, the solution must present precisely eight instances of each shape considering the cube's layout. The only feasible configuration that adheres to these requirements is "none of the above," as specifically outlined in choice E.

Keywords

2x2x2 cube

shapes constraint

vertex representation

feasible configuration

choice E