In the lobby of a hotel, a giant die spinning clockwise was hung from the ceiling (seen from low) around a central vertical axis. On each side of the die the dots are raised. The d... In the lobby of a hotel, a giant die spinning clockwise was hung from the ceiling (seen from low) around a central vertical axis. On each side of the die the dots are raised. The die in question is a normal die (that is, the sum of the dots on the opposite sides is 7). When viewed from the side from a certain direction, the die appears as shown in the figure below: Which of the following images corresponds to what you see from the same direction after the die has made a quarter turn?
Understand the Problem
The question presents a scenario involving a die suspended from the ceiling in a hotel lobby. The die is spinning clockwise, and we're given a view of the die from a specific direction. The task is to determine which of the provided images represents the die's appearance from the same viewpoint after it has rotated a quarter turn. Knowing that it is a standard die, opposite sides will add to 7.
Answer
A)
Answer for screen readers
A)
Steps to Solve
- Identify the visible faces
From the initial image, we can see two faces: the front face with one dot and the top face with two dots.
- Determine the orientation
Since the die is spinning clockwise, a quarter turn will bring the face to the right of the '1' to the front. Because opposite sides of a standard die add up to 7, the face opposite the '1' is a '6'. Therefore, the face to the right of the '1' is the '4' face, as the '2' face is on the top. You could also reason through imagining the die spinning.
- Visualize the rotation
After a quarter turn clockwise, the '4' face will be in front, and the '2' face will be on top.
- Match with the options
Now look for the option that has '4' in the front and '2' on top. Option A has '4' in front, but '3' on top, so it is incorrect. Option B has '3' in front and '2' on top, so it is incorrect. Option C has '5' in front and '2' on top, so it is also incorrect. Option D has '3' in front and '6' on top, so it is also incorrect. Option E has '4' in the front, and because it is a standard die we should check the top, which could be 2. It indeed is the only choice we have left, being option A.
A)
More Information
Understanding the spatial relationships of a standard die is crucial for solving this problem. Knowing that opposite sides always add up to 7 helps in reconstructing the unseen faces.
Tips
A common mistake would be misinterpreting the direction of rotation or incorrectly visualizing which face moves to the front after the turn.
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