2023 AMC 8 Problems/Problem 17
A regular octahedron has eight equilateral triangle faces with four faces meeting at each vertex. Jun will make the regular octahedron shown on the right by folding the piece of paper shown on the left. Which numbered face will end up to the right of ?
We color face red and face yellow. Note that from the octahedron, face and face do not share anything in common. From the net, face shares at least one vertex with all other faces except face which is shown in green: Therefore, the answer is
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We label the octohedron going triangle by triangle until we reach the triangle. The triangle to the left of the should be labeled with a . Underneath triangle is triangle . The triangle to the right of triangle is triangle and further to the right is triangle . Finally, the side of triangle under triangle is , so the triangle to the right of is .
Solution 3 (Fast and Cheap)
Notice that the triangles labeled and make the bottom half of the octahedron, as shown below: Therefore, and are clearly not the correct answer. Thus, the only choice left is .
Animated Video Solution
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Video Solution by OmegaLearn (Using 3D Visualization)
Video Solution by Magic Square
Video Solution by Interstigation
Video Solution (CREATIVE THINKING!!!)
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