2023 AMC 8 Problem 17

Below is the video solution and professionally curated solution for Problem 17 of the 2023 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2023 AMC 8 solutions, or check the answer key.

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Concepts:net (3D geometry)polyhedron

Difficulty rating: 1580

17.

A regular octahedron has eight equilateral triangle faces with four faces meeting at each vertex. Jun will make the regular octahedron shown in the figure by folding the piece of paper below. Which numbered face will end up to the right of the shaded region Q?Q?

11

22

33

44

55

Video solution:
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Written solution:

Begin by observing that when folded, the sides labelled 2,2, 3,3, 4,4, and 55 form the bottom half of the octahedron. As such, the remaining four faces must make up the top half of the octahedron.

From here, we have narrowed down our possibilities to 1,1, 6,6, and 7.7. We can see that 66 will be the number to the left of the shaded region Q.Q. This also gives us that 77 is to the left of 6.6.

Therefore, we know that the only remaining face, 1,1, must be to the right of the shaded region Q.Q.

Thus, A is the correct answer.

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