2023 AMC 8 Problems/Problem 17
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Solution 3 (Fast and Cheap)
- 5 Solution 4 (Really Simple Reasoning)
- 6 Video Solution by Math-X (Simple Visualization)
- 7 Video Solution (CREATIVE THINKING!!!)
- 8 Animated Video Solution
- 9 Video Solution by OmegaLearn (Using 3D Visualization)
- 10 Video Solution by Magic Square
- 11 Video Solution by Interstigation
- 12 See Also
Problem
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 ?
Solution 1
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
~UnknownMonkey, apex304, MRENTHUSIASM
Solution 2
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 .
~hdanger
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 .
~andy_lee
Solution 4 (Really Simple Reasoning)
The first half of the octahedron will need triangles connected to one another to form it. We can choose the triangles , , , and and form the half around the vertex they all share. That leaves triangles , , , and to form the second half. Triangle will definitely share its sides with triangles and , leaving them to share their second side with triangle . Since triangle will certainly share its left side with triangle , the only triangle left to share its right side is triangle
~ProProtractor
Video Solution by Math-X (Simple Visualization)
https://youtu.be/Ku_c1YHnLt0?si=XilaQFDcnGR8ak7W&t=3364
~Math-X
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Animated Video Solution
~Star League (https://starleague.us)
Video Solution by OmegaLearn (Using 3D Visualization)
https://www.youtube.com/watch?v=nVSF2ujZkPE&ab_channel=SohilRathi
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=3789
Video Solution by Interstigation
https://youtu.be/DBqko2xATxs&t=2195
See Also
2023 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.