Difference between revisions of "2023 AMC 8 Problems/Problem 17"
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− | ~Education, the Study of Everything | + | ~Education, the Study of Everything, nanaj |
==Animated Video Solution== | ==Animated Video Solution== |
Revision as of 23:20, 16 January 2024
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Solution 3 (Fast and Cheap)
- 5 Video Solution by Math-X (Simple Visualization)
- 6 Video Solution (CREATIVE THINKING!!!)
- 7 Animated Video Solution
- 8 Video Solution by OmegaLearn (Using 3D Visualization)
- 9 Video Solution by Magic Square
- 10 Video Solution by Interstigation
- 11 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
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, nanaj
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.