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Difference between revisions of "2024 AMC 8 Problems/Problem 20"
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==Problem==
 
==Problem==
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Any three vertices of the cube <math>PQRSTUVW</math>, shown in the figure below, can be connected to form a triangle. (For example, vertices <math>P</math>, <math>Q</math>, and <math>R</math> can be connected to form isosceles <math>\triangle PQR</math>.) How many of these triangles are equilateral and contain <math>P</math> as a vertex?
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<math>\textbf{(A)}0 \qquad \textbf{(B) }1 \qquad \textbf{(C) }2 \qquad \textbf{(D) }3 \qquad \textbf{(E) }6</math>
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==Solution 1==
 
==Solution 1==
  

Revision as of 12:38, 26 January 2024

Problem

Any three vertices of the cube $PQRSTUVW$, shown in the figure below, can be connected to form a triangle. (For example, vertices $P$, $Q$, and $R$ can be connected to form isosceles $\triangle PQR$.) How many of these triangles are equilateral and contain $P$ as a vertex?

$\textbf{(A)}0 \qquad \textbf{(B) }1 \qquad \textbf{(C) }2 \qquad \textbf{(D) }3 \qquad \textbf{(E) }6$

Solution 1

Video Solution 1 by Math-X (First understand the problem!!!)

https://youtu.be/N_9qlD9pgL0

~Math-X

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