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Source: 1981 National High School Mathematics League, Problem 5

February 20, 2020
geometry3D geometry

Problem Statement

Given a cube ABCD−A′B′C′D′ABCD-A'B'C'D', in the 1212 lines:AB′,BA′,CD′,DC′,AD′,DA′,BC′,CB′,AC,BD,A′C′,B′D′AB',BA',CD',DC',AD',DA',BC',CB',AC,BD,A'C',B'D', how many sets of lines are skew lines? (A)30(B)60(C)24(D)48\text{(A)}30\qquad\text{(B)}60\qquad\text{(C)}24\qquad\text{(D)}48
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