1981 AHSME Problems/Problem 22

Problem

How many lines in a three dimensional rectangular coordinate system pass through four distinct points of the form $(i, j, k)$ , where $i$ , $j$ , and $k$ are positive integers not exceeding four?

$\textbf{(A)}\ 60\qquad\textbf{(B)}\ 64\qquad\textbf{(C)}\ 72\qquad\textbf{(D)}\ 76\qquad\textbf{(E)}\ 100$

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1981 AHSME Problems/Problem 22

Problem

Solution