Difference between revisions of "1981 AHSME Problems/Problem 22"

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How many lines in a three dimensional rectangular coordiante system pass through four distinct points of the form <math>(i,j,k)</math>, where <math>i</math>, <math>j</math>, and <math>k</math> are positive integers not exceeding four?
 
How many lines in a three dimensional rectangular coordiante system pass through four distinct points of the form <math>(i,j,k)</math>, where <math>i</math>, <math>j</math>, and <math>k</math> 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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<math>\textbf{(A)}\ 60\qquad\textbf{(B)}\ 64\qquad\textbf{(C)}\ 72\qquad\textbf{(D)}\ 76\qquad\textbf{(E)}\ 100</math>
  
 
==Solution==
 
==Solution==
 
No solutions yet!
 
No solutions yet!

Revision as of 11:19, 14 June 2021

Problem

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

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

Solution

No solutions yet!