Question 1085988
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1.  how many collinear points are there containing 153 segments?


<pre>
<U>Answer</U>.  18 points.   

         Because {{{(18*17)/2}}} = 153.

         Or, in other words, because {{{C[18]^2}}} = {{{(18*(18-1))/2}}} = 153.

         Or, in other words, because the number of combinations of 18 points taken 2 at a time is 153.


         Or, you can solve this equation for n: {{{(n*(n-1))/2}}} = 153 and to get n = 18.
</pre>

Every two point of your collection define a segment, and, reversely, each segment is defined by two points of the collection.


Therefore, there is one-to-one correspondence between the segments and (unordered) pairs of points.