Ten soldiers puzzle This is a puzzle from one popular book called "The Man Who Counted: A Collection of Mathematical Adventures",author is Malba Tahan. How to arrange ten soldiers in five lines in such a way
that each line contains four soldiers exactly? 
 A: 5 lines times 4 soldiers on a line equals 20 = two times 10 soldiers available. This suggests that every soldier belongs to two lines.
Draw $n$ lines on the plane such that no two are parallel, and no three intersect in one point.
You can always do that: if you already have $n-1$ lines then there are finite number of slopes of those lines and finite number of points of intersection -- choose a new slope not equal to any previous and draw the line with this slope not going through any previous points of intersection.


*

*Each line contains exactly $n-1$ points of intersection with other lines.

*There are $\frac{n(n-1)}{2}$ intersection points in total.
Now, if you put a soldier at every point of intersection, then there are $\frac{n(n-1)}{2}$ soldiers arranged in $n$ lines, each containing $n-1$ soldier. For $n=5$ you get the answer: any such configuration of 5 lines would work.
A: Like this:
$\hskip1.7in$ 
A: 
This is an alternative (sorry diagram is clunky)
A: A more irregular looking solution.

