Question 971051
The number of straight lines that can be formed by joining 10 points no three of
which are in the same straight line except 7 of them which are in the same
straight line, is
<pre>{{{drawing(500,250,-8,10,-8,5,


circle(5,1,0.15),circle(5,1,0.13),circle(5,1,0.11),circle(5,1,0.09),circle(5,1,0.07),circle(5,1,0.05),circle(5,1,0.03),circle(5,1,0.01),



circle(-7,0,0.15),circle(-7,0,0.13),circle(-7,0,0.11),circle(-7,0,0.09),circle(-7,0,0.07),circle(-7,0,0.05),circle(-7,0,0.03),circle(-7,0,0.01),

circle(-4,0,0.15),circle(-4,0,0.13),circle(-4,0,0.11),circle(-4,0,0.09),circle(-4,0,0.07),circle(-4,0,0.05),circle(-4,0,0.03),circle(-4,0,0.01),

circle(-2,0,0.15),circle(-2,0,0.13),circle(-2,0,0.11),circle(-2,0,0.09),circle(-2,0,0.07),circle(-2,0,0.05),circle(-2,0,0.03),circle(-2,0,0.01),

circle(1,0,0.15),circle(1,0,0.13),circle(1,0,0.11),circle(1,0,0.09),circle(1,0,0.07),circle(1,0,0.05),circle(1,0,0.03),circle(1,0,0.01),

circle(3,0,0.15),circle(3,0,0.13),circle(3,0,0.11),circle(3,0,0.09),circle(3,0,0.07),circle(3,0,0.05),circle(3,0,0.03),circle(3,0,0.01),

circle(6,0,0.15),circle(6,0,0.13),circle(6,0,0.11),circle(6,0,0.09),circle(6,0,0.07),circle(6,0,0.05),circle(6,0,0.03),circle(6,0,0.01),

circle(9,0,0.15),circle(9,0,0.13),circle(9,0,0.11),circle(9,0,0.09),circle(9,0,0.07),circle(9,0,0.05),circle(9,0,0.03),circle(9,0,0.01),


circle(0,-5,0.15),circle(0,-5,0.13),circle(0,-5,0.11),circle(0,-5,0.09),circle(0,-5,0.07),circle(0,-5,0.05),circle(0,-5,0.03),circle(0,-5,0.01),

circle(-2,-4,0.15),circle(-2,-4,0.13),circle(-2,-4,0.11),circle(-2,-4,0.09),circle(-2,-4,0.07),circle(-2,-4,0.05),circle(-2,-4,0.03),circle(-2,-4,0.01),

locate(-7+.2,0,A),
locate(-4+.2,0,B),
locate(-2+.2,0,C),
locate(1+.2,0,D),
locate(3+.2,0,E),
locate(6+.2,0,F),
locate(9+.2,0,G),
locate(5+.2,1,H),
locate(-2+.2,-4,I),
locate(0+.2,-5,J)

)}}}

Suppose the 7 points points A through G are in the same straight line.

That's 1 straight line.

Suppose H, I, J, are not, and that no three other than A through G are 
in a straight line.

We can connect the 3 points that aren't in a straight line three
ways, HI, HJ, and IJ.

That's 3 more straight lines.

We can connect H and each of the 7 points A through G

That's 7 more straight lines

We can connect I and each of the 7 points A through G

That's 7 more straight lines 

We can connect J and each of the 7 points A through G

That's 7 more straight lines.

Total 1+3+7+7+7 = 25 lines

Edwin</pre>