Imagine a multiplication table (like the one below, except it continues on forever):
1 2 3 4
+++++
1 1  2  3  4 ...
+++++
2 2  4  6  8 ...
+++++
3 3  6  9  12...
+++++
4 4  8  12 16...
+++++
...............
Find three of the same number in a straight line somewhere within the table. If this is not possible, show why not.
(In reply to
A better answer by Old Original Oskar!)
Note that in OOO's post, when the 3 points are defined as:
(x,y), (x+a,yb), and (xac,y+bc) and he concludes that c=1,
this means that the 3rd point is identical to the 2nd point proving there can be only two numbers in straight line.

Posted by Larry
on 20060708 15:57:09 