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,y-b), and (x-ac,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.
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Posted by Larry
on 2006-07-08 15:57:09 |
re: A better answer
