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.

    1   2  3  4   5   6   7  8
  _______________________
1| 1
2| 2  4
3| 3  6   9
4| 4  8  12 16
5| 5 10 15 20 25
6| 6 12 18 24 30 36
7| 7 14 21 28 35 42 49
8| 8 16 24 32 40 48 56 64

The tabel is symmetrical.
On one half of this symmetry...
   All horizontal rows have a linear progression.
   All vertical rows have a linear progression.
   All diagonal rows, in both directions, have a
     linear progression.
   At the most, there can only be one of any given
     number in any straight line.
So, on both halves, there can only be at most 2
of any given number.