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 Multiplication Table (Posted on 2006-07-07)
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.

 No Solution Yet Submitted by tomarken Rating: 3.0000 (4 votes)

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 No Subject | Comment 7 of 12 |

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.

 Posted by stonicus on 2006-07-07 22:29:43

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