perplexus.info :: Numbers : Multiplication Table

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)

Comments: ( Back to comment list | You must be logged in to post comments.)

Getting less rigorous (spoiler)

| Comment 2 of 12 |

As I have noted, you can draw a straight line which passes through all three squares marked with a "4" in tomarken's picture, although it doesn't pass through the center of the squares.

I suspect that these are the only three squares in the whole infinite multiplication table where this is possible, but I don't want to do the math.

Posted by Steve Herman on 2006-07-07 11:08:57

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