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'Latin Numbers' printed from http://nrich.maths.org/

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In the grid below, N is a 6 digit number with a very special property: if you double the number and write it in the second row, treble the number and write it in the third row, and so on, you end up with a Latin Square. 

A Latin Square is an arrangement of numbers in a square in which each number appears exactly once in each row and column. So, for example, the number represented by ? can't be the same as B or *, and * can't be the same as D, ? or @.

 

N A B C D E F
2N            
3N   ?   *    
4N            
5N       @    
6N            


Can you find the six digit number N?

 


If you're finding it difficult to get started, click below to see a possible order in which you can work out each value (starting with cell a, then cell b, and so on...)


a m s     d
h n t     e
i o w     c
j p u     f
k q x     b
l r v     g