Τρίτη, 1 Νοεμβρίου 2016

Latin Numbers : nrich.maths.org

Latin Numbers : nrich.maths.org





Latin Numbers

Stage: 3 Challenge Level:2 Challenge Level:2




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...)


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