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    A 5*5 square is divided into 25 unit squares. One of the numbers 1,2,3,4,5 is inserted into each of the unit squares, in such a way that each column, each row and two diagonals contains the numbers 1-5 once and only once. The sum of the numbers immediatley below the diagonal from top left to bottom right is called the score.

    Show that it is impossible for the score to be 20
    What is the highest possible score?

    The first part can only be done using four 5's and that doesn't follow the rules because one of the diagonals must also contain a 5 meaning that there are two 5's in one column.

    For the second part, is it best to just try different value's say 4,5,5,5 Or set the score to 19,18,17....and see whether it's possible for them to work?
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    I don't understand the different between your two methods for the last section, but yes, it is the correct method
 
 
 
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Updated: October 19, 2008

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