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Math Help - the chessboard

  1. #1
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    Exclamation the chessboard

    help me with this amazing problem. i have it in a doc file as i dont have paint
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  2. #2
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    i also have a hint(almost the complete solution) which leads me nowhere...i can gve that to if you need.
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  3. #3
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    You will end up eight distinct numbers a,~b+8,~c+16,~d+24,~e+32,~f+40,~g+48,~h+56.
    Each of a,b,c,d,e,f,g,h is distinct and between 0 & 9.
    So the sum a+b+c+d+e+f+g+h=36
    What is \sum\limits_{k = 1}^7 {8k}  = ?
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  4. #4
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    its 224 + the 36 makes it 260.

    but could you explain again how you got those two observations?


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    Last edited by adhyeta; May 2nd 2009 at 08:55 AM. Reason: typo
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  5. #5
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    Quote Originally Posted by adhyeta View Post
    but could you explain again how you got those two observations?
    Well you play with it awhile.
    Pick at random one number from each row and column.
    See if you can put them into the form that I used.
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