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Math Help - Maths Square

  1. #1
    Alicat
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    Maths Square

    Hi hope its ok to post here I have a math problem, please can someone help?
    I have spent several days on it but just cannot complete it, The most I have managed to get is 7 numbers, then it just goes to pot

    Using the numbers 1 to 7 only, the eight white squares that surround each shaded square should add up to the number they surround. Moreover, once completed correctly, no row nor column will contain a duplicate number within a white square.

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  2. #2
    Site Founder MathGuru's Avatar
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    There are a couple of ways to try this problem . . .

    1. The way you probably have been trying is guess and check: P is probably a 7 since it is shared by the 4 largest numbers etc.

    2. Setting up simultaneous equations with all 40 variables. You would need 40 equations to solve it easily but I can only see the following:

    4 vertical rows that add up to the sum of (1 through 7)
    4 horizontal rows that add up to the sum of (1 through 7)
    9 sum of 8 variables that are surronding grey squares.

    so you have 17 equations and 40 unknowns.

    I think a combination of the two strategies will help you out. for example set up the equations and make some intelligent guesses and see where it takes you.
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  3. #3
    Site Founder MathGuru's Avatar
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    By the way I played around with this puzzle and p is probably not 7.

    Excel could be very useful for this puzzle.
    you could set up the grey squares to be sums of the surrounding squares and then start entering values.
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