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Math Help - Town Hall Tiles

  1. #1
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    Exclamation Town Hall Tiles





    The diagram above (sorry my diagram isnt too great..) contains black and white tiles in a diamond formation. There are 7 tiles across and 25 tiles in total. Now I need to find how many tiles there would be in total, if the number of tiles across was 149. The formula I am using is n+x^2/y

    So for the 7 across, the formula would be 7+x^2/y = 25

    The only problem is, I cant work out what x and y are.

    If you could help me finding what x and y are, that would be greatly appreciated.


    Holly.
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  2. #2
    Super Member
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    Quote Originally Posted by everydaysahollyday View Post



    The diagram above (sorry my diagram isnt too great..) contains black and white tiles in a diamond formation. There are 7 tiles across and 25 tiles in total. Now I need to find how many tiles there would be in total, if the number of tiles across was 149. The formula I am using is n+x^2/y

    So for the 7 across, the formula would be 7+x^2/y = 25

    The only problem is, I cant work out what x and y are.

    If you could help me finding what x and y are, that would be greatly appreciated.

    Holly.
    The standard formula for this would be  \dfrac{(n^2+1)}{2}

    In your case, working backwards, your x & y values will be:

     x = \dfrac{n-1}{2} \,\, --&-- \,\, y = 0.5

    for n=149

     x = \dfrac{149-1}{2} = 74 ;  149 + \dfrac{74^2}{0.5} \, = \, 149 + \dfrac{5476}{0.5} = 11101

    just to check

     \dfrac{(149^2+1)}{2} = 11101

    Hope that helps
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  3. #3
    MHF Contributor
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    In case this helps, Aidan's formula "comes from" the formula:
    sum of 1st n odd numbers = n^2; like 1 + 3 + 5 = 3^2

    In your example, this occurs twice (above and below the middle row),
    hence 2(1 + 3 + 5) + 7 = 25
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