
Town Hall Tiles
http://i209.photobucket.com/albums/b...ATHDIAGRAM.jpg
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.

Quote:
Originally Posted by
everydaysahollyday http://i209.photobucket.com/albums/b...ATHDIAGRAM.jpg 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 $\displaystyle \dfrac{(n^2+1)}{2}$
In your case, working backwards, your x & y values will be:
$\displaystyle x = \dfrac{n1}{2} \,\, $ & $\displaystyle \,\, y = 0.5 $
for n=149
$\displaystyle x = \dfrac{1491}{2} = 74$ ; $\displaystyle 149 + \dfrac{74^2}{0.5} \, = \, 149 + \dfrac{5476}{0.5} = 11101 $
just to check
$\displaystyle \dfrac{(149^2+1)}{2} = 11101$
Hope that helps
.

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