Town Hall Tiles

everydaysahollyday · #1 $Old$ November 3rd, 2009, 12:09 AM

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.

aidan · #2 $Old$ November 3rd, 2009, 06:43 AM

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
.

Wilmer · #3 $Old$ November 3rd, 2009, 07:57 AM

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