Please see number 1 in the series (Are you a square?) for a full description of the walk, there is street parking available in the village of Weald.
The cache is not at the posted coordinates.
This is a relatively simple puzzle, the information below will help you to solve it and might assist with a slightly harder one placed close by.
How many triangles?
Time for a change in shape. This puzzle is based on the total number of equilateral triangles in a grid of equilateral triangles.
The shape below has 4 small triangles (1x1x1) and one larger triangle (2x2x2); a total of 5.
Increasing the size by adding a third row increases the count to 13 with nine small triangle (1x1x1), three mid size (2x2x2) and a single large (3x3x3).
An exact general solution is given by N=4n3+10n2+4n-1+(-1)n/16 where n is the number of rows of small triangles in the large triangle.
So the solutions are 1, 5, 13, 27, 48, 78, 118 etc
An alternative way of solving this problem is to used N=(n(n+2)(2n+1)-1)/8 when n is an odd number
or N=(n(n+2)(2n+1))/8 when n is an even number.
If the total number of triangles (N) in a triangle with nine rows of small triangles is abc then the final coordinates are given by
N51 13.a(bxb)a E000 10.(a+a)(c-a-b)(bxb)
*** Congratulations to -KROP- on FTF ***