Kaitoke Birds
Everyone sees and hears birds when they are out looking for caches, but how many of them can you identify by name? By the time you have found this cache you will have turned into a budding ornithologist. There is a short walk to the final with some hill work required, to test your fitness as well.
The Puzzle
All of the birds in the pictures below can be seen and/or heard whilst walking around the Kaitoke area and I have personally seen all of them in the area. Some are present all year round, some are migrants, only visiting New Zealand in the summer. Some are birds of the bush, some are birds of the open fields and some can be found pretty much anywhere in the area. Some are very common, others are elusive and few and far between. Some of them have been introduced by European settlers, some are native to New Zealand (got here under their own steam) and some of these are endemic (cannot be found anywhere else except New Zealand).
Once you have identified each bird, the co-ordinates for the cache location are obtained by doing a calculation for each bird. The formula required and values for the lower case numeric variables c, m and s differ from bird to bird: so you have to identify each bird, work out what the values of c, m and s are for that bird and do the relevant simple calculation for each digit to get the final co-ordinate. The cache can then be found at S AB° CD.EFG, E HIJ° KL.MNO.
In the formulae the notation used is:
+ plus
- minus
* multiplied by
/ divided by
√ square root of
() brackets: evaluate the part of the formula inside before the rest of the equation
The Birds

A = s/3

B = (s-m-c)/2

C = s*m

D = s-c-c/m

E = (s/m)/4

F = s/√c

G = m/(s-c)

H = c/s

I = m

J = c/3

K = c*m

L = s-m-c+1

M = √(s-c)

N = m-c/m

O = s-c

The Cache
The cache is a 200 ml Sistema large enough to take small Travel Bugs or small trade items only and at the time of hiding contained a log sheet, a gel pen and a teddy bear brooch. There is also a small edible prize for the FTF. Please bring your own pen or pencil in case the gel pen has run out or has gone walkabout. Found logs online that are not also in the written log will be removed unless you provide other evidence that you really did find the cache (e.g. a photo of the cache, but don't show its actual location).
When replacing the cache after signing the log please remember to replace it exactly where you found it and ensure it is hidden from view.