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10. Simple try angles Mystery Cache

Hidden : 12/10/2020
Difficulty:
2.5 out of 5
Terrain:
2.5 out of 5

Size: Size:   micro (micro)

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Geocache Description:


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?

This problem is based around dividing a triangle in multiple triangles.

The addition of a single line increases the total number of triangle to 3.

If two lines are added the number increases to  six.

Counting for these simple diagrams is easy enough but as the number of lines increases the task get harder; an alternative way is required! A simple way is to number each segment, as shown below, and add the numbers together

Even this method is laborious at higher segment numbers, fortunately there is a technique for adding natural numbers. If the number of segments is n, the addition is given by n(n+1)/2.

For six segments this becomes 6*7/2=21

So for this puzzle. If 15 lines are used to divide a triangle into ab segments and cde triangles the cache can be found at

N51 12.(b+d)(a+e)(d-c)    E000 09.(d+e-b/e)b(b-e)

*** Congratulations to -KROP- on FTF ***

Additional Hints (Decrypt)

Abar Pbbeqvangrf jrer hcqngrq - whfg n fznyy punatr

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)