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2. Squares and wrecked angles Mystery Cache

Hidden : 12/2/2020
Difficulty:
2 out of 5
Terrain:
2 out of 5

Size: Size:   small (small)

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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 squares are there in a rectangular grid?

For a grid with the same number of horizontal and vertical squares (mxm) the total number of squares N can be found using the equation N = m(m+1)(2m+1)/6

But what happens when the grid is rectangular?

Consider three rectangles with grids of 1x4, 2x4 and 3x4 squares.

For a 1x4 grid the total number of 1x1 squares is 4.

For a 2x4 grid there are eight 1x1 squares and three 2x2 squares; 11 in total.

For a 3x4 grid there are twelve 1x1 squares, six 2x2 squares and two 3x3 squares;  20 in total.

 

The general form of the total number of squares N for a mxn grid (m<n) is N=((m(m+1)(3n-m+1)/6

If the number of squares in a grid 9x11 is given by abc the cache can be found at:

N51 13.(a+a)b(a+c)  E000 11.(a-a)c(a+c)

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

Additional Hints (Decrypt)

Fgnvejnl gb Urnira be n tngr gb abjurer. EUF ybj qbja

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)