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 complex grid?
With a complex grid it is necessary to account for squares which are present in more than one shape.
The general equation for the total number of squares in a grid with a size of nxn is N = n(n + 1)(2n + 1)/6, using this equation N has been determined or a selection of grid sizes.
| Grid size (nxn) |
Number of squares (N) |
| 1x1 |
1 |
| 2x2 |
5 |
| 3x3 |
14 |
| 4x4 |
30 |
| 5x5 |
55 |
| 6x6 |
91 |
The first comples shape consists of a 3x3 grid with a smaller 3x3 grid in the centre square. The small 3x3 grid has 14 squares, the large 3x3 grid also has 14 squares but one square has already been counted; the total number of squares is 27.
The second comples shape is a 4x4 grid with four 3x3 grids in each corner. Each 3x3 grid has 14 squares and the 4x4 grid has 40 squares but 4 have already been counted; the total is 92 (56+40-4).
So to the puzzle.
If the number of squares in the following design is abc?
The cache can be found at N51 13.(a+c)c(a+c) E000 10.(b-c)(b-c)a
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