##### This cache has been archived.

- Difficulty:

- Terrain:

Size: (regular)

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## Geocache Description:

The terrain is soggy, or very soggy, or worse.

### Long Multiplication

I learned how to do long multiplication, when I was in primary school. It isn't difficult, all you need is to know your "times table" and to be able to add. But it's a vanishing skill, in these days of calculators and spreadsheets.

You won't be able to use calculators and spreadsheets for this one.

Multiply pi (the ratio of the circumference to the diameter of a circle) by e (the base of natural logarithms). Both pi and e are "magic numbers", they turn up in all sorts of unexpected places. You should get the answer 8.539734....

But you'll need to do this calculation to rather a lot of decimal places.

### The most beautiful equation of mathematics

Just to brighten up your day, here's one of the most beautiful equations of mathematics: e ^{i*pi} + 1 = 0, where e and pi are as above, and i is the square root of -1.

### Meanwhile, back at the cache ...

For the first stage of this cache, go to:

N 51° ab.c(d+1)e

W 0° f(g-2).hjk

In the above formula, a is the 38th digit after the decimal point in the calculation you just made, b is the 32nd, c is the 35th, d is the 37th, e is the 31st.

f is the 44th, g is the 33rd, h is the 36th, j is the 27th and k is the 33rd.

Actually, you should be able to guess a, b, f and g using the usual geocacher's common sense, and that will give you a cross-check on whether you've got your sums right. Here's another cross-check. The sum of the digits a to k, is 49. And if your answer passes both those tests, you can use geochecker to make sure you have it spot on.

You'll be glad to hear that the other stages of this cache aren't so demanding on your arithmetic skills, but you will need a scientific calculator, or a phonable friend with a spreadsheet.

You should wear good waterproof boots or wellies, depending on how wet it's been recently.

The initial cash float (in an ammo box) is a bunch of non-British coins, and some obsolete British. And there's a huge cornucopia of Geocoins

There's Certificates for your trophy cabinet, for FTF, STF and TFT

You can check your answers for this puzzle on Geochecker.com.

## FTF is Amberel

## STF is Bob Smith and Bones1

**
Additional Hints**
(Decrypt)

[First stage] Jrne jryyvrf, ersyrpg ba gur pnpur anzr, naq ybbx sbe fbzrguvat gung "qbrfa'g dhvgr orybat gurer"

[Second stage] Ybbx ng Zrzbel Znc, naq lrf, vg'f va gurer.

[Third stage] Lrf, vg'f hc gurer.

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