<

## Think of a Number (#5)

A cache by colincactus Message this owner
Hidden : 12/24/2013
Difficulty:
Terrain:

Size:  (small)

#### Watch

How Geocaching Works

Please note Use of geocaching.com services is subject to the terms and conditions in our disclaimer.

### Geocache Description:

The cache is not at the posted coordinates. There's a puzzle to solve first...

This cache is the fifth in the 'Think of a Number' series of mathematically-themed puzzles. Unlike the others in the series this one isn't offset from the solution of the previous one (as daisy chaining of puzzles like that is no longer allowed). However why not try doing the others first - you might well pick up a pointer for this one.

As IceColdUK was submitting his cache Think of a Number (#3) I was preparing one with the same name and near identical co-ordinates. That coincidence inspired me to set this puzzle instead. Hopefully it won't suffer the same fate.

--------------------------------------

I'm thinking of two numbers. The first I'll call J...I'll let you into a secret: it's last three digits are 744...and the second I'll call K. They are very close.

To solve the puzzle you will have to find nine other numbers (I'll write them in increasing order and call them R,S,T,U,V,W,X,Y and Z).

They all have a certain mathematical property, and they are the only numbers with that property.

Z was once part of an April Fool in which it was claimed that applying a simple formula to Z gave our number J. You can do the same on your calculator and you'll find that it doesn't - it's actually K (or maybe you'll be fooled into thinking it's J too).

Applying that formula to X and Y will give results that in both cases are near to numbers ending with the same three digits as J.

K is named after somebody, but the person involved actually applied the formula to some other numbers instead (58 was one).

When you've identified the nine numbers calculate A and B as follows:

A = V + S*(Z-X)
B = U*(Y-V-W)

Now start at the dummy co-ordinates

Go A/1000 minutes north (if R is even) or A/1000 minutes south (if R is odd)
Go B/1000 minutes east (if T is even) or B/1000 minutes west (if T is odd)

Chmmyr: N pnfr bs zvfgnxra vqragvgl
Pnpur: Frr trbpurpx

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)

Find...

### 31 Logged Visits

27      3      1

**Warning! Spoilers may be included in the descriptions or links.