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Think of a Number (#4) Mystery Cache

Hidden : 11/22/2013
Difficulty:
3.5 out of 5
Terrain:
1.5 out of 5

Size: Size:   small (small)

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Geocache Description:

The cache is not at the posted coordinates. There's a puzzle (or four) to solve...

 


This cache is the fourth in the 'Think of a Number' series of mathematically-themed puzzles. Each cache presents its coordinates as an offset from the previous cache in the series, so to find one, you will also need to have solved all of the previous puzzles. (This is reflected in the highish D-rating of this puzzle).

For this puzzle, you need to identify a number with interesting properties. This number has (A) digits

It is one of only four positive integers which, when you add the digits of the number together (B) and multiply it by the reverse of this sum (C), the result is the original number itself.

It is also the smallest number that displays properties with a name linked to a method of public transport due to a 20th century meeting of two mathematicians. There are four significant numbers related to these properties and the sum of these numbers equals (D)

Lastly, it is mentioned in a number of episodes of a particular cartoon series due in no small part to the team of maths graduates who created and wrote the show.

Start at the solution to TOAN#3 and move (Y) thousandths of a minute south and (Z) thousandths of a minute west.

Where:

Y = (2xD)

Z = (2xA)+(A/2)+(2xB)+C

Additional Hints (Decrypt)

Haqre fgvpxbsyntr

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)