Think of a Number (#2) Mystery Cache

This cache has been archived.

IceColdUK: Visited 10 of my caches today. Three had DNFs on them; all were in place, but another was missing. Decided the time was right to archive a few - the first three of the 'Think of a Number' series plus 'Biggles'. The others are all good to go.

46 finds in thirteen years. Time to go. Thanks to all of those that tackled the puzzle and/or found the cache.

This was originally an =Andy_R puzzle. I'd have added some notes but all I have is my own solution:

S=1089=33^2
T=33
S*2=2178
U=178

More
Hidden : 11/12/2013
Difficulty:
3.5 out of 5
Terrain:
1.5 out of 5

Size: Size: micro (micro)

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Geocache Description:

Or "Think of another number". This cache is the second 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 the original, TOAN#1.

  1. Think of a number and call it N.
  2. Write N backwards to give P.
  3. Take N away from P and ignore the sign, this is Q.
  4. Write Q backwards to give R.
  5. Add Q and R to give S.

Now if you have chosen N wisely, S will be an interesting and (as far as this cache is concerned) useful number.

S has some interesting properties, all associated with words beginning with the letter 's':

  • S's first 9 multiples give a pleasing pattern.
  • S is a polygonal number.
  • S is particularly useful for readers of an African Language.
  • S has significance to those who like to talk about games.

To find the cache:

  1. Find T, where S is the T-th polygonal number, mentioned above.
    So, for example, if S were the 4th such polygonal number (it isn't) then T=4.
  2. Take the last 3 digits of the 2nd multiple of S, call them U.
  3. Start at the solution* to TOAN#1.
  4. Move T thousandths South followed by T + U thousandths West.
There are micro certificates for the first 9 finders.

GeoCheck.org

My thanks to IceColdUK for being my Cache Test Dummy, and of course for setting the original TOAN.

* For the avoidance of doubt be sure to use the solution to the puzzle not the "Better coords for the cache" given in Geocheck.

Additional Hints ()

[Puzzle:] A orgjrra P naq Z [Cache:] Onfr bs gerr oruvaq vil fgrz. [Be careful of barbed wire.]

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)

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