GC3X60D Think of a Number (#1) (Unknown Cache) in South East England, United Kingdom created by IceColdUK

This cache has been archived.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.

After 71 finds in fourteen years, time for this one to go. Thanks to all of those that tackled the puzzle and/or found the cache.

A few notes on the puzzle...

The magic number:
- 142857

The intimate relationship with a prime number (i.e. 7):
- 142857 × 1 = 142857 / 1 ÷ 7 = 0.142857...
- 142857 × 2 = 285714 / 2 ÷ 7 = 0.285714...
- 142857 × 3 = 428571 / 3 ÷ 7 = 0.428571...
- 142857 × 4 = 571428 / 4 ÷ 7 = 0.571428...
- 142857 × 5 = 714285 / 5 ÷ 7 = 0.714285...
- 142857 × 6 = 857142 / 6 ÷ 7 = 0.857142...
- 142857 × 7 = 999999 / 7 ÷ 7 = 1

The interesting properties:
- The first property makes it a Kaprekar number.
- I couldn't find a name for the second, a sort of 'Kaprekar variant'.
- And the third describes Harshad numbers.

The common approximation:
π ≈ 22 ÷ 7 = 3.142857...

Help with self-development:
- An enneagram that links the numbers is an integral part of the esoteric Fourth Way self-development method - what a load of ...!

GC3X60D ▼

A cache by IceColdUK Message this owner

Hidden : 9/20/2012

Difficulty:

Terrain:

Size: Size: other (other)

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Geocache Description:

The cache is not at the posted coordinates, and I'm afraid parking isn't great at GZ. Maybe better to cycle!

This cache has become the first in the 'Think of a Number' series of mathematically-themed puzzles. Although this cache stands alone, each of the others 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.

I have a favourite number. I was first drawn to it by its intimate relationship with a particular prime, but I've since discovered it has a few more interesting properties:

Its square can be split into two parts that sum to the original number
(such as 703: 703² = 494209; 494 + 209 = 703).
If you multiply it by the number with the same digits reversed, this can also be spit into two parts that sum to the original
(such as 990: 990 * 099 = 98010; 980 + 10 = 990).
And it is divisible by the sum of its digits
(such as 195: 1 + 9 + 5 = 15; 195 / 15 = 13).

There are a few numbers that satisfy all of these criteria, but only mine appears in a common approximation and can also help with self-development. What's not to like?!

(Assume N 51° 16 W 000° 38).