GC4RZ8M Think of a Number (#3) (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This cache has been archived.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.

Just 41 finds in the thirteen years since this cache was placed. Time to go. Thanks to all of those that tackled the puzzle and/or found the cache.

For those looking to solve BigMal70's 'Think of a Number (#4), the coords were:
- N 51° 16.093 W 000° 39.250

A few notes on the puzzle...

Both of these examples were lifted from a quirky book, 'The Man Who Counted' by Malba Tahan. It seems to be out of print at the moment, but well worth picking up a second-hand copy if you like 'recreational mathematics'.

Amicable Numbers:
Divisors of 220: 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284
Divisors of 284: 1 + 2 + 4 + 71 + 142 = 220

Quadratic Friendship:
13: 13^2 = 169; 1 + 6 + 9 = 16
16: 16^2 = 256; 2 + 5 + 6 = 13

GC4RZ8M ▼

A cache by IceColdUK Message this owner

Hidden : 11/12/2013

Difficulty:

Terrain:

Size: Size: small (small)

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Geocache Description:

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

This cache is the third 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, one number isn't enough. You need to find two pairs of 'friendly' numbers:

A and B may not be perfect but as a pair they're certainly more than sociable - the sum of the proper divisors of A equals B, and vice versa
(e.g. say X = 172, then the sum of the proper divisors of X = 1 + 2 + 4 + 43 + 86 = 136).
C and D could also be said to share a friendship - the sum of the digits of the square of C equals D, and vice versa
(e.g. say Y = 17, then Y² = 289 and the sum of the digits of the square of Y = 2 + 8 + 9 = 19).

There are many pairs that satisfy the first condition, but I think only one that satisfies the second. You are looking for the lowest (or only) pair in each case.

The cache can be found (A+B+42)/3000 minutes west and (C+D+3)/2000 minutes south of Think of a Number (#2).

Thanks to =Andy_R for believing that my original puzzle warranted a sequel, and for his help testing this one.