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## A Piece of Pi

A cache by dgauss Message this owner
Hidden : 03/14/2009
Difficulty:
Terrain:

Size:  (small)

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## Geocache Description:

The Cache is NOT at the posted coordinates. However, it can be found at N 44° 51.927, W 093° 69.485 (sort of) where Pi is (approximately)

3.14159265358979323846264
3383279502884197169399375
1058209749442953087614062
8620899862803482534211706
7982148086513282306647093
844609550582231...

A hint (sort of) (added 3/22/09). The value of pi and a study of its digits has been of interest as far back as the wheel. The digits do not repeat in a pattern, i.e. pi cannot be written as the ratio of two integer, which is to say it's not a rational number. It's irrational! And it's not algebraic, i.e. it is not the root of any polynomial equation with rational coefficients; thus it is said to be transcendental. It has been conjectured that the digits in pi are random. In that case, any finite sequence of digits would eventually occur. For example, consider the sequence of the digits in order 0123456789. Beginning at any decimal place, the odds of encountering that particular sequence is one in 10^10 because there's only one chance in 10 of the 0 being there, one chance in 10 of the 1 being next, and so on. So we'd expect to go out ten billion places to have half a chance of finding 0 thru 9 in the order 0123456789. Pi is known to and has been studied thru only one billion places so far and that sequence has not yet appeared. If we were to settle for any old order of 0123456789 the odds against finding it wouldn't be so large. Starting with the digit in any position, the chance that the next one is different is 9/10, and that the next one after that is different from the first two is 8/10, ..., and finally that the tenth one is different from the first nine is 1/10. So the odds of finding any old permutation of 0 thru 9 is (9/10)(8/10)(7/10)...(2/10)(1/10) = 9!/10^10 ~ 1/2755. So we should expect to find the ten digits in some order by the 2755th place. Of course it might happen later, or it could happen earlier. Check it out.

You can validate your puzzle solution with certitude.

The first solvers of the puzzle are:

1.      pfalstad        Thu, 26 Aug 2010 9:48:47
2.      jimbexleyspeed  Sun, 12 Sep 2010 13:48:59
3.      huskyboi2       Mon, 13 Sep 2010 17:36:35
4.      Good-Boy        Wed, 3 Nov 2010 3:46:23
5.      Quilting is fun too     Thu, 2 Dec 2010 21:15:27
6.      Essap   Fri, 4 Feb 2011 22:34:57
7.      imyz1   Mon, 7 Feb 2011 16:20:45
8.      oakwilt Thu, 10 Feb 2011 15:38:03
9.      bflentje        Fri, 11 Feb 2011 11:31:48
10.     PA-20   Thu, 10 Mar 2011 23:45:59
11.     leopold22       Sun, 13 Mar 2011 13:36:18
12.     Pippin and Merry        Wed, 14 Sep 2011 22:41:15
13.     rickrich        Fri, 4 Nov 2011 10:35:15