<

## Plouffe, There It Is!

A cache by teamajk Message this owner
Hidden : 03/14/2016
Difficulty:
Terrain:

Size:  (micro)

#### Watch

How Geocaching Works
Please note Use of geocaching.com services is subject to the terms and conditions in our disclaimer.

### Geocache Description:

There is nothing hidden at the posted coordinates, but they are a good place to park (be sure to obey the signage). You must solve the puzzle below to get the cache coordinates.

Ithacadoodle recently gave me a gorgeous Pi Day Geocoin, and I decided it really deserved a puzzle. The solution to this puzzle is a key word made up of three numbers. When you put the three numbers into the geochecker, not only will you receive this cache's coordinates, but you will receive the tracking code for the coin.

Sometimes math can seem kind of like magic. Until it was done by Simon Plouffe, David Bailey, and Peter Borwein, (whose names appear on my coin) no one would have believed that it was possible to create a formula that would compute any digit of π, without having to know the previous digits. Pretty cool, huh? Let's consider some other mathemagic ... I'll let you decide if the results are math, magic, or something else.

Problem #1: Choose the number that represents your favorite digit of π. What's that? You don't have a favorite digit of pi? The heck you say! OK, then, just pick one. Any one will do. Got one? Now spell it, count the number of letters, and let that number = Q. Now spell the number Q, count the letters and let that number = R. Now spell that number, count the letters and let that number = A.

Problem #2: Choose any non-zero digit of π. Really, any one will do as long as it's not zero. *Now, if that number is even, divide it by 2. If it's odd, multiply it by 3 and add 1 to the result. Write that number down.* Call your resulting number X. Use that number and repeat the process between the asterisks. Keep repeating the process until you start to see the same results repeating (depending on which number you chose, this could take a while ... just keep going). At that point, you'll have three numbers that keep repeating. Choose the lowest of these three, and call that number B.

Problem #3: Choose any two digits of π and write them down as a number EF. Any two digits will work, as long as E is not a zero. Add E + F and call that number G. Then subtract G from EF, and call that number HI (it's OK if H is a zero). Add H + I together and call the result MN (again, it's OK if M is a zero). Divide MN by 9, and call that number C.

To receive the information you desire, enter your three numbers ABC into the geochecker.

You can validate your puzzle solution with certitude.

Thanks to TSandCS for beta-testing.

A note to you overachievers out there: repeat problem #2 starting with a number with any number of digits (as long as they're not all zeros). See what happens. It might take you a while, but isn't that cool?

Chmmyr: Srry serr gb pnyy ba zr sbe vasbezngvba.
Pnpur: Qrgnvyrq uvqr vasb tvira va purpxre.

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)

Find...

### 52 Logged Visits

41      4      4      1      1      1

**Warning! Spoilers may be included in the descriptions or links.