142,857 Mystery Cache
Hidden : 5/29/2020
Difficulty:
1.5 out of 5
Terrain:
1.5 out of 5

Size: Size: small (small)

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Geocache Description:




142,857 may seem like any other six-digit number, but it isn’t- in fact, it’s a number unlike any other. 142,857 is so exceptional, it’s one of the very few six-digit numbers to have its own Wikipedia article.

This puzzle cache will explain why! As for the puzzle, that should be a lot simpler than it looks!

Mathematically, 142,857 is the best known example of a cyclic number in base 10, as well as the six repeating digits of the fraction 1/7: 0.142857. Therefore, when you divide 1 by 7, you get 0.142857,142857,142857...

When 142,857 is multiplied by any number from 1 to 6, the result is the same number containing the same digits in the same order, but starting in a different place.
1 × 142,857 = 142,857
2 × 142,857 = 285,714
3 × 142,857 = 428,571
4 × 142,857 = 571,428
5 × 142,857 = 714,285
6 × 142,857 = 857,142

Multiplying it by 7 is also intriguing!

7 × 142,857 = 999,999

Multiplying it by 8 gives you 1,142,856. If you take of the first digit (1) and add it to the remaining digits:
1 + 142,856 = 142857!

Splitting the number in half, 142 and 857, and then adding these two numbers together, it equals 999!




It really is a remarkable number. Now you can use it to find the cache!


Thank you to the fact book How To Avoid A Wombat’s Bum for making me aware of this number’s magical properties!

Additional Hints (Decrypt)

Onfr bs gerr, haqre fgbarf. Bccbfvgr fvqr bs gur cngu sebz gur ybar gerr.

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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