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Number Theory: A Math Puzzle That Uses No Math

A cache by _Wynn Send Message to Owner Message this owner
Hidden : 7/6/2018
2 out of 5
1.5 out of 5

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Geocache Description:

The geocache is not at the posted coordinates*. To get the actual location, you must solve the puzzle below and enter the two-word solution into the certitude checker below.

Number theory is not as scary as it sounds, and neither is this puzzle! Formerly known as the grade school subject arithmetic, it is a branch of mathematics that deals solely with integers. It seems that mathematicians really like coming up with number sequences and giving them names. I mean, really... I had no idea. Honestly, given how many of them have been defined, it's like anybody can do it. Anybody can do this puzzle too. It doesn't require any math, other than the ability to count. After solving this, I have a feeling you'll be seeing numbers and patterns everywhere...

Identify the numbers described below. All sequences used in this puzzle are in base 10, which is our normal numbering system.

 1st perfect number
 2nd perfect totient number
 3rd semiperfect number
 5th happy number
 1st primitive abundant number
 2nd superior highly composite number 
 7th Perrin number
 1st emirp
 1st highly totient number
 1st sublime number
 1st Wilson prime
 5th standard Ulam number
 8th deficient number
 3rd Mersenne prime
 3rd pentagonal number
 1st composite number
 3rd centered hexagonal number   
 4th Fubini number
 2nd untouchable number
 2nd highly cototient number 
 2nd Fibonacci number
 3rd sparsely totient number
 2nd Kaprekar number
 1st centered triangular prime
 4th tetrahedral number

You can validate your puzzle solution with certitude.

*Not part of the puzzle: The posted coordinates are the intersection of 163rd PL SE and SE 66th ST. 163 is the 9th and final Heegner number, and 66 is the 3rd sphenic number. Isn't that fascinating? No, I suppose it isn't.

Additional Hints (Decrypt)

Pnpur: N uvag vf cebivqrq va gur fbyhgvba purpxre

Decryption Key


(letter above equals below, and vice versa)



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