GC8WC74 Checksum (Unknown Cache) in Washington, United States created by PYC

This cache has been archived.

PYC: Time to get these math-heavy puzzles off the board.
This one lasted almost 3 years and ended with 7 Fav points. Container and log sheet have been removed. Feel free to reclaim your Fav points.

GC8WC74 ▼

A cache by PYC Message this owner

Hidden : 7/10/2020

Difficulty:

Terrain:

Size: Size: other (other)

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Geocache Description:

for June 4, 2021

Welcome to Checksum.

Three geocachers, Adele, Bruno, and Clio,
are working on the same Mystery geocache puzzle.
In the cache's description, instead of providing a geochecker,
the cache owner has provided two checksum numbers,
one for the sum of the last four digits of the latitude coordinates (x+x+x+x+=14) and
one for the sum of the last four digits of the longitude coordinates (y+y+y+y=21).

For the purposes of this example,
we will work with just the last four digits
of the latitude (x+x+x+x) and its checksum (14).

Adele has figured the final latitude coords to be
N 46 43.632
Adding up the last four digits gives the correct checksum number of 14
(3+6+3+2=14)

Bruno has figured the final latitude coords to be
N 46 43.263
Adding up the last four digits, also, gives the correct checksum number of 14
(3+2+6+3=14)

Clio has figured the final latitude coords to be
N 46 44.451
Adding up the last four digits, also, gives the correct checksum number of 14
(4+4+5+1=14)

According to the checksum,
all three latitudes could be correct.
How can this be?
This gets Adele, Bruno, and Clio thinking,
“How many different ways can you get the last four digits
of the latitude (or the longitude) coordinates
to add up to a specific checksum number?”

They determined that there are 540 ways
to reach a checksum of 14 using four digits.

Can you match their mathematical prowess and solve today's puzzle?

----------------------PUZZLE-------------------

Using the digits 0-9, your challenge is to determine
the total number of four digit permutations,
where the four digits add up to a certain checksum.

For example, there is
only 1 four digit permutation
that adds up to a checksum of 0,
0+0+0+0=0,
and only 1 four digit permutation
that adds up to a checksum of 36,
9+9+9+9=36.

-------

The final for this cache is at

N 46 4A.BCD W 117 0W.XYZ

---North---

How many different four digit permutations add up to a checksum of 1? That is answer A.

How many different four digit permutations add up to 27? That is answer BCD.

---West---

How many different four digit permutations add up to 34? That is answer W.
NOTE: Subtract 1 from your W answer before putting it in the final coords.

How many different four digit permutations add up to 7? That is answer XYZ.

---Checker---

And just to keep this puzzle consistent,
you can check your missing final coord digits using the following checksums.

The checksum for the missing latitude digits (A, B, C, D) is 8.

The checksum for the missing longitude digits (W, X, Y, Z) is 12.

"Help is always given at Hogwarts to those who ask for it.” -- APWBD

----------------END--OF-PUZZLE-------------------

Remember to bring your own writing utensil.
Difficulty rating is for the hide and the puzzle.

Additional Hints (Decrypt)

Abg n anab. Pnpur vf nobhg 20 srrg sebz svany pbbeqf, fb rkcnaq lbhe frnepu.

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)

This cache has been archived.

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Checksum Mystery Cache

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