# The Key to the City

This is part 9 of the puzzle series Around the World in Many Days. Each part is solvable on its own.

Deаr Puzzling,

This is a Skyscrapers puzzle. Each letter represents a unique number between 1 and 6. Numbers inside the grid can be thought of as heights of towers located in each cell; numbers outside the grid tell how many towers are visible from that direction in the row or column. A tower is visible if it does not have any higher tower in front of it in that direction. Each number is used exactly once on each row and column. The solved grid serves as a 36-letter Vigenère key to decipher where to find the final answer.

GEGKJ QYHE XSJYCH CAIH HUKJP NQHYTYOPG YL YVB YQFTYGBF HXJ YDPISH GFYWQE VWCJ ZLFHEK QSCR HEDLJO SCYSE SIAQAKUQJ

Today I have visited a remote city once filled with unimaginable riches. Can you guess where I am?

Gladys will return in Behind Great Walls.

I hope Gladys enjoys her stay at:

Timbuktu, Mali

The Puzzle:

The number 6 is very important in 6$$\times$$6 skyscraper puzzles, so we need to figure out which one is 6.

If a number on the outer is 6, then the inner squares must be in the order 1,2,3,4,5,6. And if a number on the outer is 1, then the immediate next number on the inside must be 6.

Now, O and M cannot both be 1, so Y cannot be 6.
M cannot be 6 as X and Y cannot both be 1, for a similar reason O cannot be 6.
F and O cannot both be 1 so Q cannot be 6.
F and O cannot both be 6, so Q cannot be 1, hence F cannot be 6.

So X must be 6!

Now we can replace M with 1. Q must be 1 or 2 as the 6 in the first row blocks everything after it. But 1 is taken, so Q is 2.

Observe the third row. If F was less than 4, we would see more than 2 skyscrapers from looking left to right. But this is impossible, so F>4.

As 6 is taken, F must be 5!

Y and O have to be 3 and 4 in some order. Now we look again at the third row. 4 is already used but O is also there. This means that O is 3 and Y is 4.

Now we can just solve this as a normal skyscraper puzzle:

Replacing the numbers with letters gives:

Coming to the Vigenère key:

Reading the key from left to right and using it on the message gives: "SHIFT EACH LETTER FOUR TIMES BACKWARDS IN THE ALPHABET THE ANSWER STARTS FROM BOTTOM LEFT CORNER GOING CLOCKWISE"

Doing so gives:

TIMBUKTU ( Thank you @SeptaCube for pointing this out )

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