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# 2012-11-19: Donation made, but the challenge continues

This weekend, I posted a brainteaser, promising to pay $100 to whomever solved it. Although the decoding algorithm has not yet been discovered, Mr. Batuhan Bozkurt, who found my puzzle through Reddit, did manage to figure out what the second landmark was. He generously suggested that I donate the prize money to Doctors Without Borders. That is an excellent destination for the money, so I was only too happy to oblige:

There you go, for discovering the coordinates of the Great Pyramid of Giza and the Eiffel tower, we can do a little to help people in need of medical help in places where such is direly needed.

## The challenge continues

As Mr. Bozkurt suggested, the brute force solution is not entirely satisfactory and wouldn't work when there is not a sufficiently large set of input data. Also, it wasn't exactly what I had in mind. I'm still hoping for somebody to discover the actual pattern. I can decode these numbers with pen and paper in a few minutes. Hence the following new and static set of numbers. ~~A second prize of $100 is up for grabs for the person who manages to correctly identify the third landmark ~~*and* describes how to quickly and easily extract a location encoded in this manner, effectively explaining my manual decoding process.

6549028370

9308377132

5987478672

9318473400

5758758671

1701226107

3203310324

0008077080

7467243472

4977647669

3314933944

1366336361

6388336983

1816904005

6988650225

3313573204

3363677513

1347652260

5327417344

5763780117

5633929510

5633789328

1639733691

5355453454

4762970942

4433939439

5677955559

8611231555

2312372974

9196283474

7640679475

2974972974

4375771374

5333533533

9228589625

5344734475

9690093124

8928733674

0213139200

0884819218

2112313620

9699969279

9327439234

0054403405

1991189118

3502024437

8543814253

1508069550

1872704392

6501959669

9318083111

3576755575

1745858355

8802288202

8244262894

8547446457

0005010510

1551931599

5870416497

0067651597

9732852649

3308156594

5906466417

1366338577

5863902088

3673921092

5301986352

0463999640

4352555243

1871110111

3326333663

5602990599

7074170471

4945744975

9727929597

7635536652

6628076487

2980626975

7411746499

0209674987

3110676987

4227889054

4291147358

8222333112

2326186139

4355737553

7396137966

4542844557

8226082882

2107322072

8676887286

3959753975

8568968982

3193111359

1417213379

0934698929

0098658283

2839081251

1651596922

5980877560

8980546689

8382658012

8917764639

2814515844

8912891188

0387283025

5560755055

7960290920

9117500221

4611511176

8627960562

4129549344

8117918711

9482898892

1057575051

3611444561

4529529555

0326130060

0583633056

8360969080

9120391390

9326988940

9160129317

0526949009

8120357157

0390501233

As before, post a comment with your answer **and** the process and you might win ~~$100 and~~ a lot of geek cred.

## Hints

Try figuring this out on your own as much as possible, without looking in the comments below. If you need a hint, click the button below.

Hint 9: Tbbtyr Zncf yrgf lbh frnepu sbe yngvghqr/ybatvghqr naq frr jung vf ng gung ybpngvba.

Hint 8: Vagrecerg n frdhrapr bs 7 qvtvgf nf 3 qvtvgf sbe qrterrf, 2 qvtvgf sbe zvahgrf, 2 qvtvgf sbe frpbaqf. Gur svefg pbbeqvangr vf (Abegurea) yngvghqr, gur frpbaq pbbeqvangr vf (Rnfgrea) ybatvghqr.

Hint 7: Gubfr cvacbvag na rknpg qvtvg va gur terra oybpx. Gung'f gur bar V'z ybbxvat sbe.

Hint 6: Gurer ner 2 rkprcgvbaf: 1 va n ebj, 1 va n pbyhza.

Hint 5: V pnyy guvf gur "xrl" dhnqenag. Nyy qvtvgf va gur nqwnprag, aba-xrl dhnqenagf nyfb bpphe va gur pbeerfcbaqvat ebjf/pbyhzaf va gur xrl dhnqenag, ohg fbzrguvat vf jebat...

Hint 4: Qenjvat yvarf guebhtu gur oyhr dhnqenagf guebhtu 10 qvtvgf ubevmbagnyyl nf jryy nf iregvpnyyl zrnaf gurl vagrefrpg va gur dhnqenag gung vf bccbfvgr gur terra dhnqenag.

Hint 3: Rnpu oybpx pna guhf or fcyvg hc vagb dhnqenagf bs 5k5 qvtvgf.

Hint 2: Gur 4 qvtvgf va gur zvqqyr bs rnpu oybpx nyjnlf unir 3 bqq qvtvgf (oyhr) naq 1 rira qvtvg (terra).

Hint 1: Gur frg pbafvfgf bs tebhcf bs 10k10 qvtvgf.

## Solved!

Redditor Bearasaurus found my puzzle through the Reddit discussion and was the first genius among the clever people in `/r/puzzles` to have solved the problem. He wins eternal fame and glory, and the $100 prize!

## Comments

After some eye-balling the grid, let me make some elimination guesses,

the numbers in the sets shown below cannot be at that set’s position

X: {1}, {8,9}, {6,8}, {4,7}, {5,7}, {6}, {1,4}

Y: {6}, {5,6}, {6}, {7}, {3}, {4,8,9}, {4,6,8}

i.e.,

the solution digit from the first 10x10 matrix is not 1,

the solution digit from the second 10x10 matrix is not 8 or 9, …

You do not have to declare outright the validity of my suspicion, but a nod/shake/wink would help ;)

I think your odds of finding the answer have gotten even better

*** SPOILER ALERT - COMPLETE ANSWER BELOW ***

Step 1: Break puzzle evenly into 2 rows of 7 columns, creating blocks of 10x10 digits each. Each block has a 1-digit solution that is part of the overall coordinates of the solution in the format dddmmss / dddmmss.

Step 2: Solve each 10x10 block separately. First, look at the 4 numbers that form a 2x2 square at the very center of the 10x10 block. Examining only the parity of these 4 numbers, one will be even, three will be odd. The answer is located in the 5x5 quadrant corresponding to the even number. I will use the very first 10x10 block in the new static challenge as an example.

2626513077

6549028370

9308377132

5987478672

9318473400

5758758671

1701226107

3203310324

0008077080

7467243472

At the center is:

47

75

So the answer digit is located in the top left quadrant.

Step 3: To figure out which of the digits in the top left is the answer digit, we compare the lower left quadrant to the lower right quadrant and the upper right quadrant again to the lower right quadrant. Basically, each adjacent quadrant gets compared to the diagonally opposite one. We orient our analysis horizontally if the adjacent quadrant is above or below the answer quadrant and we orient our analysis vertically if the adjacent quadrant is left or right of the answer quadrant. You will do one of each for each 10x10 block. You'll see what I mean when we get started.

Step 3a: Let's start with the lower left - lower right comparison:

57587 58671

17012 26107

32033 10324

00080 77080

74672 43472

We compare horizontally, comparing the 5 digits on the left of each row to the 5 digits on the right of each row. We are looking for a unique digit to exist in our adjacent quadrant (lower left in this case) and NOT in the diagonally opposite one. So comparing:

57587 58671 = left side unique digits are 5,7,8 and all exist at least once on the right

17012 26107 = left side unique digits are 0,1,2,7 and all exist at least once on the right

32033 10324 = left side unique digits are 0,2,3 and all exist at least once on the right

00080 77080 = left side unique digits are 0,8 and all exist at least once on the right

74672 43472 = left side unique digits are 2,4,6,7 and the number 6 DOES NOT EXIST ON THE RIGHT

The 6 is in the 3rd column, meaning the answer digit is in the 3rd column of the answer quadrant.

Step 3b: Now the upper right - lower right comparison:

13077

28370

77132

78672

73400

58671

26107

10324

77080

43472

We compare vertically, comparing the 5 digits on top of each column to the 5 digits on the bottom of each column. We are looking for a unique digit to exist in our adjacent quadrant (upper right in this case) and NOT in the diagonally opposite one. So comparing:

6th column: Upper unique digits are 1,2,7 and all exist at least once below them

7th column: Upper unique digits are 3,7,8 and all exist at least once below them

8th column: Upper unique digits are 0,1,3,4,6 and all exist at least once below them

9th column: Upper unique digits are 0,3,7 and the number 3 DOES NOT EXIST BELOW THEM

10th column: Upper unique digits are 0,2,7 and all exist at least once below them

The 3 is in the 3rd row, meaning the answer digit is in the 3rd row of the answer quadrant.

Step 4: Put it together, the number in the 3rd column and 3rd row of the answer quadrant is: 0

Step 5: Repeat for all other 10x10 blocks.

Here's the column, row, and value of each answer in the subsequent 10x10 blocks:

Block ##: C,R,V

Block 1a: 3,3,0

Block 2a: 8,8,2

Block 3a: 7,2,7

Block 4a: 4,2,1

Block 5a: 4,2,0

Block 6a: 8,3,2

Block 7a: 1,8,9

Block 1b: 7,1,0

Block 2b: 1,8,7

Block 3b: 10,3,8

Block 4b: 2,8,0

Block 5b: 10,4,2

Block 6b: 8,1,3

Block 7b: 8,10,2

The solution is located at: 027°10'29", 078°,02'32" which is the location of the TAJ MAHAL.

Ladies and gentlemen... we have a winner!

Thanks for the prize and thanks for putting together the puzzle! You've made my past few nights quite entertaining, even if the first two nights were full of dead ends =) I look forward to (hopefully) seeing many more of these challenges in the future!

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