Puzzle - First to solve wins
For years I've had an idea in my head about a way to hide some information in a bunch of numbers. I actually got around to coding an implementation and figured I'd run a competition. The first person who figures out what the famous landmark is described by the second set of numbers below and posts the correct answer in the comments wins $100.
The hint
Here's a hint. The following numbers are a reference to the Eiffel tower:
5316029264
9331032726
8233809702
5916723020
5915755151
0353853048
6221868162
9356095536
2331833183
8129329823
0223720270
1810411811
7548758277
2319583283
0128524511
6228503438
8349447999
2120355193
8839696386
5758558859
8833221833
9343395349
0806251847
3142628847
4893395643
9315958327
3805198339
7441772584
1736974989
6865529531
7749430989
1317311839
2477742784
7377934977
9519919589
7060070061
3891852193
3117957185
3137083660
8232473665
0932132160
8711578156
3559683695
0335350393
5695595685
4503044371
8573551057
4347099662
8853549397
4879598488
7347873782
3357005333
8272477477
4503404345
4668887462
3161836813
8061616506
3571773571
9601836842
0451017570
6701784546
8465773562
2463376513
4144444145
4611221664
8868586475
1313991913
4676891463
3076483644
6497194445
2573684943
1931491945
8838828380
7757285727
7090008706
9866336894
0840436397
4526182726
7510742729
2107405754
6696845820
4804848444
2031110231
1722427722
3919330399
1719181044
4914252529
4889463164
3889474918
4819384306
7119323060
7819338880
7899303371
7819328002
3419713737
7169886177
2890328898
7809798787
7665868681
4530970175
1889132792
1106972659
7189108467
9525555525
7580908908
8136111138
1609111010
4005254604
6697203565
6237281272
6653170054
6541160167
6641111161
6747170776
5664264644
9253772795
9537293353
1152121821
8650160006
2883328888
5231353133
5650140891
3231147965
2351397379
8131302691
2680145365
The puzzle
Given the above hint, what famous landmark do the numbers below refer to?
0504093875
5954600291
5889394708
5803148490
2839119339
0654333053
8904660496
5423030345
0563336326
1511407103
5347970584
0967454230
0519127208
1347111113
0367863673
3661466636
5519155451
0161910960
8210571949
9175453548
9380659587
4827059276
2947970449
5959559502
8118811288
7472774276
9999719977
4641174221
3373717883
8224843682
4393314933
3071013983
7569473033
9953274283
5489589787
4935713823
3414397723
5352533485
4378383136
3456301485
3322555322
4178519177
3452772544
7446374366
5214665145
2338516796
4763813019
0447837759
7100010899
3533796753
9488180149
5556333256
9118313864
7270227097
1188114899
2549599452
9318113965
1535136515
1271499862
9306719999
3492936555
6700899255
4715511545
3013263810
5078600390
5050973760
3788676819
7370370730
8492842829
1266166160
9535973519
0030000193
5503585503
5464474641
8409080948
6651517655
1215074706
3281120608
6409580645
3875590545
9292624748
2831170761
7391855027
7234158778
2290389106
9430399990
2894442989
7236828888
3331434233
7590111797
3733331154
2073473855
7140431810
5081430617
5715771754
8570720857
1610180111
6856586835
6669139610
7136030208
5081848546
4069282269
4186167004
4066116666
2139237922
6641841881
7737277277
8182008182
8400598645
8445108253
6492479002
8445527949
3820118901
9802558520
8445115414
8290595028
6471567176
3580868852
5344432781
7655263243
8769652248
2278710872
8222228268
6166663921
6436439642
5563352753
Post the answer as a comment below. The first person to answer correctly with an acceptable explanation to how the answer was reached (rather than just a guess) wins $100, so make sure to use your correct e-mail address so I can contact you.
Note #1: People have noted that the numbers change whenever the page is reloaded. That's as expected. This puzzle is not an encryption as much as it is an obfuscation. That the numbers change is not important, as only the pattern in them will lead to the answer, which is of course constant.
Note #2: There was a bug in my post for a short while, which made the hint and puzzle basically the resolve to the same answer. This is fixed now. If you saved a copy the numbers before, just grab a fresh set.
Solved!
The second landmark was discovered by Batuhan Bozkurt, congratulations! The challenge has not yet been met entirely, though so I've decided to set a new challenge with the same method. The same $100 prize applies.
Redditor Bearasaurus has solved the final challenge too! For hints, check the followup post.
Comments
Big Ben
I'm afraid Big Ben is not it. But be sure to include some explanation as to how the answer was reached, so I know it isn't just a random guess.
I "solved" your puzzle, but I assume not in the way you wanted.
After giving it quite some hours, I failed to find any specific pattern (with a reasonable kolmogorov complexity) that would lead me to an answer. But in Reddit, you mentioned that you would be interested in statistical approaches that would lead to an answer (which I assume you are interested for increasing the security of the obfuscation?) so I exploited the fact that your website gives fresh batch of numbers at each reload so I grabbed about 1000 sets (with intervals in between, hopefully not causing trouble to your website, it handled the requests like a champ) and got to cracking.
Now your HTML formatting implies 10x10 blocks of data for each set. So that was a starting point when I first began looking at the problem. The grid is 70 x 20 so that implies 14 secret codes, 7 for each row.
I looked for what was common for each 10x10 block in each of the samples I gathered from your site. I found out that for each 10x10 block some digits occasionally never appears; for example in block 0x 0y, not all digits have to appear but one always appears at least once.
Once I looked at the remaining digits (that are common in all blocks at a particular coordinate), for the "hint", I was faced by these digits:
0485130
0021739
These are the coordinates in the form of degrees-minutes-seconds (dddmmss as you gave away generously in Reddit) of Eiffel Tower.
Once I ran the same process for the puzzle, the result was:
0295845
0310804
Which is the coordinates for the Great Pyramid of Giza.
Maybe this is disappointing, I don't know. If the website hadn't provided fresh batch of numbers, this method would not work. I assume, to strengthen the obfuscation, you could make sure one digit always appears at least once; but as long as the distribution isn't random, I suppose the answer could be extracted.
I've tried many approaches before this; I'm pretty confident that the pattern is not based on neighborhood relationships (as the answer can appear on edges, though wrapping around could be employed but still with it I failed to detect any patterns). I think it doesn't have anything (or much) to do with arithmetic on the digits (like summing / subtracting them). I tried various row/column patterns and couldn't come up with anything.
I also analyzed the 10x10 blocks containing the answer digits only once (so if the answer is 0 for that block, 0 appears only once in that block). But saw no obvious pattern at all. So this beats me in that regard.
If I am eligible for the prize for my answer, I would kindly ask you to donate it to the Doctors Without Borders foundation. If you are uncomfortable about it for some reason, you can choose to donate it somewhere else you see fit.
Thanks for the challenge, and although my curiosity has been partly satisfied, I'm still waiting for the answer that will allow me to solve this using a pen and paper using a single set of numbers.
Batuhan, the answer is indeed correct. The Great Pyramid of Giza is the one I was looking for. The method you used is indeed not the one I was hoping for, as you haven't actually figured out the way the coordinates are encoded into the sets of numbers.
Still, I'm not one to dictate how the problem should be solved. I will make a donation to Doctors Without Borders for $100 in your name and post proof that I have done so.
Since I would very much like for somebody to solve the method, I'm including this static problem for a second attempt, and another $100. Being in a comment, the following set obviously does not change and encodes a third landmark.
2626513077384364666346599932245309032974209496921885110948315551555613
6549028370497764766953274173448611231555969009312435020244378244262894
9308377132331493394457637801172312372974892873367485438142538547446457
5987478672136633636156339295109196283474021313920015080695500005010510
9318473400638833698356337893287640679475088481921818727043921551931599
5758758671181690400516397336912974972974211231362065019596695870416497
1701226107698865022553554534544375771374969996927993180831110067651597
3203310324331357320447629709425333533533932743923435767555759732852649
0008077080336367751344339394399228589625005440340517458583553308156594
7467243472134765226056779555595344734475199118911888022882025906466417
0332300493776667648725560571112261196221231229957486429403779342535143
1366338577707417047142278890548676887286598087756091175002210326130060
5863902088494574497542911473583959753975898054668946115111760583633056
3673921092972792959782223331128568968982838265801286279605628360969080
5301986352763553665223261861393193111359891776463941295493449120391390
0463999640662807648743557375531417213379281451584481179187119326988940
4352555243298062697573961379660934698929891289118894828988929160129317
1871110111741174649945428445570098658283038728302510575750510526949009
3326333663020967498782260828822839081251556075505536114445618120357157
5602990599311067698721073220721651596922796029092045295295550390501233
The challenge now is to find the answer and a step by step description of how to extract the correct digits from it.
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