NASA has spent hundreds of millions of dollars gathering data about cave systems in one region of the planet Mars. The project just finished up, and analysts will soon be ready to start analyzing the complete list of all the lengths of cave passageways.
However, the manager of the NASA data center was unhappy about his recent pay cut, and had decided to quit, but not before causing problems. First, he used his manager-level privileges to log on to the backup servers and delete all of the backup data for the cave system project, knowing that he could later blame that on another department and he would not be held responsible. However, he knew that if he altered or deleted the data on the main server, then he would be caught and spend many years in prison. Instead, he created fake data to sabotage the study, and put the text file in the same folder as the actual data, with a similar name.
But he didn't stop there! Knowing that he was not very skilled in creating data, he didn't know how believable his fake data would be, so he asked two friends for help. He explained the task to them and requested 500 fake data points, ranging between 10 and 99,999 (since any passageway at least 10 feet long was classified as its own passageway). One of the friends was a mathematically-inclined (but not brilliant) intern from the data center who had recently quit, and the other one wasn't very math-minded, but did work for the state lottery. They did as they were asked, and he put their fake data files into the same folder as the other 2 files. Then he submitted his 2-week notice that he was leaving his job.
[2 weeks later]
Today, when the analysts started analysis, they saw the 4 different data files in the folder, all with nearly the same time stamp. They figured out what had happened, but they are not sure which data file is the right one.
Here are the comma-separated data files, containing the lengths of cave passageways (rounded to the nearest foot). The order of numbers in each file appears random, but is actually the order in which the data was recorded (which is not important).
File A
41050,98026,41938,39381,1045,97472,51703,30377,75372,75309,78343,99036,75408,70667,89774,70002,5097,61742,94616,23463,84846,88702,18597,74446,93228,33341,28485,98423,61427,84341,9799,70743,48021,21144,22010,64840,7475,19554,10217,27524,76597,9070,12286,93984,60312,28973,94055,63258,76096,7887,12612,99797,58620,98829,22238,92713,55891,25876,82304,25952,98076,59944,48189,92035,68632,64751,61087,87282,7781,15843,92947,92493,99250,96661,16096,17061,94168,42362,46406,55357,8555,20205,57032,66867,84021,96631,4734,63426,48889,45497,58226,52729,52658,82993,56513,65993,55056,66841,58809,85054,32010,75380,463,61616,78582,83395,79596,30370,56880,53140,61191,55123,91865,31791,88886,61104,77691,47831,48680,43460,8464,7055,25197,58750,90168,42552,56945,28278,71074,32556,45801,71878,52522,9398,48117,21029,87662,27554,61111,49741,94721,82090,43066,35250,86231,70691,85977,92585,80862,85569,47080,9258,60444,8530,74430,80369,58381,94000,33628,82054,39398,71689,98519,56625,71930,93326,92301,30603,78417,71845,5715,74574,21810,45677,78871,80477,96839,55668,40428,90622,79301,90130,71499,95016,35910,93,86361,35809,53697,93082,8228,50428,86155,37872,51383,95949,9311,3171,34503,90655,74333,79247,7153,86971,97154,93701,65094,37023,94144,63786,4318,21926,28855,46348,58618,74274,35808,32079,66531,23969,5522,898,41166,41472,24671,9782,76597,5400,75648,91068,40815,57376,9554,96045,9562,26241,36632,61529,33499,31301,2005,61342,5694,4395,66230,61262,89484,96819,7613,4199,63792,22623,90801,90762,63008,63633,49323,37831,23594,50201,45283,69978,77300,34212,984,27867,82006,66391,51280,22889,31130,73150,20555,80150,43159,6137,75266,60612,28163,45344,69124,8354,51287,47606,84299,43180,64470,9139,19235,92058,73896,56535,26198,27038,61373,77262,9992,49708,3796,5158,69022,87934,76263,80053,20509,77691,71432,61867,39256,45213,98428,86327,34782,4799,31437,90828,80365,35442,1653,34143,84737,85459,76016,80901,35774,8868,87978,61669,11906,1698,11713,86946,29694,95622,99909,54504,99841,23658,32968,56220,47136,40976,96521,96319,41605,99829,45741,89666,69240,81010,85316,86587,10428,34052,64339,51147,51463,8608,12962,30626,58716,3685,18802,14130,67344,67377,82035,78767,70738,37714,40841,70226,99876,64362,61647,56810,36430,14136,86488,40407,65471,61720,22341,27308,59065,76543,14382,10678,58363,48516,48894,26914,13476,22203,48235,59081,96912,84838,80694,63956,60770,74846,70739,77694,58521,19777,8751,29012,86265,27631,43357,22594,7302,28441,62299,60896,24142,61573,38647,24448,70070,85524,89316,58467,54355,60345,98618,49783,48003,87225,65663,87880,84674,98442,55193,54593,3156,32392,45233,31554,41171,96207,14652,16297,31240,84013,54925,48578,44692,97775,59327,2925,32952,76215,61846,85000,81905,13932,59659,60745,94063,7202,11593,47043,18661,11788,35255,9622,50155,32101,47339,73778,5614,92081,569,63034,57246,87807,32915,1912,69437,4537,15466,95584,18446,68437,35389,60802,70909,95128,60537,69851,31124,71714,16042,40076,58640,31628,38410,14356
File B
91691,88462,65945,6184,34325,44339,69698,4286,22141,20186,44975,43597,96829,77866,7252,54008,21738,19743,8101,60443,82617,6851,35716,63086,36076,47458,98331,72521,35251,38997,48146,38296,22915,35492,76652,94287,58518,8231,56425,14023,98610,81957,64723,60408,63160,29617,28192,50648,85324,65164,79515,94465,45487,16505,57011,50404,61971,34423,33873,60873,43760,84050,52344,64020,61635,37047,83692,26705,34174,68583,31705,57819,99367,53781,93042,2584,73720,67228,30392,13506,58101,38355,44658,56364,67926,58956,21839,21690,11318,8899,28636,95459,97586,72035,87291,20492,65393,50878,54978,64335,38670,95348,92502,57695,7060,55568,18068,24166,43499,18730,34039,46185,75185,77576,73050,31232,29463,36601,317,14914,85335,98240,80874,82321,53747,96363,31671,80999,5246,24337,24367,82528,91680,18931,59898,46036,35777,95686,62359,65077,84826,53667,68313,25407,17211,19482,5642,80960,15082,87462,94179,27129,80813,70555,20023,94550,97800,63378,37137,19655,78046,92770,53552,44759,28259,58320,11076,10635,79768,44202,56989,78594,93293,28129,3229,57561,176,21060,41536,92535,71585,59230,89258,72566,91356,28949,57950,64062,53612,50107,5289,37000,10650,64444,42826,61001,39581,52143,53813,88926,42770,66730,61860,73477,29846,95376,24869,90696,40818,86561,98154,17851,32828,46486,13913,67501,92912,48088,25454,19737,91336,2561,87618,5332,38007,18249,1292,75057,48859,63883,22607,97957,75335,30694,62332,63525,52708,79295,69202,23584,88030,13634,12907,71531,15959,19372,61677,13021,59064,60147,23883,48380,23336,58929,15531,39795,71411,93948,64617,45541,69894,7336,34395,79809,12797,93800,39257,14708,45522,85826,3532,64933,6568,32807,35960,33565,60315,93438,2629,32594,36507,82399,27730,83577,43704,73512,38106,28205,18796,75407,21575,8155,69672,59273,52280,53999,4071,26300,15114,26193,95288,59232,31951,54460,85169,75012,1057,84003,70446,33623,16002,49505,56582,36807,92824,3890,39204,68168,91911,87683,74667,16026,84036,38859,47884,48955,47293,51690,12548,19201,6583,32916,69812,75262,51360,21814,3542,11904,5549,80243,59004,86368,13076,87519,92905,16420,30597,85887,36612,9278,37300,74286,17600,59874,20179,51240,43653,35821,94017,75815,93242,88656,15629,74356,52223,23899,20467,27719,51548,16602,62403,95977,8708,28605,18709,97767,44601,51425,45192,76236,77358,13087,69218,97381,48966,49755,39053,61344,94556,73018,8014,1261,49952,39087,66684,42116,45594,42306,92432,47997,51843,52026,50225,70509,90687,58022,90903,41685,92828,50644,11434,14357,38632,49443,63988,68154,43980,76108,57144,34881,79318,17168,91165,61167,86338,43114,3008,69265,63087,44647,24765,68231,93843,41002,12308,29837,73680,53948,7802,66507,98169,86749,52515,36734,88973,35273,43551,20971,11902,25951,46933,86801,24532,14094,85484,12119,649,86074,57796,40663,4373,12522,35569,45552,82769,88487,87849,41418,52744,88319,49029,36650,66149,51882,39211,43936,6292,87335,99410,41702,51750,37708,98231,31065,50180,24532,73126,62976,18342,62243,30702,62598,95874,53871,79319,60885,52998,18545,59121,64350
File C
96954,54615,28496,90692,46070,90096,35182,34835,30444,39432,1746,41055,12120,21303,37632,41930,970,39960,3926,15703,18380,2538,85552,869,10,88240,31341,4192,59198,21165,1781,63350,39670,1932,13610,11994,29728,11921,10086,43625,633,31758,54131,181,484,1110,24021,19811,16561,12483,664,123,219,3029,49997,26601,29318,3787,42574,48659,15382,1031,16117,25652,16918,28469,176,45567,25463,53151,1338,67662,658,3194,64703,22706,13129,47515,744,23043,12713,138,14663,7179,1440,13959,20788,7429,15271,4572,10473,14,24864,1782,89982,24256,60550,65475,43065,28938,26099,12043,15889,862,49217,55160,13080,33780,51251,48870,24073,32038,18,20129,16589,30301,26395,29836,11,16382,26514,595,374,82549,135,30149,48380,26171,25942,55089,53658,689,364,55221,17284,33114,57967,35500,574,50755,1252,39432,17937,13848,16369,22757,20726,19814,1216,49543,196,4143,54882,56734,11157,17685,10461,28370,17205,32508,31700,40495,17199,582,1886,44196,29891,1289,23334,32919,35218,43559,1903,225,14659,12230,28536,39024,24261,16456,16686,30170,152,7973,71284,813,83671,22212,10227,24243,748,172,24998,51693,181,46951,297,21645,17273,11278,1949,16351,23584,505,29505,11432,724,44522,45811,1586,60504,18062,670,18146,52856,61636,21983,976,80611,14191,84781,99125,35759,71589,11643,90843,3516,177,48,26312,27208,18124,12451,58201,72,31227,54201,13747,723,59987,15516,14795,9711,30930,3365,49528,88826,77243,95170,80774,32145,33390,31622,73089,5816,10310,89394,1004,24638,4923,25126,91059,15961,1826,40161,48490,51643,18550,22305,37355,1634,78750,6947,58777,15246,13178,13316,78603,28552,18625,15853,36304,25904,10702,79349,51567,78165,12072,17732,10618,160,25225,4788,46976,1667,75940,95315,49286,12689,73443,46367,77414,52191,60115,78232,94845,56429,77,7465,73710,60092,49601,49409,83002,86608,71563,28246,59807,13653,1210,3703,83780,57681,27322,37867,1000,4757,10652,19718,64762,63461,3891,9975,1580,38368,11342,73451,10996,72366,61801,6011,26471,26542,66239,18355,9413,27143,13028,22342,15816,33859,32837,40541,69729,14702,68239,22583,39337,15778,33081,49219,63797,12971,27552,37537,140,2448,13390,15744,28067,61129,1851,46811,50059,40624,105,1194,20040,39627,14447,20,33,2473,39144,19819,22229,44792,85437,172,2661,67807,34,35869,88637,3054,62108,85445,91064,62141,50342,93530,12752,31831,1464,279,37514,80745,18020,1221,93376,338,23846,350,16399,22489,8178,2485,66521,21909,56424,19558,46144,55297,52489,31303,27341,14972,14118,20930,11197,43125,65617,77243,29448,26393,80375,14699,47237,12987,5792,248,16264,25320,11228,60540,19430,41909,87067,11267,16434,27299,19195,6497,95398,39801,28648,3991,28,5385,38402,97163,61444,15500,99896,66699,47976,20559,10910,3696,24333,18087,82598,3917,81305,22458,56347,25021,19376,79014,27470,19400,1745,19671,91712,59696,26494,65125,13665,13740,11031,91653,72433,9313,50376,1056,21492,24154,25706,44787,46269
File D
96356,54607,27997,89863,45152,89915,35049,34534,29457,38995,1404,40187,11757,21238,37485,41537,241,39452,3513,15385,17899,1295,15410,804,297,87992,30658,4049,58916,20701,1193,12597,39667,1580,13524,11280,29162,11163,9223,1591,352,30928,54004,342,51,1025,23300,19455,16128,11652,15284,393,741,2393,49269,26043,28877,3209,41649,47779,15330,792,15713,24673,16430,27823,159,45024,24912,53016,474,66977,315,2823,64020,22082,12130,47227,74099,22912,12166,258,14289,6702,923,13068,20624,6774,14757,3973,10146,380,24176,824,89293,24050,59718,65169,42410,28474,26053,11563,15384,26,48517,54163,12349,33388,50791,47910,23960,31354,902,19172,16181,29891,26064,29616,953,15506,26127,330,320,82262,22,29991,47658,25514,25814,54956,53464,75,503,54465,16454,32583,57601,34889,164,49933,657,39149,17447,13026,16164,22441,20283,19467,925,49541,309,3437,54079,56025,10436,17682,10442,28325,16711,31979,30986,40401,16906,498,1281,43498,29242,354,22950,32525,34462,43417,1518,113,14278,11243,27624,38299,23860,16422,16429,29519,69,7262,71244,81584,83233,21381,10223,23940,245,468,24640,50995,81,46430,402,21065,17114,10925,1920,15692,23022,4284,28976,10839,119,43896,45224,935,59745,17296,11,17961,52536,61613,21908,97363,79659,13470,14027,19,35248,70805,11279,89899,3083,62,248,25375,27192,18038,11608,57458,21,31096,53430,13556,182,59382,15432,14680,8951,30894,2570,49521,87922,76923,1594,80359,31177,33270,30786,72274,5198,9831,88395,591,23751,4583,24308,90266,15880,1031,39696,48037,51380,18503,22126,37219,1406,78194,6821,58412,15084,12434,13026,77776,168,17842,15471,35945,25699,10489,78583,51515,77641,11680,17021,10289,351,24407,4039,46631,1223,75566,94609,48347,11843,72933,45400,76587,51754,59134,77398,94068,55577,469,6588,72748,59532,49408,49295,82093,86582,70569,28170,59458,13358,549,2836,83721,56993,26384,37399,530,4561,10617,19527,64562,63084,3474,9900,1368,37695,11234,72778,10516,71921,61259,5920,26015,26326,65805,18005,8564,26146,12256,21585,15153,33537,32335,40260,68820,14298,68018,22572,38959,15038,32394,49193,62804,12864,27251,37172,535,2410,12948,15564,27929,60539,1228,45843,49084,39820,119,639,19192,38931,14206,879,478,2261,38685,19011,21706,44,84558,705,2018,66901,326,34920,87856,2302,61514,84,90552,61745,49484,93362,12065,31430,936,76,36753,80355,17509,811,92853,578,23386,403,15845,21757,7908,2337,66385,21055,56304,19282,46090,54762,51919,30628,26465,14846,14029,20459,10562,42373,64,77103,28952,26152,79668,14067,46849,12441,5484,420,15571,24881,11112,60359,19334,41577,86574,10462,15930,26920,18405,6265,94873,38812,27834,3274,916,4865,37937,96333,60844,14525,99097,66118,47729,19664,10104,3050,23489,17592,82379,3857,80827,21751,55564,24973,18913,78279,26649,18781,1457,19296,90899,59215,25594,64951,13162,13504,10265,91326,71539,9247,49695,900,21420,23276,25458,199,45594
Can you figure out which data file is most likely the real one, and why?
